12a
0393
(K12a
0393
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 10 12 5 1 8 4 7
Solving Sequence
4,11 5,8
9 12 3 7 1 10 6 2
c
4
c
8
c
11
c
3
c
7
c
12
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.16436 × 10
820
u
170
− 7.16961 × 10
820
u
169
+ ··· + 1.69091 × 10
821
b − 3.15772 × 10
824
,
2.26218 × 10
824
u
170
− 1.11946 × 10
825
u
169
+ ··· + 1.66706 × 10
825
a − 9.23150 × 10
828
,
u
171
− 2u
170
+ ··· + 4671u + 9859i
I
u
2
= h−1.47468 × 10
22
u
40
− 9.65322 × 10
22
u
39
+ ··· + 1.45371 × 10
21
b − 2.19717 × 10
23
,
4.08057 × 10
20
u
40
− 2.19309 × 10
23
u
39
+ ··· + 1.45371 × 10
21
a − 5.58423 × 10
23
, u
41
+ u
40
+ ··· + 16u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 212 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
= h2.16 × 10
820
u
170
− 7.17 × 10
820
u
169
+ · · · + 1.69 × 10
821
b − 3.16 ×
10
824
, 2.26 × 10
824
u
170
− 1.12 × 10
825
u
169
+ · · · + 1.67 × 10
825
a − 9.23 ×
10
828
, u
171
− 2u
170
+ · · · + 4671u + 9859i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
−0.135698u
170
+ 0.671518u
169
+ ··· + 3689.38u + 5537.58
−0.128000u
170
+ 0.424010u
169
+ ··· + 603.968u + 1867.47
a
9
=
−0.319349u
170
+ 1.10997u
169
+ ··· + 3616.53u + 7614.90
−0.305108u
170
+ 0.760621u
169
+ ··· − 874.296u + 2568.95
a
12
=
u
u
a
3
=
−0.632479u
170
+ 1.87166u
169
+ ··· + 2965.36u + 12068.5
−0.678695u
170
+ 1.60465u
169
+ ··· − 1882.78u + 7820.21
a
7
=
−0.231129u
170
+ 0.997129u
169
+ ··· + 4697.68u + 7825.97
−0.223431u
170
+ 0.749621u
169
+ ··· + 1612.26u + 4155.86
a
1
=
0.697139u
170
− 1.39628u
169
+ ··· + 5773.34u − 2258.59
0.597639u
170
− 1.19850u
169
+ ··· + 4279.61u − 2387.93
a
10
=
−1.50364u
170
+ 2.34391u
169
+ ··· − 21755.3u − 2660.63
−0.880774u
170
+ 1.08735u
169
+ ··· − 16968.6u − 4931.27
a
6
=
−0.828240u
170
+ 0.786031u
169
+ ··· − 18991.7u − 7508.20
−0.511994u
170
+ 0.263356u
169
+ ··· − 14937.7u − 7521.50
a
2
=
−0.482941u
170
+ 0.744544u
169
+ ··· − 5025.31u + 1650.19
−0.152795u
170
+ 0.157950u
169
+ ··· − 2168.84u + 595.438
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.62396u
170
− 2.54230u
169
+ ··· + 19935.1u + 2386.95
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
171
+ 78u
170
+ ··· + 2521u + 49
c
2
, c
5
u
171
+ 4u
170
+ ··· + 111u + 7
c
3
u
171
− u
170
+ ··· − 404430848u + 29671424
c
4
, c
11
u
171
− 2u
170
+ ··· + 4671u + 9859
c
6
u
171
− 3u
170
+ ··· + 37835u + 2123
c
7
, c
12
u
171
+ 2u
170
+ ··· − 528354u + 43591
c
8
u
171
+ 5u
170
+ ··· + 61115146u + 5504449
c
9
u
171
+ 8u
170
+ ··· − 25208926u + 28448137
c
10
u
171
+ 8u
170
+ ··· + 208397u + 48167
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
171
+ 46y
170
+ ··· + 1499345y −2401
c
2
, c
5
y
171
− 78y
170
+ ··· + 2521y −49
c
3
y
171
+ 15y
170
+ ··· − 5219403641651200y −880393402187776
c
4
, c
11
y
171
+ 92y
170
+ ··· − 778002993y −97199881
c
6
y
171
+ 41y
170
+ ··· + 1410817697y −4507129
c
7
, c
12
y
171
+ 126y
170
+ ··· − 157098337588y −1900175281
c
8
y
171
− 47y
170
+ ··· + 638582748630030y −30298958793601
c
9
y
171
+ 46y
170
+ ··· − 25343801026808550y −809296498770769
c
10
y
171
− 10y
170
+ ··· + 163308109881y −2320059889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.522816 + 0.862319I
a = −1.38476 + 0.76073I
b = −0.23131 + 1.56919I
2.60729 − 1.52346I 0
u = 0.522816 − 0.862319I
a = −1.38476 − 0.76073I
b = −0.23131 − 1.56919I
2.60729 + 1.52346I 0
u = 0.909426 + 0.435762I
a = −0.119413 − 0.866013I
b = 0.390430 + 0.327958I
4.06706 + 0.85033I 0
u = 0.909426 − 0.435762I
a = −0.119413 + 0.866013I
b = 0.390430 − 0.327958I
4.06706 − 0.85033I 0
u = −0.408687 + 0.900797I
a = 0.513684 − 0.597894I
b = 1.42692 − 1.76208I
5.28982 − 5.58495I 0
