12a
1153
(K12a
1153
)
A knot diagram
1
Linearized knot diagam
4 9 7 10 11 1 3 12 2 5 6 8
Solving Sequence
5,10
11 6 12
2,4
1 7 3 9 8
c
10
c
5
c
11
c
4
c
1
c
6
c
3
c
9
c
8
c
2
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.92523 × 10
127
u
89
+ 3.07371 × 10
128
u
88
+ ··· + 5.59035 × 10
128
b + 1.35846 × 10
130
,
− 2.38182 × 10
128
u
89
+ 6.32318 × 10
129
u
88
+ ··· + 6.42890 × 10
129
a + 1.54116 × 10
131
,
u
90
− u
89
+ ··· + 42u − 23i
I
u
2
= hu
19
− u
18
+ ··· + b − u, −u
19
+ u
18
+ ··· + a − u, u
20
− 2u
19
+ ··· − 7u
2
+ 1i
I
u
3
= h2b − a − 1, a
2
+ 3, u + 1i
* 3 irreducible components of dim
C
= 0, with total 112 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
= h7.93 × 10
127
u
89
+ 3.07 × 10
128
u
88
+ · · · + 5.59 × 10
128
b + 1.36 ×
10
130
, −2.38 × 10
128
u
89
+ 6.32 × 10
129
u
88
+ · · · + 6.43 × 10
129
a + 1.54 ×
10
131
, u
90
− u
89
+ · · · + 42u − 23i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
0.0370486u
89
− 0.983555u
88
+ ··· + 46.7107u − 23.9724
−0.141766u
89
− 0.549825u
88
+ ··· + 26.6619u − 24.3001
a
4
=
u
u
a
1
=
0.154839u
89
− 0.652648u
88
+ ··· + 31.8915u − 18.1094
−0.0239759u
89
− 0.218917u
88
+ ··· + 11.8427u − 18.4371
a
7
=
−0.246377u
89
− 0.228324u
88
+ ··· + 12.1157u + 8.38131
−0.916252u
89
+ 0.319252u
88
+ ··· − 15.5123u − 10.8053
a
3
=
0.501815u
89
+ 0.758825u
88
+ ··· − 42.7975u + 32.0231
−0.197294u
89
+ 1.30218u
88
+ ··· − 76.8115u + 9.02154
a
9
=
0.0157211u
89
− 0.164426u
88
+ ··· + 9.47923u − 22.2811
0.281354u
89
− 0.146535u
88
+ ··· + 7.20437u + 20.3485
a
8
=
0.0160725u
89
− 0.401426u
88
+ ··· + 17.9232u − 9.14048
−0.0306325u
89
− 0.222591u
88
+ ··· + 6.58810u + 23.5750
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.20940u
89
+ 1.41711u
88
+ ··· − 91.7193u + 35.6522
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
− 5u
89
+ ··· − 37888032u + 5971091
c
2
, c
9
u
90
+ u
89
+ ··· − 37544u − 17471
c
3
, c
7
u
90
− 3u
89
+ ··· + 642u − 241
c
4
, c
5
, c
10
c
11
u
90
+ u
89
+ ··· − 42u − 23
c
6
u
90
− u
89
+ ··· − 383961u − 84943
c
8
, c
12
u
90
+ 3u
89
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
− 49y
89
+ ··· − 1076958384213138y + 35653927730281
c
2
, c
9
y
90
+ 79y
89
+ ··· + 6461797462y + 305235841
c
3
, c
7
y
90
+ 59y
89
+ ··· + 1230010y + 58081
c
4
, c
5
, c
10
c
11
y
90
− 113y
89
+ ··· − 12666y + 529
c
6
y
90
− 23y
89
+ ··· − 105154505343y + 7215313249
c
8
, c
12
y
90
+ 45y
89
+ ··· + 76y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.012970 + 0.095264I
a = −0.077161 − 1.261250I
b = 0.71779 − 1.34685I
−5.25522 − 3.65690I 0
