12a
0111
(K12a
0111
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 12 4 7 6 1 9 10
Solving Sequence
4,7
8 9
3,12
6 10 1 11 5 2
c
7
c
8
c
3
c
6
c
9
c
12
c
11
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.82793 × 10
271
u
117
+ 1.79494 × 10
271
u
116
+ ··· + 1.57559 × 10
272
b − 2.36204 × 10
273
,
− 6.75801 × 10
271
u
117
− 1.31065 × 10
272
u
116
+ ··· + 1.57559 × 10
272
a − 1.75047 × 10
273
,
u
118
+ 2u
117
+ ··· + 160u + 32i
I
u
2
= h2u
2
+ b + u + 3, 7u
2
+ a + 3u + 12, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, 16v
4
+ 47v
3
+ 36v
2
+ 29b + 104v −5, v
5
+ 3v
4
+ 3v
3
+ 8v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 126 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
= h1.83 × 10
271
u
117
+ 1.79 × 10
271
u
116
+ · · · + 1.58 × 10
272
b − 2.36 ×
10
273
, −6.76 × 10
271
u
117
− 1.31 × 10
272
u
116
+ · · · + 1.58 × 10
272
a − 1.75 ×
10
273
, u
118
+ 2u
117
+ · · · + 160u + 32i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
12
=
0.428919u
117
+ 0.831847u
116
+ ··· + 72.9363u + 11.1100
−0.116015u
117
− 0.113922u
116
+ ··· + 53.2325u + 14.9914
a
6
=
0.151804u
117
+ 0.549454u
116
+ ··· + 138.561u + 28.8762
−0.0972105u
117
− 0.128968u
116
+ ··· + 27.0148u + 5.98614
a
10
=
0.446880u
117
+ 0.822605u
116
+ ··· + 2.30703u − 6.05829
0.0819943u
117
+ 0.0874611u
116
+ ··· − 60.6561u − 13.0649
a
1
=
0.381325u
117
+ 0.734164u
116
+ ··· + 16.2430u − 2.30564
0.0732515u
117
+ 0.0465062u
116
+ ··· − 69.4204u − 15.1813
a
11
=
0.410377u
117
+ 0.747830u
116
+ ··· + 32.7496u + 1.84294
−0.0763814u
117
− 0.0467982u
116
+ ··· + 60.6601u + 16.1046
a
5
=
0.161618u
117
+ 0.417138u
116
+ ··· + 78.0186u + 13.7872
−0.219707u
117
− 0.317027u
116
+ ··· + 61.7756u + 16.0928
a
2
=
−0.305156u
117
− 0.565775u
116
+ ··· + 3.95305u + 5.31050
−0.0281133u
117
+ 0.0595301u
116
+ ··· + 84.6108u + 17.6725
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.287760u
117
− 0.227055u
116
+ ··· + 36.3944u + 24.9413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
118
+ 65u
117
+ ··· + 172u + 1
c
2
, c
4
u
118
− 7u
117
+ ··· − 2u + 1
c
3
, c
7
u
118
+ 2u
117
+ ··· + 160u + 32
c
5
u
118
+ 4u
117
+ ··· + 8634757u + 591517
c
6
u
118
+ 67u
116
+ ··· + 196401u + 29189
c
8
u
118
− 36u
117
+ ··· − 20992u + 1024
c
9
u
118
− 9u
117
+ ··· + 2u − 1
c
10
, c
12
u
118
− 5u
117
+ ··· + 143u − 1
c
11
u
118
+ 20u
117
+ ··· + 156u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
118
− 17y
117
+ ··· − 21024y + 1
c
2
, c
4
y
118
− 65y
117
+ ··· − 172y + 1
c
3
, c
7
y
118
+ 36y
117
+ ··· + 20992y + 1024
c
5
y
118
+ 46y
117
+ ··· − 9372454336793y + 349892361289
c
6
y