u = −0.408687 − 0.900797I
a = 0.513684 + 0.597894I
b = 1.42692 + 1.76208I
5.28982 + 5.58495I 0
u = 0.360268 + 0.917654I
a = 0.520539 + 1.062350I
b = 1.47874 + 1.40925I
−0.0998941 − 0.0172681I 0
u = 0.360268 − 0.917654I
a = 0.520539 − 1.062350I
b = 1.47874 − 1.40925I
−0.0998941 + 0.0172681I 0
u = 0.245163 + 0.991099I
a = −0.008836 − 0.982029I
b = −1.27704 − 1.77108I
−1.25424 + 5.11311I 0
u = 0.245163 − 0.991099I
a = −0.008836 + 0.982029I
b = −1.27704 + 1.77108I
−1.25424 − 5.11311I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959438 + 0.132908I
a = 0.752972 + 0.258045I
b = −0.185217 + 0.308499I
−3.70458 − 0.52517I 0
u = −0.959438 − 0.132908I
a = 0.752972 − 0.258045I
b = −0.185217 − 0.308499I
−3.70458 + 0.52517I 0
u = 0.450784 + 0.931709I
a = −0.641768 − 0.682341I
b = −1.45912 − 1.78519I
3.89033 + 11.06030I 0
u = 0.450784 − 0.931709I
a = −0.641768 + 0.682341I
b = −1.45912 + 1.78519I
3.89033 − 11.06030I 0
u = 0.143513 + 0.952277I
a = −0.126743 + 0.262061I
b = 0.268539 + 0.771000I
−0.77746 + 1.36820I 0
u = 0.143513 − 0.952277I
a = −0.126743 − 0.262061I
b = 0.268539 − 0.771000I
−0.77746 − 1.36820I 0
u = −0.327368 + 0.999695I
a = −0.525772 + 0.390138I
b = −0.047209 + 1.285440I
−0.24255 + 1.97395I 0
u = −0.327368 − 0.999695I
a = −0.525772 − 0.390138I
b = −0.047209 − 1.285440I
−0.24255 − 1.97395I 0
u = −0.892591 + 0.560383I
a = 0.126506 − 0.724879I
b = −0.481848 + 0.396131I
3.64192 − 5.10552I 0
u = −0.892591 − 0.560383I
a = 0.126506 + 0.724879I
b = −0.481848 − 0.396131I
3.64192 + 5.10552I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372716 + 0.988870I
a = 0.460916 − 1.169530I
b = −0.23905 − 1.70014I
−2.77213 − 1.78404I 0
u = −0.372716 − 0.988870I
a = 0.460916 + 1.169530I
b = −0.23905 + 1.70014I
−2.77213 + 1.78404I 0
u = 0.274336 + 1.024780I
a = 0.571806 + 0.302014I
b = −1.38226 + 0.57658I
0.50931 + 6.41538I 0
u = 0.274336 − 1.024780I
a = 0.571806 − 0.302014I
b = −1.38226 − 0.57658I
0.50931 − 6.41538I 0
u = −0.254872 + 0.898952I
a = −0.959077 + 0.046936I
b = 1.022820 − 0.168338I
3.63281 − 0.53934I 0
u = −0.254872 − 0.898952I
a = −0.959077 − 0.046936I
b = 1.022820 + 0.168338I
3.63281 + 0.53934I 0
u = −0.766566 + 0.742347I
a = 0.187282 − 0.294692I
b = −0.574949 + 0.697972I
3.14382 − 0.82943I 0
u = −0.766566 − 0.742347I
a = 0.187282 + 0.294692I
b = −0.574949 − 0.697972I
3.14382 + 0.82943I 0
u = 0.665772 + 0.843021I
a = −0.209489 + 0.100833I
b = 0.612905 + 0.963363I
2.99332 + 4.80623I 0
u = 0.665772 − 0.843021I
a = −0.209489 − 0.100833I
b = 0.612905 − 0.963363I
2.99332 − 4.80623I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292872 + 0.873573I
a = 0.78424 + 1.95800I
b = 1.87599 + 2.23240I
2.88872 − 6.87672I 0
u = 0.292872 − 0.873573I
a = 0.78424 − 1.95800I
b = 1.87599 − 2.23240I
2.88872 + 6.87672I 0
u = −0.422237 + 0.814113I
a = 1.75628 + 0.42376I
b = 0.505283 + 1.221520I
4.82984 − 2.83468I 0
u = −0.422237 − 0.814113I
a = 1.75628 − 0.42376I
b = 0.505283 − 1.221520I
4.82984 + 2.83468I 0
u = −0.314631 + 0.855483I
a = −0.41465 + 1.87494I
b = −1.51920 + 2.19832I
4.75267 + 1.76525I 0
u = −0.314631 − 0.855483I
a = −0.41465 − 1.87494I
b = −1.51920 − 2.19832I
4.75267 − 1.76525I 0
u = 0.236266 + 0.872240I
a = −2.96674 + 0.18166I
b = −1.59394 + 0.69961I
3.00396 + 9.29509I 0
u = 0.236266 − 0.872240I
a = −2.96674 − 0.18166I
b = −1.59394 − 0.69961I
3.00396 − 9.29509I 0
u = −0.899123 + 0.016968I
a = 1.049410 − 0.458297I
b = 0.061777 − 0.424488I
−0.18450 + 9.24033I 0
u = −0.899123 − 0.016968I
a = 1.049410 + 0.458297I
b = 0.061777 + 0.424488I
−0.18450 − 9.24033I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274759 + 0.844572I
a = 2.61389 + 0.22936I
b = 1.23531 + 0.83487I
