12a
0616
(K12a
0616
)
A knot diagram
1
Linearized knot diagam
3 7 9 1 11 2 5 12 4 8 6 10
Solving Sequence
3,9
4
7,10
2 1 5 6 12 8 11
c
3
c
9
c
2
c
1
c
4
c
6
c
12
c
8
c
11
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.87565 × 10
37
u
44
+ 2.88467 × 10
37
u
43
+ ··· + 1.79366 × 10
38
b − 2.28855 × 10
38
,
− 6.32625 × 10
36
u
44
− 1.60162 × 10
37
u
43
+ ··· + 1.79366 × 10
38
a + 2.72634 × 10
38
,
u
45
− 16u
43
+ ··· + 8u + 8i
I
u
2
= h1.05402 × 10
619
u
135
− 1.25591 × 10
619
u
134
+ ··· + 1.02383 × 10
619
b − 5.96436 × 10
620
,
− 1.18864 × 10
621
u
135
+ 2.70367 × 10
621
u
134
+ ··· + 9.11212 × 10
620
a + 2.71391 × 10
623
,
u
136
− u
135
+ ··· − 1494u − 89i
I
u
3
= h−u
10
+ 4u
8
− 6u
6
+ u
5
+ 3u
4
− 2u
3
+ b + u − 1, u
10
− u
9
− 5u
8
+ 4u
7
+ 9u
6
− 6u
5
− 5u
4
+ 3u
3
− 2u
2
+ a + 2,
u
11
− 5u
9
+ 9u
7
− u
6
− 5u
5
+ 3u
4
− 2u
3
− 2u
2
+ 2u − 1i
I
u
4
= h−1.69543 × 10
27
u
37
+ 1.23907 × 10
27
u
36
+ ··· + 5.29826 × 10
24
b + 1.95738 × 10
28
,
− 1.69867 × 10
27
u
37
+ 1.42937 × 10
27
u
36
+ ··· + 5.29826 × 10
24
a + 1.47189 × 10
28
, u
38
− 7u
36
+ ··· − 8u − 8i
* 4 irreducible components of dim
C
= 0, with total 230 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
= h1.88 × 10
37
u
44
+ 2.88 × 10
37
u
43
+ · · · + 1.79 × 10
38
b − 2.29 ×
10
38
, −6.33 × 10
36
u
44
− 1.60 × 10
37
u
43
+ · · · + 1.79 × 10
38
a + 2.73 ×
10
38
, u
45
− 16u
43
+ · · · + 8u + 8i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
0.0352702u
44
+ 0.0892935u
43
+ ··· + 0.195710u − 1.51999
−0.104571u
44
− 0.160827u
43
+ ··· + 2.45646u + 1.27591
a
10
=
−u
−u
3
+ u
a
2
=
−0.0844913u
44
− 0.185903u
43
+ ··· − 0.0125427u + 2.53802
0.127167u
44
+ 0.359944u
43
+ ··· − 2.61521u − 2.76088
a
1
=
0.0426760u
44
+ 0.174042u
43
+ ··· − 2.62775u − 0.222856
0.127167u
44
+ 0.359944u
43
+ ··· − 2.61521u − 2.76088
a
5
=
0.100777u
44
+ 0.0808879u
43
+ ··· − 1.02805u + 0.638734
−0.186080u
44
− 0.0634539u
43
+ ··· + 0.572085u + 0.149929
a
6
=
−0.266430u
44
− 0.128670u
43
+ ··· + 1.92246u − 0.109400
−0.0702591u
44
+ 0.300563u
43
+ ··· + 0.746284u − 1.52508
a
12
=
−0.0625033u
44
− 0.153291u
43
+ ··· + 0.239176u + 1.76637
0.128670u
44
+ 0.318945u
43
+ ··· − 2.02204u − 2.13144
a
8
=
0.130212u
44
+ 0.255879u
43
+ ··· − 3.03747u − 2.28189
−0.111369u
44
− 0.357286u
43
+ ··· + 3.45797u + 1.82626
a
11
=
0.0661668u
44
+ 0.165654u
43
+ ··· − 1.78287u − 0.365073
−0.171893u
44
+ 0.256339u
43
+ ··· − 1.05904u − 2.69352
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.795897u
44
− 0.590986u
43
+ ··· + 11.4411u − 4.15369
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 18u
44
+ ··· + 380u + 16
c
2
, c
6
u
45
− 10u
44
+ ··· − 42u + 4
c
3
, c
5
, c
9
c
11
u
45
− 16u
43
+ ··· + 8u + 8
c
4
, c
7
u
45
− 2u
44
+ ··· − 40u + 7
c
8
u
45
− 24u
44
+ ··· − 7732u + 1004
c
10
, c
12
u
45
+ 2u
44
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
+ 14y
44
+ ··· + 10480y −256
c
2
, c
6
y
45
− 18y
44
+ ··· + 380y −16
c
3
, c
5
, c
9
c
11
y
45
− 32y
44
+ ··· + 192y −64
c
4
, c
7
y
45
− 24y
44
+ ··· + 1446y −49
c
8
y
45
+ 8y
44
+ ··· + 10364936y −1008016
c
10
, c
12
y
45
+ 30y
44
+ ··· + 41y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904711 + 0.385250I
a = 0.775036 + 0.660431I
b = −0.673502 − 0.733229I
−0.249509 + 1.130960I −6.86085 − 2.19066I
u = −0.904711 − 0.385250I
a = 0.775036 − 0.660431I
b = −0.673502 + 0.733229I
−0.249509 − 1.130960I −6.86085 + 2.19066I
u = 0.291429 + 0.928185I
a = −0.43451 − 1.45901I
b = 0.540257 + 0.739442I
2.51773 + 3.15764I −2.59892 − 1.94301I
u = 0.291429 − 0.928185I
a = −0.43451 + 1.45901I
b = 0.540257 − 0.739442I
2.51773 − 3.15764I −2.59892 + 1.94301I
u = 0.959241 + 0.088882I
a = −0.730428 + 0.364288I
b = 0.803063 − 0.960107I
−2.83419 + 2.13670I −12.63162 − 3.17567I
u = 0.959241 − 0.088882I
a = −0.730428 − 0.364288I
b = 0.803063 + 0.960107I
−2.83419 − 2.13670I −12.63162 + 3.17567I
u = −1.022320 + 0.200125I
a = 0.84782 + 1.55652I
b = 1.145680 − 0.824759I
−3.88575 + 4.69033I −15.6882 − 1.6037I
u = −1.022320 − 0.200125I
a = 0.84782 − 1.55652I
b = 1.145680 + 0.824759I
−3.88575 − 4.69033I −15.6882 + 1.6037I
u = −0.227858 + 1.046760I
a = −0.46979 − 1.39136I
b = 1.046270 + 0.629755I
1.01643 − 8.38679I −5.74189 + 7.05298I
u = −0.227858 − 1.046760I
a = −0.46979 + 1.39136I
b = 1.046270 − 0.629755I
1.01643 + 8.38679I −5.74189 − 7.05298I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.020840 + 0.474470I
a = −0.30089 + 1.87615I
b = −0.965362 − 0.683314I
−1.09453 − 6.53330I −6.25242 + 7.09488I
u = 1.020840 − 0.474470I
a = −0.30089 − 1.87615I
b = −0.965362 + 0.683314I
−1.09453 + 6.53330I −6.25242 − 7.09488I
u = 0.978894 + 0.615603I
a = 1.11563 − 1.20609I
b = −0.581777 + 0.504686I
−5.20551 − 3.24310I −11.09110 + 2.51409I
u = 0.978894 − 0.615603I
a = 1.11563 + 1.20609I
b = −0.581777 − 0.504686I
−5.20551 + 3.24310I −11.09110 − 2.51409I