u = 1.012970 − 0.095264I
a = −0.077161 + 1.261250I
b = 0.71779 + 1.34685I
−5.25522 + 3.65690I 0
u = 0.857581 + 0.461252I
a = −1.45181 − 1.18703I
b = 0.328398 − 1.371680I
−8.90905 − 6.49876I 0
u = 0.857581 − 0.461252I
a = −1.45181 + 1.18703I
b = 0.328398 + 1.371680I
−8.90905 + 6.49876I 0
u = −0.949097 + 0.212026I
a = −0.61914 + 1.31760I
b = 0.478508 + 0.868615I
−3.71502 + 2.89112I 0
u = −0.949097 − 0.212026I
a = −0.61914 − 1.31760I
b = 0.478508 − 0.868615I
−3.71502 − 2.89112I 0
u = −0.758287 + 0.530225I
a = 1.031630 − 0.931605I
b = −0.00618 − 1.50531I
−8.33159 + 1.02539I 0
u = −0.758287 − 0.530225I
a = 1.031630 + 0.931605I
b = −0.00618 + 1.50531I
−8.33159 − 1.02539I 0
u = −0.905905 + 0.175822I
a = −0.552584 + 1.000800I
b = 0.560162 + 0.490336I
−3.65291 + 2.91212I 0
u = −0.905905 − 0.175822I
a = −0.552584 − 1.000800I
b = 0.560162 − 0.490336I
−3.65291 − 2.91212I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.909719 + 0.579164I
a = 0.94929 − 1.26410I
b = −0.50964 − 1.44518I
−6.3264 + 13.2229I 0
u = −0.909719 − 0.579164I
a = 0.94929 + 1.26410I
b = −0.50964 + 1.44518I
−6.3264 − 13.2229I 0
u = 0.888563 + 0.619652I
a = 0.83455 + 1.14442I
b = −0.316840 + 1.346050I
−2.42194 − 6.81135I 0
u = 0.888563 − 0.619652I
a = 0.83455 − 1.14442I
b = −0.316840 − 1.346050I
−2.42194 + 6.81135I 0
u = 0.115526 + 0.862957I
a = 0.192538 + 0.083063I
b = 0.173180 + 1.221970I
−0.04214 + 1.86425I 0
u = 0.115526 − 0.862957I
a = 0.192538 − 0.083063I
b = 0.173180 − 1.221970I
−0.04214 − 1.86425I 0
u = 0.981169 + 0.591185I
a = −0.956676 − 0.747354I
b = −0.140122 − 1.272130I
−6.57746 + 3.74120I 0
u = 0.981169 − 0.591185I
a = −0.956676 + 0.747354I
b = −0.140122 + 1.272130I
−6.57746 − 3.74120I 0
u = −1.076100 + 0.414278I
a = −0.89733 + 1.13386I
b = 0.062943 + 1.084810I
−3.86394 + 2.62701I 0
u = −1.076100 − 0.414278I
a = −0.89733 − 1.13386I
b = 0.062943 − 1.084810I
−3.86394 − 2.62701I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.011701 + 0.834793I
a = −0.123216 + 0.122071I
b = 0.360219 − 1.321610I
−3.59507 − 8.53511I 0
u = −0.011701 − 0.834793I
a = −0.123216 − 0.122071I
b = 0.360219 + 1.321610I
−3.59507 + 8.53511I 0
u = 0.749413 + 0.327729I
a = −0.087691 + 0.377673I
b = −1.302630 + 0.116841I
−1.31373 − 7.06051I 0
u = 0.749413 − 0.327729I
a = −0.087691 − 0.377673I
b = −1.302630 − 0.116841I
−1.31373 + 7.06051I 0
u = −1.195240 + 0.007025I
a = −0.74496 + 1.26726I
b = −0.152260 + 0.624422I
−3.53900 + 2.66619I 0
u = −1.195240 − 0.007025I
a = −0.74496 − 1.26726I
b = −0.152260 − 0.624422I
−3.53900 − 2.66619I 0
u = −0.630929 + 0.422737I