4.85993 − 4.46120I 0
u = −0.274759 − 0.844572I
a = 2.61389 − 0.22936I
b = 1.23531 − 0.83487I
4.85993 + 4.46120I 0
u = 0.430302 + 1.026590I
a = −0.410664 − 1.274410I
b = 0.32087 − 1.70052I
−3.73105 + 5.90089I 0
u = 0.430302 − 1.026590I
a = −0.410664 + 1.274410I
b = 0.32087 + 1.70052I
−3.73105 − 5.90089I 0
u = 0.707719 + 0.863811I
a = 1.08340 − 0.92715I
b = 0.48199 − 1.56754I
−2.63787 − 0.95993I 0
u = 0.707719 − 0.863811I
a = 1.08340 + 0.92715I
b = 0.48199 + 1.56754I
−2.63787 + 0.95993I 0
u = −0.238291 + 1.095200I
a = 0.398044 − 1.127660I
b = 0.05045 − 1.70633I
−3.72734 − 2.25632I 0
u = −0.238291 − 1.095200I
a = 0.398044 + 1.127660I
b = 0.05045 + 1.70633I
−3.72734 + 2.25632I 0
u = −0.390649 + 0.786306I
a = 0.50511 + 1.49272I
b = −0.66572 + 2.00062I
4.93676 − 0.71005I 0
u = −0.390649 − 0.786306I
a = 0.50511 − 1.49272I
b = −0.66572 − 2.00062I
4.93676 + 0.71005I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.115242 + 0.857886I
a = 1.45827 − 0.76807I
b = −0.321149 − 0.984223I
−0.47057 − 3.45920I 0
u = 0.115242 − 0.857886I
a = 1.45827 + 0.76807I
b = −0.321149 + 0.984223I
−0.47057 + 3.45920I 0
u = 0.859103 + 0.011211I
a = −0.940607 + 0.513658I
b = 0.025476 + 0.460900I
2.03834 + 3.63505I 0
u = 0.859103 − 0.011211I
a = −0.940607 − 0.513658I
b = 0.025476 − 0.460900I
2.03834 − 3.63505I 0
u = 0.120820 + 1.149140I
a = −0.261231 − 1.286510I
b = −0.12370 − 1.95510I
−6.29019 − 0.80071I 0
u = 0.120820 − 1.149140I
a = −0.261231 + 1.286510I
b = −0.12370 + 1.95510I
−6.29019 + 0.80071I 0
u = 1.106340 + 0.335545I
a = −0.892783 − 0.385309I
b = −0.165992 + 0.564515I
−0.03939 − 5.59646I 0
u = 1.106340 − 0.335545I
a = −0.892783 + 0.385309I
b = −0.165992 − 0.564515I
−0.03939 + 5.59646I 0
u = −0.208012 + 0.817367I
a = −0.045393 − 0.296055I
b = 1.41154 − 1.85724I
3.97238 − 1.73980I 0
u = −0.208012 − 0.817367I
a = −0.045393 + 0.296055I
b = 1.41154 + 1.85724I
3.97238 + 1.73980I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443856 + 0.706608I
a = −1.10179 + 1.23259I
b = 0.17499 + 1.89028I
3.11287 + 5.57851I 0
u = 0.443856 − 0.706608I
a = −1.10179 − 1.23259I
b = 0.17499 − 1.89028I
3.11287 − 5.57851I 0
u = −0.377519 + 1.105720I
a = −0.411133 − 0.495722I
b = −1.083460 − 0.467912I
−3.10737 + 2.60472I 0
u = −0.377519 − 1.105720I
a = −0.411133 + 0.495722I
b = −1.083460 + 0.467912I
−3.10737 − 2.60472I 0
u = 1.141560 + 0.273493I
a = −0.925304 − 0.570444I
b = −0.285548 + 0.438239I
4.0738 − 14.1133I 0
u = 1.141560 − 0.273493I
a = −0.925304 + 0.570444I
b = −0.285548 − 0.438239I
4.0738 + 14.1133I 0
u = 0.415281 + 1.106680I
a = −0.201541 − 1.230520I
b = 0.46732 − 1.54298I
−4.54754 + 0.61795I 0
u = 0.415281 − 1.106680I
a = −0.201541 + 1.230520I
b = 0.46732 + 1.54298I
−4.54754 − 0.61795I 0
u = 0.359487 + 1.128460I
a = 0.419687 + 0.572015I
b = −0.04631 + 1.55412I
0.28034 + 3.67321I 0
u = 0.359487 − 1.128460I
a = 0.419687 − 0.572015I
b = −0.04631 − 1.55412I
0.28034 − 3.67321I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148170 + 0.295364I
a = 0.870882 − 0.541423I
b = 0.228446 + 0.436299I
6.18565 + 8.35593I 0
u = −1.148170 − 0.295364I
a = 0.870882 + 0.541423I
b = 0.228446 − 0.436299I
6.18565 − 8.35593I 0
u = 0.156475 + 0.782638I
a = −2.65771 − 0.48023I
b = −1.029510 − 0.011476I
0.78856 + 2.58407I 0
u = 0.156475 − 0.782638I
a = −2.65771 + 0.48023I
b = −1.029510 + 0.011476I
0.78856 − 2.58407I 0
u = −0.388171 + 1.141170I
a = 0.019116 − 0.992835I
b = −0.593102 − 1.180020I
−4.34916 − 3.57966I 0
u = −0.388171 − 1.141170I
a = 0.019116 + 0.992835I
b = −0.593102 + 1.180020I
−4.34916 + 3.57966I 0
u = −0.419844 + 0.671040I
a = −1.60421 + 0.77038I
b = 0.221550 + 0.210808I
5.98352 + 2.02173I 0
u = −0.419844 − 0.671040I