u = −1.163800 + 0.253636I
a = 0.203998 + 1.019120I
b = 0.52185 − 1.33849I
−3.59461 + 7.16172I −13.9703 − 16.0708I
u = −1.163800 − 0.253636I
a = 0.203998 − 1.019120I
b = 0.52185 + 1.33849I
−3.59461 − 7.16172I −13.9703 + 16.0708I
u = −0.018703 + 0.798685I
a = 0.055612 − 0.481025I
b = −1.034700 + 0.034835I
−2.63491 − 2.04726I −9.46082 + 3.30363I
u = −0.018703 − 0.798685I
a = 0.055612 + 0.481025I
b = −1.034700 − 0.034835I
−2.63491 + 2.04726I −9.46082 − 3.30363I
u = 1.151030 + 0.417515I
a = 0.725309 − 0.192269I
b = 0.305939 + 0.102470I
−5.78366 − 3.80601I −9.91407 + 4.67226I
u = 1.151030 − 0.417515I
a = 0.725309 + 0.192269I
b = 0.305939 − 0.102470I
−5.78366 + 3.80601I −9.91407 − 4.67226I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.248160 + 0.077435I
a = −1.32534 + 0.49770I
b = −1.141000 − 0.123861I
−10.48110 + 2.35369I −18.9561 − 2.8828I
u = −1.248160 − 0.077435I
a = −1.32534 − 0.49770I
b = −1.141000 + 0.123861I
−10.48110 − 2.35369I −18.9561 + 2.8828I
u = 1.252930 + 0.009637I
a = 0.284744 + 0.342965I
b = 1.47674 − 0.38102I
−7.85271 + 0.47117I −15.8357 − 5.3347I
u = 1.252930 − 0.009637I
a = 0.284744 − 0.342965I
b = 1.47674 + 0.38102I
−7.85271 − 0.47117I −15.8357 + 5.3347I
u = 1.267410 + 0.296047I
a = −0.0569045 + 0.0061166I
b = 0.475570 − 0.657004I
−5.73835 − 4.35066I −13.57540 + 0.I
u = 1.267410 − 0.296047I
a = −0.0569045 − 0.0061166I
b = 0.475570 + 0.657004I
−5.73835 + 4.35066I −13.57540 + 0.I
u = −1.110060 + 0.763457I
a = −0.05040 − 2.03163I
b = −1.018720 + 0.538721I
−6.57662 + 7.58601I 0
u = −1.110060 − 0.763457I
a = −0.05040 + 2.03163I
b = −1.018720 − 0.538721I
−6.57662 − 7.58601I 0
u = −1.359340 + 0.258516I
a = 1.15485 + 1.06411I
b = 1.052060 − 0.610951I
−7.36488 + 9.33824I 0
u = −1.359340 − 0.258516I
a = 1.15485 − 1.06411I
b = 1.052060 + 0.610951I
−7.36488 − 9.33824I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.282780 + 0.587640I
a = −0.763655 − 0.695209I
b = 0.492075 + 1.014950I
−3.7445 + 14.5021I 0
u = −1.282780 − 0.587640I
a = −0.763655 + 0.695209I
b = 0.492075 − 1.014950I
−3.7445 − 14.5021I 0
u = 0.058203 + 0.585764I
a = −0.60903 + 2.25179I
b = 0.926049 − 0.672054I
1.38722 + 3.01128I −3.65555 − 3.26283I
u = 0.058203 − 0.585764I
a = −0.60903 − 2.25179I
b = 0.926049 + 0.672054I
1.38722 − 3.01128I −3.65555 + 3.26283I
u = −1.298980 + 0.557564I
a = 0.345931 + 0.131800I
b = 1.017790 + 0.327046I
−7.94405 + 1.42176I 0
u = −1.298980 − 0.557564I
a = 0.345931 − 0.131800I
b = 1.017790 − 0.327046I
−7.94405 − 1.42176I 0
u = 1.347670 + 0.427366I
a = −0.370615 + 0.537392I
b = −1.394210 − 0.057858I
−11.1522 − 11.4348I 0
u = 1.347670 − 0.427366I
a = −0.370615 − 0.537392I
b = −1.394210 + 0.057858I
−11.1522 + 11.4348I 0
u = 0.283063 + 0.486915I
a = −1.61731 + 0.55400I
b = 0.295704 − 0.516656I
1.74313 + 1.16289I 2.28789 − 2.49598I
u = 0.283063 − 0.486915I
a = −1.61731 − 0.55400I
b = 0.295704 + 0.516656I
1.74313 − 1.16289I 2.28789 + 2.49598I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.117616 + 0.550594I
a = −1.18286 + 1.76664I
b = 0.803679 − 0.659214I
1.77588 + 2.15091I −4.72793 − 2.98792I
u = −0.117616 − 0.550594I
a = −1.18286 − 1.76664I
b = 0.803679 + 0.659214I
1.77588 − 2.15091I −4.72793 + 2.98792I
u = 1.33191 + 0.63733I
a = 0.46686 − 1.74546I
b = 1.164940 + 0.710104I
−5.8474 − 20.7422I 0
u = 1.33191 − 0.63733I
a = 0.46686 + 1.74546I
b = 1.164940 − 0.710104I
−5.8474 + 20.7422I 0
u = −0.376602
a = −0.128105
b = −0.516838
−0.695273 −14.5010
9
II. I
u
2
= h1.05 × 10
619
u
135
− 1.26 × 10
619
u
134
+ · · · + 1.02 × 10
619
b − 5.96 ×
10
620
, −1.19 × 10
621
u
135
+ 2.70 × 10
621
u
134
+ · · · + 9.11 × 10
620
a + 2.71 ×
10
623
, u
136
− u
135
+ · · · − 1494u − 89i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
1.30446u
135
− 2.96712u
134
+ ··· − 4742.96u − 297.835
−1.02949u
135
+ 1.22668u
134
+ ··· + 799.084u + 58.2551
a
10
=
−u
−u
3
+ u
a
2
=
−1.09661u
135
+ 2.44759u
134
+ ··· + 3627.11u + 227.336
−0.172930u
135
− 0.127330u
134
+ ··· − 620.903u − 37.8494
a
1
=
−1.26954u
135
+ 2.32026u
134
+ ··· + 3006.21u + 189.486
−0.172930u
135
− 0.127330u
134
+ ··· − 620.903u − 37.8494
a
5
=
−1.00266u
135
+ 0.871325u
134
+ ··· + 1587.86u + 115.545
0.0247029u
135
− 0.235462u
134
+ ··· − 632.856u − 37.5718
a
6
=
−0.598205u
135
+ 0.431891u
134
+ ··· − 759.069u − 46.0205
0.0784493u
135
− 0.0845611u
134
+ ··· + 425.706u + 28.2223
a
12
=
−0.819782u
135
+ 1.79695u
134
+ ··· + 2727.66u + 169.316
−0.297854u
135
+ 0.0811558u
134
+ ··· − 412.200u − 24.2248
a
8
=
0.0821989u
135
− 0.625403u
134
+ ··· − 1545.30u − 107.137
−0.298922u
135
+ 0.283406u
134
+ ··· + 170.611u + 13.1531
a
11
=
2.35550u
135
− 3.14795u
134
+ ··· − 2226.09u − 157.879
−0.438678u
135
+ 1.24542u
134
+ ··· + 1399.86u + 85.6694
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.69391u
135
− 6.14888u
134
+ ··· − 9904.87u − 630.170
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