a = 0.1320450 − 0.0192536I
b = −0.736208 − 0.094191I
2.14970 + 2.95397I 0. − 5.77136I
u = −0.630929 − 0.422737I
a = 0.1320450 + 0.0192536I
b = −0.736208 + 0.094191I
2.14970 − 2.95397I 0. + 5.77136I
u = −0.683833 + 0.159729I
a = −0.30569 + 3.42355I
b = 0.306313 + 0.952007I
−1.89496 + 5.35806I −9.62311 − 9.49203I
u = −0.683833 − 0.159729I
a = −0.30569 − 3.42355I
b = 0.306313 − 0.952007I
−1.89496 − 5.35806I −9.62311 + 9.49203I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438158 + 0.548624I
a = 0.972243 + 0.724630I
b = −0.148755 − 1.072620I
−0.18298 + 1.88594I −8.05875 − 4.24644I
u = −0.438158 − 0.548624I
a = 0.972243 − 0.724630I
b = −0.148755 + 1.072620I
−0.18298 − 1.88594I −8.05875 + 4.24644I
u = 0.540460 + 0.448177I
a = 0.541123 − 0.872191I
b = 0.484861 + 0.598278I
−1.06587 − 2.16161I −7.84161 + 4.07570I
u = 0.540460 − 0.448177I
a = 0.541123 + 0.872191I
b = 0.484861 − 0.598278I
−1.06587 + 2.16161I −7.84161 − 4.07570I
u = 0.691662
a = −0.137190
b = 0.501893
−1.21324 −7.56480
u = −0.674141 + 0.102515I
a = 1.00488 − 1.94243I
b = −0.25194 − 1.83276I
−7.28568 + 0.43053I −12.84317 + 4.45391I
u = −0.674141 − 0.102515I
a = 1.00488 + 1.94243I
b = −0.25194 + 1.83276I
−7.28568 − 0.43053I −12.84317 − 4.45391I
u = 0.673258 + 0.060594I
a = 1.05103 − 2.74686I
b = 0.047191 − 1.063590I
−0.669088 − 1.009510I −8.02815 + 0.51628I
u = 0.673258 − 0.060594I
a = 1.05103 + 2.74686I
b = 0.047191 + 1.063590I
−0.669088 + 1.009510I −8.02815 − 0.51628I
u = −0.033569 + 0.644884I
a = 0.604100 + 0.465382I
b = −0.125543 − 1.364100I
−6.24678 + 2.78122I −9.13407 − 2.15165I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.033569 − 0.644884I
a = 0.604100 − 0.465382I
b = −0.125543 + 1.364100I
−6.24678 − 2.78122I −9.13407 + 2.15165I
u = −0.303612 + 0.561553I
a = −0.118298 + 1.016180I
b = 0.433202 + 0.176963I
3.15527 + 0.45173I 2.37144 − 2.33678I
u = −0.303612 − 0.561553I
a = −0.118298 − 1.016180I
b = 0.433202 − 0.176963I
3.15527 − 0.45173I 2.37144 + 2.33678I
u = 1.40345 + 0.22038I
a = −0.202364 + 0.963975I
b = −0.093332 + 0.518362I
−2.28469 − 3.22073I 0
u = 1.40345 − 0.22038I
a = −0.202364 − 0.963975I
b = −0.093332 − 0.518362I
−2.28469 + 3.22073I 0
u = 1.50828 + 0.07397I
a = −0.449420 − 0.256556I
b = 0.443654 − 0.858953I
−6.34987 − 3.87000I 0
u = 1.50828 − 0.07397I
a = −0.449420 + 0.256556I
b = 0.443654 + 0.858953I
−6.34987 + 3.87000I 0
u = 0.144300 + 0.451946I
a = −0.51701 − 1.95209I
b = 0.804357 − 0.071594I
0.48887 + 4.31858I −0.92438 − 2.28385I
u = 0.144300 − 0.451946I
a = −0.51701 + 1.95209I
b = 0.804357 + 0.071594I