a = −1.60421 − 0.77038I
b = 0.221550 − 0.210808I
5.98352 − 2.02173I 0
u = 0.436436 + 1.129700I
a = 0.001555 − 0.319600I
b = 0.520056 − 0.249339I
−1.05269 + 1.66505I 0
u = 0.436436 − 1.129700I
a = 0.001555 + 0.319600I
b = 0.520056 + 0.249339I
−1.05269 − 1.66505I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738744 + 0.258733I
a = −1.22091 + 0.81500I
b = −0.708497 − 0.264821I
−0.694702 − 0.275037I 0
u = −0.738744 − 0.258733I
a = −1.22091 − 0.81500I
b = −0.708497 + 0.264821I
−0.694702 + 0.275037I 0
u = 0.225192 + 1.197090I
a = −0.527945 − 1.273280I
b = −0.36794 − 1.77147I
−5.86598 + 5.62963I 0
u = 0.225192 − 1.197090I
a = −0.527945 + 1.273280I
b = −0.36794 + 1.77147I
−5.86598 − 5.62963I 0
u = 0.492463 + 0.605874I
a = 1.63519 + 1.01348I
b = −0.093735 + 0.292088I
4.85467 − 7.15417I 0
u = 0.492463 − 0.605874I
a = 1.63519 − 1.01348I
b = −0.093735 − 0.292088I
4.85467 + 7.15417I 0
u = 0.620395 + 1.064620I
a = 0.38314 − 1.46906I
b = −0.22856 − 2.01854I
−3.44295 + 6.23211I 0
u = 0.620395 − 1.064620I
a = 0.38314 + 1.46906I
b = −0.22856 + 2.01854I
−3.44295 − 6.23211I 0
u = −0.321074 + 1.191310I
a = 0.613365 − 0.923046I
b = 0.364120 − 1.194290I
−4.39198 − 2.68022I 0
u = −0.321074 − 1.191310I
a = 0.613365 + 0.923046I
b = 0.364120 + 1.194290I
−4.39198 + 2.68022I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.189110 + 0.371110I
a = 0.622727 − 0.428024I
b = 0.013470 + 0.406843I
7.28017 + 3.81548I 0
u = −1.189110 − 0.371110I
a = 0.622727 + 0.428024I
b = 0.013470 − 0.406843I
7.28017 − 3.81548I 0
u = 0.472184 + 1.156310I
a = −0.59336 − 1.32160I
b = −1.28367 − 1.98916I
−0.73295 + 6.48144I 0
u = 0.472184 − 1.156310I
a = −0.59336 + 1.32160I
b = −1.28367 + 1.98916I
−0.73295 − 6.48144I 0
u = −0.502038 + 1.155380I
a = 0.68290 − 1.48024I
b = 1.28742 − 2.14190I
−2.24635 − 10.55610I 0
u = −0.502038 − 1.155380I
a = 0.68290 + 1.48024I
b = 1.28742 + 2.14190I
−2.24635 + 10.55610I 0
u = −0.712297 + 0.191516I
a = −1.31149 + 1.30360I
b = −0.521245 + 0.041234I
0.54925 + 5.96235I 0
u = −0.712297 − 0.191516I
a = −1.31149 − 1.30360I
b = −0.521245 − 0.041234I
0.54925 − 5.96235I 0
u = −0.517576 + 1.157000I
a = 0.38791 − 1.62308I
b = 0.99696 − 2.19800I
−3.38588 − 4.47085I 0
u = −0.517576 − 1.157000I
a = 0.38791 + 1.62308I
b = 0.99696 + 2.19800I
−3.38588 + 4.47085I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428089 + 1.194050I
a = −0.512233 − 1.265770I
b = −1.27779 − 1.87533I
−0.86391 + 6.40475I 0
u = 0.428089 − 1.194050I
a = −0.512233 + 1.265770I
b = −1.27779 + 1.87533I
−0.86391 − 6.40475I 0
u = 0.077315 + 0.720625I
a = 0.282842 − 0.173027I
b = −0.99146 − 2.02770I
1.89574 − 4.40727I 0
u = 0.077315 − 0.720625I
a = 0.282842 + 0.173027I
b = −0.99146 + 2.02770I
1.89574 + 4.40727I 0
u = 0.720261 + 0.072252I
a = 0.78213 + 1.37239I
b = 0.384496 − 0.155217I
2.37177 − 2.16911I 0
u = 0.720261 − 0.072252I
a = 0.78213 − 1.37239I
b = 0.384496 + 0.155217I
2.37177 + 2.16911I 0
u = −0.300750 + 1.254370I
a = 0.52386 − 1.33141I
b = 1.40445 − 1.83298I
−2.59933 − 3.36377I 0
u = −0.300750 − 1.254370I
a = 0.52386 + 1.33141I
b = 1.40445 + 1.83298I
−2.59933 + 3.36377I 0
u = 1.230950 + 0.414044I
a = −0.453333 − 0.353159I
b = 0.089262 + 0.381206I
6.09815 + 2.21552I 0
u = 1.230950 − 0.414044I
a = −0.453333 + 0.353159I
b = 0.089262 − 0.381206I
6.09815 − 2.21552I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363759 + 1.250300I
a = 0.869644 − 0.391526I
b = 0.725913 − 0.403659I
−1.67404 − 8.42737I 0
u = −0.363759 − 1.250300I
a = 0.869644 + 0.391526I
b = 0.725913 + 0.403659I
−1.67404 + 8.42737I 0
u = 0.391387 + 1.243600I
a = −0.647592 − 0.298947I
b = −0.415732 − 0.263693I
−0.18558 + 3.44846I 0
u = 0.391387 − 1.243600I