68
+ 32u
67
+ ··· + 16464u + 1849)
2
c
2
, c
6
(u
68
+ 4u
67
+ ··· − 120u − 43)
2
c
3
, c
5
, c
9
c
11
u
136
− u
135
+ ··· − 1494u − 89
c
4
, c
7
u
136
− 3u
135
+ ··· − 5351856u + 103993
c
8
(u
68
+ 10u
67
+ ··· + 14u + 1)
2
c
10
, c
12
u
136
+ 14u
135
+ ··· − 1293886u − 83089
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
68
+ 12y
67
+ ··· + 42268244y + 3418801)
2
c
2
, c
6
(y
68
− 32y
67
+ ··· − 16464y + 1849)
2
c
3
, c
5
, c
9
c
11
y
136
− 71y
135
+ ··· + 801262y + 7921
c
4
, c
7
y
136
+ 9y
135
+ ··· − 15840027966342y + 10814544049
c
8
(y
68
+ 6y
67
+ ··· − 190y + 1)
2
c
10
, c
12
y
136
− 2y
135
+ ··· + 154307077926y + 6903781921
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925086 + 0.391915I
a = 1.36638 + 1.38167I
b = −0.820960 + 0.447182I
0.906398 + 0.207630I 0
u = 0.925086 − 0.391915I
a = 1.36638 − 1.38167I
b = −0.820960 − 0.447182I
0.906398 − 0.207630I 0
u = 0.989075
a = 0.712095
b = 1.51343
−7.69031 0
u = 0.969957 + 0.104435I
a = −1.17113 + 1.42725I
b = −0.953322 − 0.767248I
−2.91253 − 2.99862I 0
u = 0.969957 − 0.104435I
a = −1.17113 − 1.42725I
b = −0.953322 + 0.767248I
−2.91253 + 2.99862I 0
u = −0.976826 + 0.315814I
a = −1.44119 − 0.95354I
b = −1.153420 + 0.511740I
0.28525 + 4.98766I 0
u = −0.976826 − 0.315814I
a = −1.44119 + 0.95354I
b = −1.153420 − 0.511740I
0.28525 − 4.98766I 0
u = 0.345380 + 0.893987I
a = −0.27019 + 1.52843I
b = −0.335348 − 0.576748I
2.71790 + 0.57544I 0
u = 0.345380 − 0.893987I
a = −0.27019 − 1.52843I
b = −0.335348 + 0.576748I
2.71790 − 0.57544I 0
u = 0.973866 + 0.372475I
a = −1.19965 + 2.57130I
b = −0.897555 − 0.648418I
−0.58087 − 6.80332I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973866 − 0.372475I
a = −1.19965 − 2.57130I
b = −0.897555 + 0.648418I
−0.58087 + 6.80332I 0
u = 0.952664
a = −1.01518
b = −1.75919
−7.40980 0
u = 0.936933 + 0.140070I
a = 1.58819 − 1.91607I
b = −0.719953 + 0.709662I
−2.18721 − 4.85558I 0
u = 0.936933 − 0.140070I
a = 1.58819 + 1.91607I
b = −0.719953 − 0.709662I
−2.18721 + 4.85558I 0
u = −0.762365 + 0.728204I
a = −1.25225 − 1.03421I
b = 0.905636 + 0.400851I
−5.57459 − 1.63327I 0
u = −0.762365 − 0.728204I
a = −1.25225 + 1.03421I
b = 0.905636 − 0.400851I
−5.57459 + 1.63327I 0
u = −1.026590 + 0.262553I
a = −2.43774 − 1.24961I
b = −0.926794 + 0.477530I
0.50785 + 3.58327I 0
u = −1.026590 − 0.262553I
a = −2.43774 + 1.24961I
b = −0.926794 − 0.477530I
0.50785 − 3.58327I 0
u = −0.903087 + 0.254105I
a = 0.98467 − 2.69637I
b = −0.964612 + 0.657589I
−2.93934 + 10.11590I 0
u = −0.903087 − 0.254105I
a = 0.98467 + 2.69637I
b = −0.964612 − 0.657589I
−2.93934 − 10.11590I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609437 + 0.711249I
a = −1.300460 + 0.297499I
b = 0.927180 − 0.419329I
0.27458 + 1.60627I 0
u = 0.609437 − 0.711249I
a = −1.300460 − 0.297499I
b = 0.927180 + 0.419329I
0.27458 − 1.60627I 0
u = −0.970003 + 0.445147I
a = 1.361510 + 0.310735I
b = −0.761870 − 0.715848I
−0.18514 + 1.56099I 0
u = −0.970003 − 0.445147I
a = 1.361510 − 0.310735I
b = −0.761870 + 0.715848I
−0.18514 − 1.56099I 0
u = −0.417474 + 0.986241I
a = −0.19584 + 1.74464I
b = 0.646187 − 0.741324I
2.74505 + 2.93414I 0
u = −0.417474 − 0.986241I
a = −0.19584 − 1.74464I
b = 0.646187 + 0.741324I
2.74505 − 2.93414I 0
u = 0.912998 + 0.121195I
a = 3.40408 − 1.48710I
b = 0.784183 + 0.435265I
−2.05944 + 3.53631I 0
u = 0.912998 − 0.121195I
a = 3.40408 + 1.48710I
b = 0.784183 − 0.435265I
−2.05944 − 3.53631I 0
u = −0.199454 + 1.061150I
a = 0.25360 − 1.66075I
b = −0.479086 + 0.860207I
−0.33553 − 8.62751I 0
u = −0.199454 − 1.061150I
a = 0.25360 + 1.66075I
b = −0.479086 − 0.860207I
−0.33553 + 8.62751I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667865 + 0.624724I
a = 0.387361 + 0.749515I
b = −0.761870 − 0.715848I
−0.18514 + 1.56099I 0
u = −0.667865 − 0.624724I
a = 0.387361 − 0.749515I
b = −0.761870 + 0.715848I
−0.18514 − 1.56099I 0
u = −0.212818 + 1.074840I
a = −0.748943 − 0.360920I
b = 1.199230 + 0.069488I
−6.23292 + 6.40778I 0
u = −0.212818 − 1.074840I
a = −0.748943 + 0.360920I
b = 1.199230 − 0.069488I
−6.23292 − 6.40778I 0
u = 1.030740 + 0.372194I
a = 1.05992 − 1.40506I
b = 1.223400 + 0.666080I
−3.14096 − 11.89110I 0
u = 1.030740 − 0.372194I
a = 1.05992 + 1.40506I
b = 1.223400 − 0.666080I
−3.14096 + 11.89110I 0
u = 0.838147 + 0.712291I
a = 0.069704 + 1.370090I
b = −0.897555 − 0.648418I
−0.58087 − 6.80332I 0
u = 0.838147 − 0.712291I
a = 0.069704 − 1.370090I
b = −0.897555 + 0.648418I
−0.58087 + 6.80332I 0
u = −0.827154 + 0.299291I
a = −0.589029 + 0.033834I
b = 0.254703 + 1.067970I
−0.26659 + 5.76949I 0
u = −0.827154 − 0.299291I
a = −0.589029 − 0.033834I
b = 0.254703 − 1.067970I
−0.26659 − 5.76949I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129002 + 0.869008I
a = 0.145241 − 0.920534I
b = −1.016810 + 0.483226I
−4.57419 + 3.97041I 0
u = −0.129002 − 0.869008I