0.48887 − 4.31858I −0.92438 + 2.28385I
u = 0.222649 + 0.417701I
a = 1.208810 − 0.224028I
b = −0.549524 + 0.619458I
−0.305635 − 0.881854I −4.92602 + 3.47601I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.222649 − 0.417701I
a = 1.208810 + 0.224028I
b = −0.549524 − 0.619458I
−0.305635 + 0.881854I −4.92602 − 3.47601I
u = −1.53355 + 0.11529I
a = −0.612137 − 0.121716I
b = −0.316181 + 0.577678I
−7.97086 + 4.15764I 0
u = −1.53355 − 0.11529I
a = −0.612137 + 0.121716I
b = −0.316181 − 0.577678I
−7.97086 − 4.15764I 0
u = 0.455234 + 0.019153I
a = 1.86166 + 0.55835I
b = −0.503361 + 0.850806I
0.087702 − 0.656020I −8.74359 − 0.87707I
u = 0.455234 − 0.019153I
a = 1.86166 − 0.55835I
b = −0.503361 − 0.850806I
0.087702 + 0.656020I −8.74359 + 0.87707I
u = −1.58900 + 0.02697I
a = −0.263885 + 1.064150I
b = 0.805040 + 0.921807I
−7.18439 + 0.98071I 0
u = −1.58900 − 0.02697I
a = −0.263885 − 1.064150I
b = 0.805040 − 0.921807I
−7.18439 − 0.98071I 0
u = 1.59941 + 0.09338I
a = 0.354560 − 0.276286I
b = 1.000530 − 0.274393I
−5.48344 − 4.72712I 0
u = 1.59941 − 0.09338I
a = 0.354560 + 0.276286I
b = 1.000530 + 0.274393I
−5.48344 + 4.72712I 0
u = 0.186645 + 0.338776I
a = 1.176650 − 0.184939I
b = −0.277893 + 0.577578I
−0.293445 − 0.966895I −5.72850 + 6.30392I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.186645 − 0.338776I
a = 1.176650 + 0.184939I
b = −0.277893 − 0.577578I
−0.293445 + 0.966895I −5.72850 − 6.30392I
u = −0.287943 + 0.234517I
a = 1.82271 − 0.65644I
b = −0.624740 + 0.858555I
−0.80294 − 3.88261I −4.29656 − 1.29503I
u = −0.287943 − 0.234517I
a = 1.82271 + 0.65644I
b = −0.624740 − 0.858555I
−0.80294 + 3.88261I −4.29656 + 1.29503I
u = −1.63002 + 0.01524I
a = −0.37399 − 2.31738I
b = 0.119340 − 1.308960I
−8.78831 + 1.28372I 0
u = −1.63002 − 0.01524I
a = −0.37399 + 2.31738I
b = 0.119340 + 1.308960I
−8.78831 − 1.28372I 0
u = 1.63236 + 0.03832I
a = −0.09253 + 2.59020I
b = −0.181723 + 1.182940I
−10.04520 − 6.06116I 0
u = 1.63236 − 0.03832I
a = −0.09253 − 2.59020I
b = −0.181723 − 1.182940I
−10.04520 + 6.06116I 0
u = −1.63618
a = −0.235304
b = −0.875768
−9.43889 0
u = 1.63978 + 0.01940I
a = −0.01052 − 2.33295I
b = 0.53247 − 1.99550I
−15.5099 − 0.8376I 0
u = 1.63978 − 0.01940I
a = −0.01052 + 2.33295I
b = 0.53247 + 1.99550I
−15.5099 + 0.8376I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64318 + 0.08271I
a = 0.970520 + 0.369129I
b = 1.64897 + 0.16956I
−9.64971 + 8.56439I 0
u = −1.64318 − 0.08271I
a = 0.970520 − 0.369129I
b = 1.64897 − 0.16956I
−9.64971 − 8.56439I 0
u = 1.64607 + 0.17474I
a = −0.63968 − 1.88241I