a = −0.647592 + 0.298947I
b = −0.415732 + 0.263693I
−0.18558 − 3.44846I 0
u = −0.814721 + 1.018870I
a = −0.531460 − 0.837492I
b = 0.015260 − 1.409170I
0.03542 − 3.21441I 0
u = −0.814721 − 1.018870I
a = −0.531460 + 0.837492I
b = 0.015260 + 1.409170I
0.03542 + 3.21441I 0
u = 0.161018 + 1.306420I
a = 0.180923 + 0.441279I
b = −0.605033 + 0.882738I
−6.43143 − 1.68566I 0
u = 0.161018 − 1.306420I
a = 0.180923 − 0.441279I
b = −0.605033 − 0.882738I
−6.43143 + 1.68566I 0
u = −0.382459 + 0.566458I
a = −0.943960 − 0.302728I
b = −0.417876 + 0.733678I
−1.57334 − 1.53009I 0
u = −0.382459 − 0.566458I
a = −0.943960 + 0.302728I
b = −0.417876 − 0.733678I
−1.57334 + 1.53009I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470125 + 1.238920I
a = 0.317987 + 0.898592I
b = 0.03987 + 1.82267I
−1.68286 + 8.35218I 0
u = 0.470125 − 1.238920I
a = 0.317987 − 0.898592I
b = 0.03987 − 1.82267I
−1.68286 − 8.35218I 0
u = −0.488091 + 1.250130I
a = −0.310242 + 0.967239I
b = −0.04273 + 1.85787I
−3.8982 − 14.1640I 0
u = −0.488091 − 1.250130I
a = −0.310242 − 0.967239I
b = −0.04273 − 1.85787I
−3.8982 + 14.1640I 0
u = −0.434696 + 1.284700I
a = −0.157892 + 0.815977I
b = 0.01363 + 1.81951I
−8.04984 − 5.26008I 0
u = −0.434696 − 1.284700I
a = −0.157892 − 0.815977I
b = 0.01363 − 1.81951I
−8.04984 + 5.26008I 0
u = 0.450723 + 1.283490I
a = −0.181582 + 0.687267I
b = 0.061831 + 1.391640I
−1.78545 + 1.21839I 0
u = 0.450723 − 1.283490I
a = −0.181582 − 0.687267I
b = 0.061831 − 1.391640I
−1.78545 − 1.21839I 0
u = 0.475367 + 0.398286I
a = 1.254560 − 0.480802I
b = 0.577393 + 0.525369I
−1.99917 − 2.12741I −8.00000 + 2.51382I
u = 0.475367 − 0.398286I
a = 1.254560 + 0.480802I
b = 0.577393 − 0.525369I
−1.99917 + 2.12741I −8.00000 − 2.51382I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.442386 + 1.308270I
a = 0.251345 + 0.780246I
b = 0.12685 + 1.45490I
−4.24368 + 4.33829I 0
u = −0.442386 − 1.308270I
a = 0.251345 − 0.780246I
b = 0.12685 − 1.45490I
−4.24368 − 4.33829I 0
u = 0.647761 + 1.237630I
a = 0.169953 + 0.856109I
b = 0.81887 + 1.69652I
3.27782 + 4.21966I 0
u = 0.647761 − 1.237630I
a = 0.169953 − 0.856109I
b = 0.81887 − 1.69652I
3.27782 − 4.21966I 0
u = 0.594032 + 0.001320I
a = −0.648130 + 1.057640I
b = 0.313222 + 0.666446I
3.35777 + 0.21005I −1.70819 − 1.96335I
u = 0.594032 − 0.001320I
a = −0.648130 − 1.057640I
b = 0.313222 − 0.666446I
3.35777 − 0.21005I −1.70819 + 1.96335I
u = −0.374077 + 1.357760I
a = 0.609691 − 1.213940I
b = 1.40098 − 1.66595I
−2.23995 − 9.20664I 0
u = −0.374077 − 1.357760I
a = 0.609691 + 1.213940I
b = 1.40098 + 1.66595I
−2.23995 + 9.20664I 0
u = −0.656233 + 1.251970I
a = −0.211218 + 0.974269I
b = −0.88810 + 1.80620I
4.37338 − 10.24420I 0
u = −0.656233 − 1.251970I
a = −0.211218 − 0.974269I
b = −0.88810 − 1.80620I
4.37338 + 10.24420I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64172 + 1.26295I
a = 0.133193 + 1.183320I
b = 0.85766 + 2.00847I
−3.03118 + 11.83030I 0
u = 0.64172 − 1.26295I
a = 0.133193 − 1.183320I
b = 0.85766 − 2.00847I
−3.03118 − 11.83030I 0
u = −0.50624 + 1.33298I
a = 0.062793 + 0.715903I
b = −0.22845 + 1.71817I
−7.50335 − 5.04059I 0
u = −0.50624 − 1.33298I
a = 0.062793 − 0.715903I
b = −0.22845 − 1.71817I
−7.50335 + 5.04059I 0
u = 0.520857 + 0.236165I
a = 1.60435 + 1.81934I
b = 0.227801 + 0.071552I
2.03566 − 2.41610I −1.86591 + 1.09875I
u = 0.520857 − 0.236165I
a = 1.60435 − 1.81934I
b = 0.227801 − 0.071552I
2.03566 + 2.41610I −1.86591 − 1.09875I
u = −0.64901 + 1.27560I
a = −0.271825 + 1.199250I
b = −0.98087 + 2.00240I
3.0608 − 14.6941I 0
u = −0.64901 − 1.27560I
a = −0.271825 − 1.199250I
b = −0.98087 − 2.00240I
3.0608 + 14.6941I 0
u = 0.544892 + 0.162581I
a = 1.42807 − 0.63202I