a = 0.145241 + 0.920534I
b = −1.016810 − 0.483226I
−4.57419 − 3.97041I 0
u = −0.843800 + 0.191474I
a = 1.95784 + 1.93264I
b = 0.927180 − 0.419329I
0.27458 + 1.60627I 0
u = −0.843800 − 0.191474I
a = 1.95784 − 1.93264I
b = 0.927180 + 0.419329I
0.27458 − 1.60627I 0
u = −0.782237 + 0.368356I
a = −1.87574 + 1.11859I
b = 0.957635 + 0.489487I
−2.72091 − 7.35302I 0
u = −0.782237 − 0.368356I
a = −1.87574 − 1.11859I
b = 0.957635 − 0.489487I
−2.72091 + 7.35302I 0
u = 0.728026 + 0.438957I
a = 0.408231 + 0.497241I
b = −0.335348 + 0.576748I
2.71790 − 0.57544I 0
u = 0.728026 − 0.438957I
a = 0.408231 − 0.497241I
b = −0.335348 − 0.576748I
2.71790 + 0.57544I 0
u = −0.051573 + 1.161320I
a = −0.60038 + 1.33025I
b = 0.856982 − 0.653873I
1.91544 + 1.58382I 0
u = −0.051573 − 1.161320I
a = −0.60038 − 1.33025I
b = 0.856982 + 0.653873I
1.91544 − 1.58382I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.142080 + 0.244273I
a = −0.249359 − 0.653884I
b = −0.252896 + 0.577977I
−2.57074 + 0.03213I 0
u = −1.142080 − 0.244273I
a = −0.249359 + 0.653884I
b = −0.252896 − 0.577977I
−2.57074 − 0.03213I 0
u = 0.753902 + 0.345217I
a = −0.523155 − 0.823578I
b = 0.646187 + 0.741324I
2.74505 − 2.93414I 0
u = 0.753902 − 0.345217I
a = −0.523155 + 0.823578I
b = 0.646187 − 0.741324I
2.74505 + 2.93414I 0
u = 1.152740 + 0.258537I
a = −0.867906 − 0.182712I
b = −1.276920 + 0.320168I
−10.08000 + 0.06598I 0
u = 1.152740 − 0.258537I
a = −0.867906 + 0.182712I
b = −1.276920 − 0.320168I
−10.08000 − 0.06598I 0
u = 0.468915 + 1.102320I
a = −0.84436 + 1.29181I
b = 1.031160 − 0.685683I
1.58692 + 2.47123I 0
u = 0.468915 − 1.102320I
a = −0.84436 − 1.29181I
b = 1.031160 + 0.685683I
1.58692 − 2.47123I 0
u = 1.113450 + 0.465551I
a = −0.200078 + 0.891001I
b = −0.275997 − 0.746459I
−0.62032 − 5.12893I 0
u = 1.113450 − 0.465551I
a = −0.200078 − 0.891001I
b = −0.275997 + 0.746459I
−0.62032 + 5.12893I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.066870 + 0.600839I
a = 0.74671 − 2.13567I
b = 0.905636 + 0.400851I
−5.57459 − 1.63327I 0
u = 1.066870 − 0.600839I
a = 0.74671 + 2.13567I
b = 0.905636 − 0.400851I
−5.57459 + 1.63327I 0
u = −0.756349 + 0.142756I
a = 0.856554 − 0.025826I
b = −0.953322 − 0.767248I
−2.91253 − 2.99862I 0
u = −0.756349 − 0.142756I
a = 0.856554 + 0.025826I
b = −0.953322 + 0.767248I
−2.91253 + 2.99862I 0
u = −1.154330 + 0.430414I
a = −0.427811 + 1.049550I
b = 0.805455 + 0.178381I
−6.09941 + 5.67914I 0
u = −1.154330 − 0.430414I
a = −0.427811 − 1.049550I
b = 0.805455 − 0.178381I
−6.09941 − 5.67914I 0
u = 0.204667 + 1.216490I
a = 0.63617 − 1.30650I
b = −1.113130 + 0.655195I
−2.2541 + 14.2573I 0
u = 0.204667 − 1.216490I
a = 0.63617 + 1.30650I
b = −1.113130 − 0.655195I
−2.2541 − 14.2573I 0
u = −1.169230 + 0.422065I
a = −0.265816 − 0.329693I
b = 0.078657 + 0.789019I
−5.79756 + 4.00477I 0
u = −1.169230 − 0.422065I
a = −0.265816 + 0.329693I
b = 0.078657 − 0.789019I
−5.79756 − 4.00477I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631760 + 0.371860I
a = −0.181768 − 1.109020I
b = −0.572935 + 0.905299I
0.18870 − 2.58655I 0
u = −0.631760 − 0.371860I
a = −0.181768 + 1.109020I
b = −0.572935 − 0.905299I
0.18870 + 2.58655I 0
u = 1.235650 + 0.321189I
a = 1.170020 − 0.676584I
b = 1.057930 + 0.086681I
−6.60249 − 1.94550I 0
u = 1.235650 − 0.321189I
a = 1.170020 + 0.676584I
b = 1.057930 − 0.086681I
−6.60249 + 1.94550I 0
u = −0.005243 + 1.280270I
a = −0.24929 + 1.46601I
b = 0.865008 − 0.611749I
1.90475 + 3.36723I 0
u = −0.005243 − 1.280270I
a = −0.24929 − 1.46601I
b = 0.865008 + 0.611749I
1.90475 − 3.36723I 0
u = −1.213830 + 0.425770I
a = 0.834747 + 0.455836I
b = 1.199230 + 0.069488I
−6.23292 + 6.40778I 0
u = −1.213830 − 0.425770I
a = 0.834747 − 0.455836I
b = 1.199230 − 0.069488I
−6.23292 − 6.40778I 0
u = −0.691305 + 0.073531I
a = −0.55253 − 2.81419I
b = 0.856982 + 0.653873I
1.91544 − 1.58382I 0
u = −0.691305 − 0.073531I
a = −0.55253 + 2.81419I
b = 0.856982 − 0.653873I
1.91544 + 1.58382I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.183640 + 0.558804I
a = 0.781738 + 0.643576I
b = −0.572935 − 0.905299I
0.18870 + 2.58655I 0
u = −1.183640 − 0.558804I
a = 0.781738 − 0.643576I
b = −0.572935 + 0.905299I
0.18870 − 2.58655I 0
u = 0.630831 + 0.252224I
a = −2.16640 − 1.60106I
b = 0.865008 + 0.611749I
1.90475 − 3.36723I 0
u = 0.630831 − 0.252224I
a = −2.16640 + 1.60106I
b = 0.865008 − 0.611749I
1.90475 + 3.36723I 0
u = −0.204936 + 0.646408I
a = 1.49344 − 0.21658I
b = −0.998895 + 0.340741I
−3.31082 − 1.58168I 0
u = −0.204936 − 0.646408I
a = 1.49344 + 0.21658I
b = −0.998895 − 0.340741I
−3.31082 + 1.58168I 0
u = −1.298940 + 0.302426I
a = −0.564197 + 0.445620I
b = −0.998895 − 0.340741I
−3.31082 + 1.58168I 0
u = −1.298940 − 0.302426I
a = −0.564197 − 0.445620I
b = −0.998895 + 0.340741I
−3.31082 − 1.58168I 0
u = 1.206640 + 0.573220I
a = 0.807070 − 0.482658I
b = −0.479086 + 0.860207I
−0.33553 − 8.62751I 0