b = 0.09702 − 1.62425I
−16.5366 − 3.8070I 0
u = 1.64607 − 0.17474I
a = −0.63968 + 1.88241I
b = 0.09702 + 1.62425I
−16.5366 + 3.8070I 0
u = 1.66541 + 0.03233I
a = −0.060097 + 0.537563I
b = −0.879840 + 0.217747I
−12.60920 − 3.59916I 0
u = 1.66541 − 0.03233I
a = −0.060097 − 0.537563I
b = −0.879840 − 0.217747I
−12.60920 + 3.59916I 0
u = −1.66382 + 0.13223I
a = 0.72905 − 1.80069I
b = −0.48612 − 1.42287I
−17.6040 + 8.8049I 0
u = −1.66382 − 0.13223I
a = 0.72905 + 1.80069I
b = −0.48612 + 1.42287I
−17.6040 − 8.8049I 0
u = −1.68038 + 0.17715I
a = −0.46078 + 1.91226I
b = 0.41651 + 1.49721I
−11.2168 + 9.9098I 0
u = −1.68038 − 0.17715I
a = −0.46078 − 1.91226I
b = 0.41651 − 1.49721I
−11.2168 − 9.9098I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68472 + 0.16892I
a = −0.42408 − 1.97664I
b = 0.61190 − 1.57435I
−15.2323 − 16.1682I 0
u = 1.68472 − 0.16892I
a = −0.42408 + 1.97664I
b = 0.61190 + 1.57435I
−15.2323 + 16.1682I 0
u = 1.69447 + 0.10434I
a = 0.47504 + 1.73465I
b = −0.396008 + 1.266770I
−13.37100 − 4.57563I 0
u = 1.69447 − 0.10434I
a = 0.47504 − 1.73465I
b = −0.396008 − 1.266770I
−13.37100 + 4.57563I 0
u = 1.70372 + 0.05355I
a = 0.01280 + 1.54850I
b = −0.721684 + 1.064470I
−13.13290 − 3.93184I 0
u = 1.70372 − 0.05355I
a = 0.01280 − 1.54850I
b = −0.721684 − 1.064470I
−13.13290 + 3.93184I 0
u = −1.70643 + 0.03143I
a = −0.37326 − 1.89806I
b = −0.89338 − 1.67140I
−14.8726 + 4.2127I 0
u = −1.70643 − 0.03143I
a = −0.37326 + 1.89806I
b = −0.89338 + 1.67140I
−14.8726 − 4.2127I 0
u = −1.72856 + 0.14953I
a = 0.56663 − 1.47750I
b = −0.131725 − 1.304230I
−16.0616 − 0.7646I 0
u = −1.72856 − 0.14953I
a = 0.56663 + 1.47750I
b = −0.131725 + 1.304230I
−16.0616 + 0.7646I 0
13
II.
I
u
2
= hu
19
−u
18
+· · ·+b−u, −u
19
+u
18
+· · ·+a−u, u
20
−2u
19
+· · ·−7u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
19
− u
18
+ ··· − 7u
2
+ u
−u
19
+ u
18
+ ··· − 3u
2
+ u
a
4
=
u
u
a
1
=
−2u
19
+ u
18
+ ··· + 3u + 2
−4u
19
+ 3u
18
+ ··· + 3u + 2
a
7
=
−2u
19
+ 2u
18
+ ··· + 3u + 1
−2u
19
+ u
18
+ ··· + 2u + 3
a
3
=
−u
16
+ u
15
+ ··· + 6u − 1
u
19
− 2u
18
+ ··· − u − 2
a
9
=
2u
19
− 3u
18
+ ··· − 7u − 1
−u
18
+ 13u
16
+ ··· − 3u − 1
a
8
=
−2u
18
+ 25u
16
+ ··· − 5u + 1
−u
19
− u
18
+ ··· − 3u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 14u
19
− 8u
18
− 182u
17
+ 111u
16
+ 973u
15
− 643u
14
− 2726u
13
+ 1996u
12
+ 4164u
11
−
3523u
10
− 3100u
9
+ 3390u
8
+ 456u
7
− 1408u
6
+ 581u
5
− 52u
4
− 136u
3
+ 102u
2
+ u − 21
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 7u
19
+ ··· − 7u + 1
c
2
u
20
− u
19
+ ··· + u + 1
c
3
u
20