b = 0.679826 + 0.218593I
−1.92563 + 3.11240I −9.93844 − 6.49156I
u = 0.544892 − 0.162581I
a = 1.42807 + 0.63202I
b = 0.679826 − 0.218593I
−1.92563 − 3.11240I −9.93844 + 6.49156I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64444 + 1.28179I
a = 0.288296 + 1.258350I
b = 1.00264 + 2.05279I
0.8786 + 20.4203I 0
u = 0.64444 − 1.28179I
a = 0.288296 − 1.258350I
b = 1.00264 − 2.05279I
0.8786 − 20.4203I 0
u = 0.47267 + 1.35967I
a = −0.520671 − 1.113190I
b = −1.24876 − 1.57396I
−1.27419 + 5.60333I 0
u = 0.47267 − 1.35967I
a = −0.520671 + 1.113190I
b = −1.24876 + 1.57396I
−1.27419 − 5.60333I 0
u = −0.01229 + 1.45574I
a = −0.113439 + 0.362821I
b = 0.503699 + 0.685443I
−0.82468 + 3.68210I 0
u = −0.01229 − 1.45574I
a = −0.113439 − 0.362821I
b = 0.503699 − 0.685443I
−0.82468 − 3.68210I 0
u = 1.50110 + 0.00916I
a = 0.142621 + 0.318709I
b = 0.193413 − 0.394151I
5.80454 − 2.48084I 0
u = 1.50110 − 0.00916I
a = 0.142621 − 0.318709I
b = 0.193413 + 0.394151I
5.80454 + 2.48084I 0
u = 0.10474 + 1.51348I
a = 0.069136 + 0.391493I
b = −0.598683 + 0.654252I
−2.60975 − 9.16870I 0
u = 0.10474 − 1.51348I
a = 0.069136 − 0.391493I
b = −0.598683 − 0.654252I
−2.60975 + 9.16870I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478701 + 0.026645I
a = −1.130160 + 0.700094I
b = −0.632644 + 0.032512I
−1.087000 − 0.269208I −7.50861 − 1.22660I
u = −0.478701 − 0.026645I
a = −1.130160 − 0.700094I
b = −0.632644 − 0.032512I
−1.087000 + 0.269208I −7.50861 + 1.22660I
u = −0.474330 + 0.044991I
a = 0.70887 − 1.51617I
b = −0.483206 − 0.789765I
1.97022 − 5.09274I −4.00700 + 4.13201I
u = −0.474330 − 0.044991I
a = 0.70887 + 1.51617I
b = −0.483206 + 0.789765I
1.97022 + 5.09274I −4.00700 − 4.13201I
u = −0.78245 + 1.38030I
a = 0.145855 − 0.721295I
b = 0.722185 − 1.153840I
2.23739 − 4.72523I 0
u = −0.78245 − 1.38030I
a = 0.145855 + 0.721295I
b = 0.722185 + 1.153840I
2.23739 + 4.72523I 0
u = 0.69871 + 1.43611I
a = −0.307780 − 0.755402I
b = −0.92272 − 1.16743I
1.28246 + 9.82011I 0
u = 0.69871 − 1.43611I
a = −0.307780 + 0.755402I
b = −0.92272 + 1.16743I
1.28246 − 9.82011I 0
u = −1.60498 + 0.35017I
a = −0.245929 + 0.154231I
b = −0.146754 − 0.476689I
5.84641 − 3.29781I 0
u = −1.60498 − 0.35017I
a = −0.245929 − 0.154231I
b = −0.146754 + 0.476689I
5.84641 + 3.29781I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341138
a = −1.64479
b = −0.425108
−0.864587 −11.3420
22
II. I
u
2
= h−1.47 × 10
22
u
40
− 9.65 × 10
22
u
39
+ · · · + 1.45 × 10
21
b − 2.20 ×
10
23
, 4.08 × 10
20
u
40
− 2.19 × 10
23
u
39
+ · · · + 1.45 × 10
21
a − 5.58 ×
10
23
, u
41
+ u
40
+ · · · + 16u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
−0.280700u
40
+ 150.861u
39
+ ··· − 91.8952u + 384.136
10.1443u
40
+ 66.4040u
39
+ ··· − 0.280700u + 151.142
a
9
=
0.719300u
40
+ 151.861u
39
+ ··· − 91.8952u + 384.136
11.1443u
40
+ 67.4040u
39
+ ··· + 0.719300u + 151.142
a
12
=
u
u
a
3
=
−284.587u
40
− 187.873u
39
+ ··· − 688.029u + 188.609
−204.233u
40
− 143.941u
39
+ ··· − 523.057u + 122.095
a
7
=
3.88878u
40
+ 190.990u
39
+ ··· − 102.320u + 479.018
14.3137u
40
+ 106.532u
39
+ ··· − 10.7057u + 246.024
a
1
=
92.2701u
40
+ 124.294u
39
+ ··· + 185.120u + 46.7070
66.5579u
40
+ 134.994u
39
+ ··· + 124.515u + 156.462
a
10
=
−213.271u
40
− 434.044u
39
+ ··· − 397.779u − 542.363
−126.187u
40
− 305.229u
39
+ ··· − 238.371u − 459.244
a
6
=
−93.3704u
40
− 283.715u
39
+ ··· − 145.530u − 518.477
−2.74709u
40
− 97.3313u
39
+ ··· + 5.71575u − 275.659
a
2
=
−187.050u
40
− 245.106u
39
+ ··· − 526.273u − 126.714
−74.8426u
40
− 103.662u
39
+ ··· − 248.151u − 97.0573
(ii) Obstruction class = 1
(iii) Cusp Shapes =
568177341231088321507990
1453711757268553750381
u
40
+
418250464738411314973923