u = 1.206640 − 0.573220I
a = 0.807070 + 0.482658I
b = −0.479086 − 0.860207I
−0.33553 + 8.62751I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040012 + 0.660433I
a = −0.262338 − 0.737892I
b = −0.252896 + 0.577977I
−2.57074 + 0.03213I 0
u = −0.040012 − 0.660433I
a = −0.262338 + 0.737892I
b = −0.252896 − 0.577977I
−2.57074 − 0.03213I 0
u = 1.269730 + 0.435353I
a = 1.07987 − 1.31003I
b = 1.127820 + 0.507549I
−8.73742 − 8.51212I 0
u = 1.269730 − 0.435353I
a = 1.07987 + 1.31003I
b = 1.127820 − 0.507549I
−8.73742 + 8.51212I 0
u = 1.240160 + 0.515934I
a = −0.546149 + 0.907148I
b = 0.254703 − 1.067970I
−0.26659 − 5.76949I 0
u = 1.240160 − 0.515934I
a = −0.546149 − 0.907148I
b = 0.254703 + 1.067970I
−0.26659 + 5.76949I 0
u = −0.640822 + 0.122913I
a = 0.628426 − 1.201680I
b = 1.031160 + 0.685683I
1.58692 − 2.47123I 0
u = −0.640822 − 0.122913I
a = 0.628426 + 1.201680I
b = 1.031160 − 0.685683I
1.58692 + 2.47123I 0
u = 1.330300 + 0.253070I
a = −0.561032 − 0.429886I
b = −1.016810 + 0.483226I
−4.57419 + 3.97041I 0
u = 1.330300 − 0.253070I
a = −0.561032 + 0.429886I
b = −1.016810 − 0.483226I
−4.57419 − 3.97041I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.343330 + 0.296012I
a = 0.296187 − 1.039790I
b = 0.078657 + 0.789019I
−5.79756 + 4.00477I 0
u = 1.343330 − 0.296012I
a = 0.296187 + 1.039790I
b = 0.078657 − 0.789019I
−5.79756 − 4.00477I 0
u = −0.330502 + 1.336560I
a = 0.752176 + 0.914715I
b = −1.153420 − 0.511740I
0.28525 − 4.98766I 0
u = −0.330502 − 1.336560I
a = 0.752176 − 0.914715I
b = −1.153420 + 0.511740I
0.28525 + 4.98766I 0
u = 0.448899 + 1.321000I
a = 0.479620 + 1.157290I
b = −0.926794 − 0.477530I
0.50785 − 3.58327I 0
u = 0.448899 − 1.321000I
a = 0.479620 − 1.157290I
b = −0.926794 + 0.477530I
0.50785 + 3.58327I 0
u = 0.421282 + 0.431473I
a = 0.472397 − 0.578811I
b = −1.077780 + 0.697217I
−1.36667 + 8.47028I −6.00000 − 3.66392I
u = 0.421282 − 0.431473I
a = 0.472397 + 0.578811I
b = −1.077780 − 0.697217I
−1.36667 − 8.47028I −6.00000 + 3.66392I
u = 1.267980 + 0.593186I
a = −0.54291 + 1.77696I
b = −1.077780 − 0.697217I
−1.36667 − 8.47028I 0
u = 1.267980 − 0.593186I
a = −0.54291 − 1.77696I
b = −1.077780 + 0.697217I
−1.36667 + 8.47028I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.269030 + 0.595415I
a = −0.69559 − 1.79644I
b = −1.113130 + 0.655195I
−2.2541 + 14.2573I 0
u = −1.269030 − 0.595415I
a = −0.69559 + 1.79644I
b = −1.113130 − 0.655195I
−2.2541 − 14.2573I 0
u = 1.20856 + 0.76717I
a = −0.564595 + 0.393514I
b = 0.784183 − 0.435265I
−2.05944 − 3.53631I 0
u = 1.20856 − 0.76717I
a = −0.564595 − 0.393514I
b = 0.784183 + 0.435265I
−2.05944 + 3.53631I 0
u = −0.28778 + 1.42085I
a = 0.038244 + 1.139890I
b = −0.820960 − 0.447182I
0.906398 − 0.207630I 0
u = −0.28778 − 1.42085I
a = 0.038244 − 1.139890I
b = −0.820960 + 0.447182I
0.906398 + 0.207630I 0
u = −1.33532 + 0.66664I
a = 0.24518 + 1.61062I
b = 1.223400 − 0.666080I
−3.14096 + 11.89110I 0
u = −1.33532 − 0.66664I
a = 0.24518 − 1.61062I
b = 1.223400 + 0.666080I
−3.14096 − 11.89110I 0
u = 1.46850 + 0.28697I
a = 0.920290 + 0.569863I
b = 0.805455 − 0.178381I
−6.09941 − 5.67914I 0
u = 1.46850 − 0.28697I
a = 0.920290 − 0.569863I
b = 0.805455 + 0.178381I
−6.09941 + 5.67914I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35813 + 0.63874I
a = 0.529192 + 0.551252I
b = −0.719953 − 0.709662I
−2.18721 + 4.85558I 0
u = −1.35813 − 0.63874I
a = 0.529192 − 0.551252I
b = −0.719953 + 0.709662I
−2.18721 − 4.85558I 0
u = −1.50725
a = 0.232128
b = −1.75919
−7.40980 0
u = −1.34980 + 0.67362I
a = 0.65268 + 1.48090I
b = 0.957635 − 0.489487I
−2.72091 + 7.35302I 0
u = −1.34980 − 0.67362I
a = 0.65268 − 1.48090I
b = 0.957635 + 0.489487I
−2.72091 − 7.35302I 0
u = 1.54192
a = −0.00335629
b = 1.51343
−7.69031 0
u = −1.46376 + 0.58158I
a = −0.097113 − 1.041970I
b = −1.276920 + 0.320168I
−10.08000 + 0.06598I 0
u = −1.46376 − 0.58158I
a = −0.097113 + 1.041970I
b = −1.276920 − 0.320168I
−10.08000 − 0.06598I 0
u = 1.46672 + 0.62280I
a = −0.54525 + 1.51720I
b = −0.964612 − 0.657589I
−2.93934 − 10.11590I 0
u = 1.46672 − 0.62280I
a = −0.54525 − 1.51720I
b = −0.964612 + 0.657589I
−2.93934 + 10.11590I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59494 + 0.21027I
a = 0.163658 − 0.563554I
b = 1.127820 + 0.507549I
−8.73742 − 8.51212I 0
u = −1.59494 − 0.21027I
a = 0.163658 + 0.563554I
b = 1.127820 − 0.507549I
−8.73742 + 8.51212I 0
u = −0.127984 + 0.130583I
a = 4.54520 − 4.68829I
b = −0.275997 − 0.746459I
−0.62032 − 5.12893I −1.28170 + 6.02401I
u = −0.127984 − 0.130583I
a = 4.54520 + 4.68829I
b = −0.275997 + 0.746459I
−0.62032 + 5.12893I −1.28170 − 6.02401I
u = −0.0378961 + 0.0930082I
a = 4.22004 − 8.03735I
b = 1.057930 + 0.086681I
−6.60249 − 1.94550I −14.2889 + 0.8778I
u = −0.0378961 − 0.0930082I
a = 4.22004 + 8.03735I
b = 1.057930 − 0.086681I
−6.60249 + 1.94550I −14.2889 − 0.8778I
26
III.