− u
19
+ ··· + u + 1
c
4
, c
5
u
20
+ 2u
19
+ ··· − 7u
2
+ 1
c
6
u
20
+ 2u
19
+ ··· + u + 1
c
7
u
20
+ u
19
+ ··· − u + 1
c
8
u
20
+ u
19
+ ··· − u + 1
c
9
u
20
+ u
19
+ ··· − u + 1
c
10
, c
11
u
20
− 2u
19
+ ··· − 7u
2
+ 1
c
12
u
20
− u
19
+ ··· + u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 3y
19
+ ··· − 5y + 1
c
2
, c
9
y
20
+ 21y
19
+ ··· + 15y + 1
c
3
, c
7
y
20
+ 13y
19
+ ··· + 11y + 1
c
4
, c
5
, c
10
c
11
y
20
− 28y
19
+ ··· − 14y + 1
c
6
y
20
+ 2y
19
+ ··· + 9y + 1
c
8
, c
12
y
20
+ 15y
19
+ ··· + 21y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.236780 + 0.257246I
a = −0.160920 + 1.140040I
b = 0.304832 + 0.961803I
−2.96433 + 4.09234I −8.21729 − 6.76865I
u = −1.236780 − 0.257246I
a = −0.160920 − 1.140040I
b = 0.304832 − 0.961803I
−2.96433 − 4.09234I −8.21729 + 6.76865I
u = 0.676350 + 0.266205I
a = −0.97121 − 1.61423I
b = 0.16047 − 1.77044I
−7.09778 − 0.93539I −6.18058 + 8.72308I
u = 0.676350 − 0.266205I
a = −0.97121 + 1.61423I
b = 0.16047 + 1.77044I
−7.09778 + 0.93539I −6.18058 − 8.72308I
u = 1.366380 + 0.211467I
a = 0.58002 + 1.30951I
b = 0.344378 + 1.031880I
−3.26524 − 1.54191I −7.52291 − 2.90402I
u = 1.366380 − 0.211467I
a = 0.58002 − 1.30951I
b = 0.344378 − 1.031880I
−3.26524 + 1.54191I −7.52291 + 2.90402I
u = 0.467911 + 0.387225I
a = 1.13017 − 1.14976I
b = −0.147056 + 0.694920I
0.91339 − 1.46665I −0.60659 + 3.36448I
u = 0.467911 − 0.387225I
a = 1.13017 + 1.14976I
b = −0.147056 − 0.694920I
0.91339 + 1.46665I −0.60659 − 3.36448I
u = 0.040099 + 0.531181I
a = −0.496026 − 0.240428I
b = −0.253507 + 0.945631I
1.15814 − 0.98852I −0.555070 + 1.124089I
u = 0.040099 − 0.531181I
a = −0.496026 + 0.240428I
b = −0.253507 − 0.945631I
1.15814 + 0.98852I −0.555070 − 1.124089I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53052 + 0.04941I
a = 0.340914 + 0.433719I
b = 0.436448 − 0.482124I
−7.53461 − 5.30221I −9.13332 + 7.29862I
u = 1.53052 − 0.04941I
a = 0.340914 − 0.433719I
b = 0.436448 + 0.482124I
−7.53461 + 5.30221I −9.13332 − 7.29862I
u = −1.55472 + 0.09338I
a = −0.710342 − 0.085200I
b = 0.248590 + 0.542254I
−6.02214 + 3.05677I −5.71579 + 1.69066I
u = −1.55472 − 0.09338I
a = −0.710342 + 0.085200I
b = 0.248590 − 0.542254I
−6.02214 − 3.05677I −5.71579 − 1.69066I
u = −0.336288 + 0.122318I
a = −1.74662 + 2.45740I
b = −0.475237 − 0.606200I
−1.00182 + 4.64059I −7.03732 − 7.06030I
u = −0.336288 − 0.122318I
a = −1.74662 − 2.45740I
b = −0.475237 + 0.606200I
−1.00182 − 4.64059I −7.03732 + 7.06030I
u = −1.66475 + 0.07750I
a = 0.09942 − 2.10149I
b = −0.43525 − 1.80930I
−15.4766 + 2.2859I −11.50746 − 1.72176I