1453711757268553750381
u
39
+ ··· +
1157014307294773757273725
1453711757268553750381
u −
385823938298514861699465
1453711757268553750381
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
41
− 23u
40
+ ··· + 138u − 9
c
2
u
41
+ 3u
40
+ ··· + 23u
2
− 3
c
3
u
41
− 7u
39
+ ··· − u + 1
c
4
u
41
+ u
40
+ ··· + 16u
2
+ 1
c
5
u
41
− 3u
40
+ ··· − 23u
2
+ 3
c
6
u
41
+ 4u
40
+ ··· + 4u − 1
c
7
u
41
+ u
40
+ ··· − 7u − 1
c
8
u
41
− 8u
39
+ ··· + u − 1
c
9
u
41
− u
40
+ ··· + 7u − 1
c
10
u
41
+ 19u
40
+ ··· + 160u + 11
c
11
u
41
− u
40
+ ··· − 16u
2
− 1
c
12
u
41
− u
40
+ ··· − 7u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 5y
40
+ ··· − 414y −81
c
2
, c
5
y
41
− 23y
40
+ ··· + 138y −9
c
3
y
41
− 14y
40
+ ··· − 5y −1
c
4
, c
11
y
41
+ 19y
40
+ ··· − 32y −1
c
6
y
41
+ 24y
40
+ ··· − 2y −1
c
7
, c
12
y
41
+ 37y
40
+ ··· − 55y −1
c
8
y
41
− 16y
40
+ ··· + 31y −1
c
9
y
41
+ 5y
40
+ ··· − 21y −1
c
10
y
41
+ 9y
40
+ ··· − 118y −121
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409777 + 0.900801I
a = −0.544341 − 1.119450I
b = −0.730677 − 1.094590I
−4.03483 + 1.67732I −15.7065 − 1.9092I
u = −0.409777 − 0.900801I
a = −0.544341 + 1.119450I
b = −0.730677 + 1.094590I
−4.03483 − 1.67732I −15.7065 + 1.9092I
u = −0.657601 + 0.825266I
a = 0.601074 − 0.268176I
b = −0.357033 + 0.531973I
3.12416 − 2.18877I −5.69210 + 4.74067I
u = −0.657601 − 0.825266I
a = 0.601074 + 0.268176I
b = −0.357033 − 0.531973I
3.12416 + 2.18877I −5.69210 − 4.74067I
u = 0.302331 + 1.034790I
a = −0.637238 − 0.149825I
b = 0.950086 − 0.176237I
0.25466 + 6.20458I −14.8235 − 3.5089I
u = 0.302331 − 1.034790I
a = −0.637238 + 0.149825I
b = 0.950086 + 0.176237I
0.25466 − 6.20458I −14.8235 + 3.5089I
u = −0.331807 + 1.036480I
a = 0.21858 − 1.49669I
b = −0.28766 − 1.69564I
−4.71056 − 4.64876I −15.0367 + 4.9275I
u = −0.331807 − 1.036480I
a = 0.21858 + 1.49669I
b = −0.28766 + 1.69564I
−4.71056 + 4.64876I −15.0367 − 4.9275I
u = −0.874408
a = −0.824516
b = 0.134886
−3.51423 −6.86190
u = 0.317154 + 1.082840I
a = −0.574788 − 1.214640I
b = 0.06114 − 1.52733I
−3.95324 + 1.56546I −8.00000 + 0.I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317154 − 1.082840I
a = −0.574788 + 1.214640I
b = 0.06114 + 1.52733I
−3.95324 − 1.56546I −8.00000 + 0.I
u = −0.188677 + 0.809103I
a = 0.686531 + 0.487499I
b = −1.06188 + 1.56291I
3.95567 − 1.37596I −0.82626 − 3.55586I
u = −0.188677 − 0.809103I
a = 0.686531 − 0.487499I
b = −1.06188 − 1.56291I
3.95567 + 1.37596I −0.82626 + 3.55586I
u = 0.113083 + 0.798094I
a = −0.047789 + 0.770469I
b = 1.18245 + 2.09762I
1.57638 − 4.35308I −16.7694 + 3.0661I
u = 0.113083 − 0.798094I
a = −0.047789 − 0.770469I
b = 1.18245 − 2.09762I
1.57638 + 4.35308I −16.7694 − 3.0661I
u = 0.568179 + 1.064920I
a = 0.134359 − 0.780118I
b = 0.095548 − 1.119810I
−1.70449 + 2.54931I 0
u = 0.568179 − 1.064920I
a = 0.134359 + 0.780118I
b = 0.095548 + 1.119810I
−1.70449 − 2.54931I 0
u = 0.466980 + 1.200370I
a = −0.32410 − 1.49493I
b = −1.12190 − 2.07011I
−1.81978 + 7.59271I 0
u = 0.466980 − 1.200370I
a = −0.32410 + 1.49493I
b = −1.12190 + 2.07011I
−1.81978 − 7.59271I 0
u = −0.417071 + 1.236700I
a = 0.72424 − 1.41848I
b = 1.49790 − 1.90624I
−1.99856 − 4.69047I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.417071 − 1.236700I
a = 0.72424 + 1.41848I
b = 1.49790 + 1.90624I
−1.99856 + 4.69047I 0
u = 0.188229 + 0.655395I
a = 0.720166 − 0.397307I
b = 0.830114 + 0.485063I
−2.35382 + 0.82742I −15.8192 − 0.6411I
u = 0.188229 − 0.655395I
a = 0.720166 + 0.397307I
b = 0.830114 − 0.485063I
−2.35382 − 0.82742I −15.8192 + 0.6411I
u = 0.022708 + 0.633531I
a = −3.07327 + 1.11819I
b = −1.11126 + 1.58977I
3.36999 + 8.29380I −6.06255 − 6.83732I