I
u
3
= h−u
10
+ 4u
8
+ · · · + b − 1, u
10
− u
9
+ · · · + a + 2, u
11
− 5u
9
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−u
10
+ u
9
+ 5u
8
− 4u
7
− 9u
6
+ 6u
5
+ 5u
4
− 3u
3
+ 2u
2
− 2
u
10
− 4u
8
+ 6u
6
− u
5
− 3u
4
+ 2u
3
− u + 1
a
10
=
−u
−u
3
+ u
a
2
=
u
10
− 5u
8
+ 9u
6
− 5u
4
− 2u
2
+ 2
−u
10
+ 4u
8
− 5u
6
+ 2u
2
− u
a
1
=
−u
8
+ 4u
6
− 5u
4
− u + 2
−u
10
+ 4u
8
− 5u
6
+ 2u
2
− u
a
5
=
−u
6
+ 2u
4
− u
2
−u
8
+ 3u
6
− 3u
4
+ u
2
a
6
=
u
9
− 4u
7
+ 5u
5
− 2u
−u
9
+ 3u
7
+ u
6
− 2u
5
− 2u
4
− 2u
3
+ u
2
a
12
=
u
10
− 5u
8
+ 9u
6
− u
5
− 5u
4
+ 2u
3
− 2u
2
− u + 2
−u
10
+ 4u
8
− 5u
6
+ 2u
2
a
8
=
−u
10
+ 5u
8
− u
7
− 9u
6
+ 3u
5
+ 5u
4
− 2u
3
+ 2u
2
− 2
u
10
− u
9
− 4u
8
+ 3u
7
+ 5u
6
− 2u
5
− u
3
− 2u
2
+ u
a
11
=
−u
8
+ 4u
6
− u
5
− 5u
4
+ 2u
3
− u + 2
u
8
− u
7
− 3u
6
+ 2u
5
+ 2u
4
− u
3
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
10
− 6u
9
+ 21u
8
+ 24u
7
− 32u
6
− 25u
5
+ 22u
4
− 11u
3
− 11u
2
+ 17u − 12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 5u
10
+ ··· + 5u − 1
c
2
u
11
+ u
10
− 2u
9
− 3u
8
+ u
7
− 5u
5
− 3u
4
+ 3u
3
+ 2u
2
− u − 1
c
3
, c
11
u
11
− 5u
9
+ 9u
7
− u
6
− 5u
5
+ 3u
4
− 2u
3
− 2u
2
+ 2u − 1
c
4
, c
7
u
11
+ 4u
9
+ 9u
7
+ 4u
6
+ 9u
5
+ 3u
4
− 2u
2
− 2u − 1
c
5
, c
9
u
11
− 5u
9
+ 9u
7
+ u
6
− 5u
5
− 3u
4
− 2u
3
+ 2u
2
+ 2u + 1
c
6
u
11
− u
10
− 2u
9
+ 3u
8
+ u
7
− 5u
5
+ 3u
4
+ 3u
3
− 2u
2
− u + 1
c
8
u
11
+ 7u
10
+ ··· + 15u + 1
c
10
, c
12
u
11
+ 2u
10
+ u
9
− 2u
8
− 6u
7
+ 4u
5
+ 5u
4
− 2u
3
− 2u
2
− u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− y
10
+ ··· − 7y − 1
c
2
, c
6
y
11
− 5y
10
+ ··· + 5y − 1
c
3
, c
5
, c
9
c
11
y
11
− 10y
10
+ ··· − 6y
2
− 1
c
4
, c
7
y
11
+ 8y
10
+ ··· + 2y
2
− 1
c
8
y
11
+ 13y
10
+ ··· + 57y − 1
c
10
, c
12
y
11
− 2y
10
+ ··· + 5y − 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.151450 + 0.270588I
a = 0.057282 + 1.256840I
b = 0.604363 − 0.960598I
−3.51965 + 6.44020I −11.72259 − 5.01138I
u = −1.151450 − 0.270588I
a = 0.057282 − 1.256840I
b = 0.604363 + 0.960598I
−3.51965 − 6.44020I −11.72259 + 5.01138I
u = 1.24623
a = 0.311518
b = 1.62310
−8.31862 −25.6080
u = 0.070231 + 0.702666I
a = 0.397232 + 1.070860I
b = −0.853743 − 0.619035I
3.02416 − 2.43083I 1.37345 + 3.51612I
u = 0.070231 − 0.702666I
a = 0.397232 − 1.070860I
b = −0.853743 + 0.619035I
3.02416 + 2.43083I 1.37345 − 3.51612I
u = −1.321920 + 0.360279I
a = −0.342346 − 0.245725I
b = −0.641158 − 0.438088I
−4.84069 + 5.32060I −7.78196 − 5.42981I
u = −1.321920 − 0.360279I
a = −0.342346 + 0.245725I
b = −0.641158 + 0.438088I
−4.84069 − 5.32060I −7.78196 + 5.42981I
u = 1.382780 + 0.278995I
a = −0.948214 + 0.830037I
b = −1.066310 − 0.544965I
−6.39167 − 9.47527I −9.39685 + 9.35255I
u = 1.382780 − 0.278995I
a = −0.948214 − 0.830037I
b = −1.066310 + 0.544965I
−6.39167 + 9.47527I −9.39685 − 9.35255I
u = 0.397248 + 0.387400I
a = −2.31971 + 0.36228I
b = 0.645300 − 0.284628I
1.082750 + 0.592653I −4.66794 + 3.37871I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397248 − 0.387400I
a = −2.31971 − 0.36228I
b = 0.645300 + 0.284628I
1.082750 − 0.592653I −4.66794 − 3.37871I
31
IV.