u = −1.66475 − 0.07750I
a = 0.09942 + 2.10149I
b = −0.43525 + 1.80930I
−15.4766 − 2.2859I −11.50746 + 1.72176I
u = 1.71129 + 0.03601I
a = −0.06541 + 1.69236I
b = −0.683669 + 1.135430I
−12.99190 − 4.52813I −8.52367 + 9.83951I
u = 1.71129 − 0.03601I
a = −0.06541 − 1.69236I
b = −0.683669 − 1.135430I
−12.99190 + 4.52813I −8.52367 − 9.83951I
18
III. I
u
3
= h2b − a − 1, a
2
+ 3, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
6
=
1
0
a
12
=
0
1
a
2
=
a
1
2
a +
1
2
a
4
=
−1
−1
a
1
=
1
2
a +
1
2
1
a
7
=
1
2
a +
3
2
1
a
3
=
a − 1
1
2
a −
1
2
a
9
=
1
2
a −
1
2
1
2
a −
1
2
a
8
=
1
2
a −
1
2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
9
c
12
u
2
− u + 1
c
2
, c
7
, c
8
u
2
+ u + 1
c
4
, c
5
, c
6
(u − 1)
2
c
10
, c
11
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
c
12
y
2
+ y + 1
c
4
, c
5
, c
6
c
10
, c
11
(y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.73205I
b = 0.500000 + 0.866025I
−3.28987 + 4.05977I −9.00000 − 6.92820I
u = −1.00000
a = − 1.73205I
b = 0.500000 − 0.866025I
−3.28987 − 4.05977I −9.00000 + 6.92820I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
20
− 7u
19
+ ··· − 7u + 1)
· (u
90
− 5u
89
+ ··· − 37888032u + 5971091)
c
2
(u
2
+ u + 1)(u
20
− u
19
+ ··· + u + 1)(u
90
+ u
89
+ ··· − 37544u − 17471)
c
3
(u
2
− u + 1)(u
20
− u
19
+ ··· + u + 1)(u
90
− 3u
89
+ ··· + 642u − 241)
c
4
, c
5
((u − 1)
2
)(u
20
+ 2u
19
+ ··· − 7u
2
+ 1)(u
90
+ u
89
+ ··· − 42u − 23)
c
6
((u − 1)
2
)(u
20
+ 2u
19
+ ··· + u + 1)(u
90
− u
89
+ ··· − 383961u − 84943)
c
7
(u
2
+ u + 1)(u
20
+ u
19
+ ··· − u + 1)(u
90
− 3u
89
+ ··· + 642u − 241)
c
8
(u
2
+ u + 1)(u
20
+ u
19
+ ··· − u + 1)(u
90
+ 3u
89
+ ··· − 4u − 1)
c
9
(u
2
− u + 1)(u
20
+ u
19
+ ··· − u + 1)(u
90
+ u
89
+ ··· − 37544u − 17471)
c
10
, c
11
((u + 1)
2
)(u
20
− 2u
19
+ ··· − 7u
2
+ 1)(u
90
+ u
89
+ ··· − 42u − 23)
c
12
(u
2
− u + 1)(u
20
− u
19
+ ··· + u + 1)(u
90
+ 3u
89
+ ··· − 4u − 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
20
− 3y
19
+ ··· − 5y + 1)
· (y
90
− 49y
89
+ ··· − 1076958384213138y + 35653927730281)
c
2
, c
9
(y
2
+ y + 1)(y
20
+ 21y
19
+ ··· + 15y + 1)
· (y
90
+ 79y
89
+ ··· + 6461797462y + 305235841)
c
3
, c
7
(y
2
+ y + 1)(y
20
+ 13y
19
+ ··· + 11y + 1)
· (y
90
+ 59y
89
+ ··· + 1230010y + 58081)
c
4
, c
5
, c
10
c
11
((y −1)
2
)(y
20
− 28y
19
+ ··· − 14y + 1)
· (y
90
− 113y
89
+ ··· − 12666y + 529)
c
6
((y −1)
2
)(y
20
+ 2y
19
+ ··· + 9y + 1)
· (y
90
− 23y
89
+ ··· − 105154505343y + 7215313249)
c
8
, c
12
(y
2
+ y + 1)(y
20
+ 15y
19
+ ··· + 21y + 1)(y
90
+ 45y
89
+ ··· + 76y + 1)
24