u = 0.022708 − 0.633531I
a = −3.07327 − 1.11819I
b = −1.11126 − 1.58977I
3.36999 − 8.29380I −6.06255 + 6.83732I
u = −0.086889 + 0.626552I
a = 2.50876 + 0.84786I
b = 0.56171 + 1.56319I
5.04306 − 3.42296I −3.69821 + 1.80474I
u = −0.086889 − 0.626552I
a = 2.50876 − 0.84786I
b = 0.56171 − 1.56319I
5.04306 + 3.42296I −3.69821 − 1.80474I
u = 0.542734 + 0.300118I
a = 1.81316 + 1.01197I
b = 0.441570 − 0.678988I
1.11164 − 3.56856I −6.21674 + 4.42673I
u = 0.542734 − 0.300118I
a = 1.81316 − 1.01197I
b = 0.441570 + 0.678988I
1.11164 + 3.56856I −6.21674 − 4.42673I
u = −0.421374 + 1.348100I
a = 0.776685 − 0.793038I
b = 1.43231 − 1.20697I
−0.34046 − 9.79113I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421374 − 1.348100I
a = 0.776685 + 0.793038I
b = 1.43231 + 1.20697I
−0.34046 + 9.79113I 0
u = −0.49193 + 1.33074I
a = 0.012829 − 0.712139I
b = 0.20866 − 1.74798I
−7.41515 − 5.23834I 0
u = −0.49193 − 1.33074I
a = 0.012829 + 0.712139I
b = 0.20866 + 1.74798I
−7.41515 + 5.23834I 0
u = 0.50139 + 1.35961I
a = −0.476937 − 0.723090I
b = −1.04603 − 1.17966I
0.64916 + 4.85096I 0
u = 0.50139 − 1.35961I
a = −0.476937 + 0.723090I
b = −1.04603 + 1.17966I
0.64916 − 4.85096I 0
u = −0.094409 + 0.473427I
a = −3.73968 + 0.43889I
b = −1.030680 + 0.342171I
1.21017 + 1.96907I −8.16010 + 2.84355I
u = −0.094409 − 0.473427I
a = −3.73968 − 0.43889I
b = −1.030680 − 0.342171I
1.21017 − 1.96907I −8.16010 − 2.84355I
u = −1.52636 + 0.19413I
a = −0.099227 − 0.242342I
b = −0.088320 + 0.472941I
5.91001 − 3.70013I 0
u = −1.52636 − 0.19413I
a = −0.099227 + 0.242342I
b = −0.088320 − 0.472941I
5.91001 + 3.70013I 0
u = 1.54031 + 0.22352I
a = 0.233244 + 0.131215I
b = 0.006487 − 0.492983I
5.52803 + 2.16433I 0
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54031 − 0.22352I
a = 0.233244 − 0.131215I
b = 0.006487 + 0.492983I
5.52803 − 2.16433I 0
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
41
− 23u
40
+ ··· + 138u − 9)(u
171
+ 78u
170
+ ··· + 2521u + 49)
c
2
(u
41
+ 3u
40
+ ··· + 23u
2
− 3)(u
171
+ 4u
170
+ ··· + 111u + 7)
c
3
(u
41
− 7u
39
+ ··· − u + 1)
· (u
171
− u
170
+ ··· − 404430848u + 29671424)
c
4
(u
41
+ u
40
+ ··· + 16u
2
+ 1)(u
171
− 2u
170
+ ··· + 4671u + 9859)
c
5
(u
41
− 3u
40
+ ··· − 23u
2
+ 3)(u
171
+ 4u
170
+ ··· + 111u + 7)
c
6
(u
41
+ 4u
40
+ ··· + 4u − 1)(u
171
− 3u
170
+ ··· + 37835u + 2123)
c
7
(u
41
+ u
40
+ ··· − 7u − 1)(u
171
+ 2u
170
+ ··· − 528354u + 43591)
c
8
(u
41
− 8u
39
+ ··· + u − 1)(u
171
+ 5u
170
+ ··· + 6.11151 × 10
7
u + 5504449)
c
9
(u
41
− u
40
+ ··· + 7u − 1)
· (u
171
+ 8u
170
+ ··· − 25208926u + 28448137)
c
10
(u
41
+ 19u
40
+ ··· + 160u + 11)
· (u
171
+ 8u
170
+ ··· + 208397u + 48167)
c
11
(u
41
− u
40
+ ··· − 16u
2
− 1)(u
171
− 2u
170
+ ··· + 4671u + 9859)
c
12
(u
41
− u
40
+ ··· − 7u + 1)(u
171
+ 2u
170
+ ··· − 528354u + 43591)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
41
+ 5y
40
+ ··· − 414y −81)
· (y
171
+ 46y
170
+ ··· + 1499345y −2401)
c
2
, c
5
(y
41
− 23y
40
+ ··· + 138y −9)(y
171
− 78y
170
+ ··· + 2521y −49)
c
3
(y
41
− 14y
40
+ ··· − 5y −1)
· (y
171
+ 15y
170
+ ··· − 5219403641651200y −880393402187776)
c
4
, c
11
(y
41
+ 19y
40
+ ··· − 32y −1)
· (y
171
+ 92y
170
+ ··· − 778002993y −97199881)
c
6
(y
41
+ 24y
40
+ ··· − 2y −1)
· (y
171
+ 41y
170
+ ··· + 1410817697y −4507129)
c
7
, c
12
(y
41
+ 37y
40
+ ··· − 55y −1)
· (y
171
+ 126y
170
+ ··· − 157098337588y −1900175281)
c
8
(y
41
− 16y
40
+ ··· + 31y −1)
· (y
171
− 47y
170
+ ··· + 638582748630030y −30298958793601)
c
9
(y
41
+ 5y
40
+ ··· − 21y −1)
· (y
171
+ 46y
170
+ ··· − 25343801026808550y −809296498770769)
c
10
(y
41
+ 9y
40
+ ··· − 118y −121)
· (y
171
− 10y
170
+ ··· + 163308109881y −2320059889)
34