I
u
4
= h−1.70×10
27
u
37
+1.24×10
27
u
36
+· · ·+5.30×10
24
b+1.96×10
28
, −1.70×
10
27
u
37
+1.43×10
27
u
36
+· · ·+5.30×10
24
a+1.47×10
28
, u
38
−7u
36
+· · ·−8u−8i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
320.610u
37
− 269.781u
36
+ ··· + 459.319u − 2778.07
319.997u
37
− 233.863u
36
+ ··· + 1322.19u − 3694.38
a
10
=
−u
−u
3
+ u
a
2
=
274.608u
37
− 212.241u
36
+ ··· + 707.263u − 2803.79
81.1598u
37
− 55.6729u
36
+ ··· + 444.111u − 879.219
a
1
=
355.768u
37
− 267.914u
36
+ ··· + 1151.37u − 3683.01
81.1598u
37
− 55.6729u
36
+ ··· + 444.111u − 879.219
a
5
=
−560.307u
37
+ 426.125u
36
+ ··· − 1690.86u + 5625.00
−234.102u
37
+ 163.899u
36
+ ··· − 1153.60u + 2719.57
a
6
=
1111.00u
37
− 831.399u
36
+ ··· + 3504.54u − 11329.5
401.920u
37
− 289.788u
36
+ ··· + 1838.86u − 4583.33
a
12
=
227.483u
37
− 173.687u
36
+ ··· + 646.271u − 2345.76
137.037u
37
− 95.1247u
36
+ ··· + 676.758u − 1462.65
a
8
=
534.801u
37
− 415.351u
36
+ ··· + 1290.98u − 5592.67
443.750u
37
− 319.344u
36
+ ··· + 1874.40u − 4833.85
a
11
=
−1163.12u
37
+ 911.426u
36
+ ··· − 3036.30u + 12109.3
−396.422u
37
+ 270.231u
36
+ ··· − 2010.78u + 4636.37
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2118663230444741564264605988
1324563949752981045028271
u
37
+
1682461438139866615511468107
1324563949752981045028271
u
36
+
··· −
4971119587870413232610550824
1324563949752981045028271
u +
21427208892538446503281796044
1324563949752981045028271
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
− 11u
18
+ ··· + 8u − 1)
2
c
2
(u
19
− u
18
+ ··· − 2u + 1)
2
c
3
, c
11
u
38
− 7u
36
+ ··· − 8u − 8
c
4
, c
7
u
38
+ 8u
37
+ ··· − 20u + 1
c
5
, c
9
u
38
− 7u
36
+ ··· + 8u − 8
c
6
(u
19
+ u
18
+ ··· − 2u − 1)
2
c
8
(u
19
− 5u
18
+ ··· + 9u − 1)
2
c
10
, c
12
u
38
− 3u
37
+ ··· + 4u − 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
− 3y
18
+ ··· + 40y
2
− 1)
2
c
2
, c
6
(y
19
− 11y
18
+ ··· + 8y − 1)
2
c
3
, c
5
, c
9
c
11
y
38
− 14y
37
+ ··· − 1536y + 64
c
4
, c
7
y
38
+ 8y
37
+ ··· − 314y + 1
c
8
(y
19
+ y
18
+ ··· + 27y − 1)
2
c
10
, c
12
y
38
− 11y
37
+ ··· + 20y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.895574 + 0.353013I
a = −1.10550 − 1.32087I
b = 0.699213 − 0.473663I
1.220080 − 0.247886I −3.77645 + 5.75966I
u = 0.895574 − 0.353013I
a = −1.10550 + 1.32087I
b = 0.699213 + 0.473663I
1.220080 + 0.247886I −3.77645 − 5.75966I
u = −1.010990 + 0.262082I
a = 1.81826 + 1.02315I
b = 1.058470 − 0.519496I
−0.04870 + 4.32778I −13.01553 − 4.32298I
u = −1.010990 − 0.262082I
a = 1.81826 − 1.02315I
b = 1.058470 + 0.519496I
−0.04870 − 4.32778I −13.01553 + 4.32298I
u = 0.938881 + 0.496783I
a = 0.608775 + 0.005795I
b = −0.900014 + 0.043524I
−7.19798 − 3.56543I −16.9042 + 4.0677I
u = 0.938881 − 0.496783I
a = 0.608775 − 0.005795I
b = −0.900014 − 0.043524I
−7.19798 + 3.56543I −16.9042 − 4.0677I
u = 0.905399
a = −1.00100
b = −1.70004
−7.20162 14.5360
u = −0.770302 + 0.417123I
a = −0.78571 − 1.66290I
b = 0.582060
−5.25056 −12.96376 + 0.I
u = −0.770302 − 0.417123I
a = −0.78571 + 1.66290I
b = 0.582060
−5.25056 −12.96376 + 0.I
u = 0.755337 + 0.231569I
a = 1.89302 + 1.26738I
b = −0.743514 − 0.618726I
1.91902 − 2.60027I −7.81669 + 0.53490I
35
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755337 − 0.231569I
a = 1.89302 − 1.26738I
b = −0.743514 + 0.618726I
1.91902 + 2.60027I −7.81669 − 0.53490I
u = 1.094940 + 0.528473I
a = −0.318977 + 1.000950I
b = −0.375977 − 0.700747I
−1.40055 − 5.07982I 0
u = 1.094940 − 0.528473I
a = −0.318977 − 1.000950I
b = −0.375977 + 0.700747I
−1.40055 + 5.07982I 0
u = −0.770073 + 0.121528I
a = −0.12537 + 1.88132I
b = −0.998644 − 0.658078I
1.09453 − 2.40927I −16.1025 + 1.8432I
u = −0.770073 − 0.121528I
a = −0.12537 − 1.88132I
b = −0.998644 + 0.658078I
1.09453 + 2.40927I −16.1025 − 1.8432I
u = 0.204174 + 1.209660I
a = −0.198030 + 1.151590I
b = 0.699213 − 0.473663I
1.220080 − 0.247886I 0
u = 0.204174 − 1.209660I
a = −0.198030 − 1.151590I
b = 0.699213 + 0.473663I
1.220080 + 0.247886I 0
u = 1.203740 + 0.254532I
a = 0.643123 − 0.494320I
b = 1.36517
−8.51087 0
u = 1.203740 − 0.254532I
a = 0.643123 + 0.494320I
b = 1.36517
−8.51087 0
u = −0.736846 + 0.025385I
a = 0.13304 − 1.60590I
b = −0.375977 − 0.700747I
−1.40055 − 5.07982I −11.73199 + 5.00622I
36
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736846 − 0.025385I
a = 0.13304 + 1.60590I
b = −0.375977 + 0.700747I
−1.40055 + 5.07982I −11.73199 − 5.00622I
u = −0.044420 + 1.278510I
a = −0.594982 + 1.175760I
b = 1.058470 − 0.519496I
−0.04870 + 4.32778I 0
u = −0.044420 − 1.278510I
a = −0.594982 − 1.175760I
b = 1.058470 + 0.519496I
−0.04870 − 4.32778I 0
u = 0.684526 + 0.165833I
a = −0.07723 − 3.05194I
b = 1.028370 + 0.643129I
−2.66460 − 9.29619I −9.58159 + 6.06051I
u = 0.684526 − 0.165833I
a = −0.07723 + 3.05194I
b = 1.028370 − 0.643129I
−2.66460 + 9.29619I −9.58159 − 6.06051I
u = −1.242290 + 0.402620I
a = −1.34356 − 0.44247I
b = −0.900014 − 0.043524I
−7.19798 + 3.56543I 0
u = −1.242290 − 0.402620I
a = −1.34356 + 0.44247I
b = −0.900014 + 0.043524I
−7.19798 − 3.56543I 0
u = −0.343251 + 1.262530I
a = 0.67187 + 1.36800I
b = −0.998644 − 0.658078I
1.09453 − 2.40927I 0
u = −0.343251 − 1.262530I
a = 0.67187 − 1.36800I
b = −0.998644 + 0.658078I
1.09453 + 2.40927I 0
u = 0.277614 + 1.284550I
a = 0.32053 + 1.49775I
b = −0.743514 − 0.618726I
1.91902 − 2.60027I 0
37
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277614 − 1.284550I
a = 0.32053 − 1.49775I
b = −0.743514 + 0.618726I
1.91902 + 2.60027I 0
u = −0.673745 + 0.076557I
a = −3.09869 − 0.75586I
b = 0.608507 + 0.606791I
−1.35702 + 4.26093I −4.32855 − 4.14732I
u = −0.673745 − 0.076557I
a = −3.09869 + 0.75586I
b = 0.608507 − 0.606791I
−1.35702 − 4.26093I −4.32855 + 4.14732I
u = 1.25703 + 0.70421I
a = −0.503895 + 0.690602I
b = 0.608507 − 0.606791I
−1.35702 − 4.26093I 0
u = 1.25703 − 0.70421I
a = −0.503895 − 0.690602I
b = 0.608507 + 0.606791I
−1.35702 + 4.26093I 0
u = −1.38849 + 0.66696I
a = 0.43786 + 1.60559I
b = 1.028370 − 0.643129I
−2.66460 + 9.29619I 0
u = −1.38849 − 0.66696I
a = 0.43786 − 1.60559I
b = 1.028370 + 0.643129I
−2.66460 − 9.29619I 0
u = −1.56823
a = 0.251945
b = −1.70004
−7.20162 0
38
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
− 5u
10
+ ··· + 5u − 1)(u
19
− 11u
18
+ ··· + 8u − 1)
2
· (u
45
+ 18u
44
+ ··· + 380u + 16)
· (u
68
+ 32u
67
+ ··· + 16464u + 1849)
2
c
2
(u
11
+ u
10
− 2u
9
− 3u
8
+ u
7
− 5u
5
− 3u
4
+ 3u
3
+ 2u
2
− u − 1)
· ((u
19
− u
18
+ ··· − 2u + 1)
2
)(u
45
− 10u
44
+ ··· − 42u + 4)
· (u
68
+ 4u
67
+ ··· − 120u − 43)
2
c
3
, c
11
(u
11
− 5u
9
+ 9u
7
− u
6
− 5u
5
+ 3u
4
− 2u
3
− 2u
2
+ 2u − 1)
· (u
38
− 7u
36
+ ··· − 8u − 8)(u
45
− 16u
43
+ ··· + 8u + 8)
· (u
136
− u
135
+ ··· − 1494u − 89)
c
4
, c
7
(u
11
+ 4u
9
+ 9u
7
+ 4u
6
+ 9u
5
+ 3u
4
− 2u
2
− 2u − 1)
· (u
38
+ 8u
37
+ ··· − 20u + 1)(u
45
− 2u
44
+ ··· − 40u + 7)
· (u
136
− 3u
135
+ ··· − 5351856u + 103993)
c
5
, c
9
(u
11
− 5u
9
+ 9u
7
+ u
6
− 5u
5
− 3u
4
− 2u
3
+ 2u
2
+ 2u + 1)
· (u
38
− 7u
36
+ ··· + 8u − 8)(u
45
− 16u
43
+ ··· + 8u + 8)
· (u
136
− u
135
+ ··· − 1494u − 89)
c
6
(u
11
− u
10
− 2u
9
+ 3u
8
+ u
7
− 5u
5
+ 3u
4
+ 3u
3
− 2u
2
− u + 1)
· ((u
19
+ u
18
+ ··· − 2u − 1)
2
)(u
45
− 10u
44
+ ··· − 42u + 4)
· (u
68
+ 4u
67
+ ··· − 120u − 43)
2
c
8
(u
11
+ 7u
10
+ ··· + 15u + 1)(u
19
− 5u
18
+ ··· + 9u − 1)
2
· (u
45
− 24u
44
+ ··· − 7732u + 1004)(u
68
+ 10u
67
+ ··· + 14u + 1)
2
c
10
, c
12
(u
11
+ 2u
10
+ u
9
− 2u
8
− 6u
7
+ 4u
5
+ 5u
4
− 2u
3
− 2u
2
− u + 1)
· (u
38
− 3u
37
+ ··· + 4u − 1)(u
45
+ 2u
44
+ ··· + 7u + 1)
· (u
136
+ 14u
135
+ ··· − 1293886u − 83089)
39
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
− y
10
+ ··· − 7y − 1)(y
19
− 3y
18
+ ··· + 40y
2
− 1)
2
· (y
45
+ 14y
44
+ ··· + 10480y − 256)
· (y
68
+ 12y
67
+ ··· + 42268244y + 3418801)
2
c
2
, c
6
(y
11
− 5y
10
+ ··· + 5y − 1)(y
19
− 11y
18
+ ··· + 8y − 1)
2
· (y
45
− 18y
44
+ ··· + 380y − 16)
· (y
68
− 32y
67
+ ··· − 16464y + 1849)
2
c
3
, c
5
, c
9
c
11
(y
11
− 10y
10
+ ··· − 6y
2
− 1)(y
38
− 14y
37
+ ··· − 1536y + 64)
· (y
45
− 32y
44
+ ··· + 192y − 64)
· (y
136
− 71y
135
+ ··· + 801262y + 7921)
c
4
, c
7
(y
11
+ 8y
10
+ ··· + 2y
2
− 1)(y
38
+ 8y
37
+ ··· − 314y + 1)
· (y
45
− 24y
44
+ ··· + 1446y − 49)
· (y
136
+ 9y
135
+ ··· − 15840027966342y + 10814544049)
c
8
(y
11
+ 13y
10
+ ··· + 57y − 1)(y
19
+ y
18
+ ··· + 27y − 1)
2
· (y
45
+ 8y
44
+ ··· + 10364936y − 1008016)
· (y
68
+ 6y
67
+ ··· − 190y + 1)
2
c
10
, c
12
(y
11
− 2y
10
+ ··· + 5y − 1)(y
38
− 11y
37
+ ··· + 20y + 1)
· (y
45
+ 30y
44
+ ··· + 41y − 1)
· (y
136
− 2y
135
+ ··· + 154307077926y + 6903781921)
40