118
+ 134y
117
+ ··· + 56845137931y + 851997721
c
8
y
118
+ 84y
117
+ ··· − 237633536y + 1048576
c
9
y
118
− 25y
117
+ ··· − 26y + 1
c
10
, c
12
y
118
− 91y
117
+ ··· − 21455y + 1
c
11
y
118
+ 24y
117
+ ··· − 6288y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728017 + 0.694463I
a = −0.225898 − 1.018600I
b = −0.669014 − 0.910213I
−1.43969 + 2.21556I 0
u = 0.728017 − 0.694463I
a = −0.225898 + 1.018600I
b = −0.669014 + 0.910213I
−1.43969 − 2.21556I 0
u = −0.619537 + 0.765048I
a = 1.032480 − 0.585042I
b = 0.571954 − 1.180190I
−1.23232 + 1.59626I 0
u = −0.619537 − 0.765048I
a = 1.032480 + 0.585042I
b = 0.571954 + 1.180190I
−1.23232 − 1.59626I 0
u = 0.298455 + 0.934841I
a = 0.22167 + 1.86730I
b = −0.263742 + 0.980521I
−1.47083 − 5.17351I 0
u = 0.298455 − 0.934841I
a = 0.22167 − 1.86730I
b = −0.263742 − 0.980521I
−1.47083 + 5.17351I 0
u = −0.198124 + 0.953787I
a = −1.251020 + 0.555836I
b = −0.12920 + 2.72726I
0.04031 + 2.55048I 0
u = −0.198124 − 0.953787I
a = −1.251020 − 0.555836I
b = −0.12920 − 2.72726I
0.04031 − 2.55048I 0
u = 0.068591 + 0.971611I
a = 0.927780 − 0.730731I
b = −0.679586 + 0.939233I
−5.08436 − 4.73741I 0
u = 0.068591 − 0.971611I
a = 0.927780 + 0.730731I
b = −0.679586 − 0.939233I
−5.08436 + 4.73741I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031110 + 0.197972I
a = 0.876376 + 1.073180I
b = 0.785779 + 0.981729I
−3.61891 + 7.05319I 0
u = 1.031110 − 0.197972I
a = 0.876376 − 1.073180I
b = 0.785779 − 0.981729I
−3.61891 − 7.05319I 0
u = −1.050710 + 0.063861I
a = 0.714156 + 0.906732I
b = 0.625408 + 0.821210I
−3.31472 + 2.51883I 0
u = −1.050710 − 0.063861I
a = 0.714156 − 0.906732I
b = 0.625408 − 0.821210I
−3.31472 − 2.51883I 0
u = 0.272135 + 1.025000I
a = −0.382449 − 0.790293I
b = 0.514576 + 0.246566I
3.78308 − 0.01802I 0
u = 0.272135 − 1.025000I
a = −0.382449 + 0.790293I
b = 0.514576 − 0.246566I
3.78308 + 0.01802I 0
u = 0.735517 + 0.778817I
a = 0.67775 + 1.79166I
b = −0.779920 + 1.015750I
−4.73869 + 0.40842I 0
u = 0.735517 − 0.778817I
a = 0.67775 − 1.79166I
b = −0.779920 − 1.015750I
−4.73869 − 0.40842I 0
u = −0.107153 + 1.069730I
a = −1.032680 − 0.179779I
b = 0.710939 + 0.496865I
4.36870 + 2.02817I 0
u = −0.107153 − 1.069730I
a = −1.032680 + 0.179779I
b = 0.710939 − 0.496865I
4.36870 − 2.02817I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781234 + 0.740647I
a = 0.169668 − 1.117780I
b = 0.084047 − 1.022770I
−10.10770 − 4.91047I 0
u = 0.781234 − 0.740647I
a = 0.169668 + 1.117780I
b = 0.084047 + 1.022770I
−10.10770 + 4.91047I 0
u = −0.073380 + 0.920134I
a = 0.155874 − 0.282788I
b = −0.05895 − 2.14310I
0.35506 + 1.51453I 0
u = −0.073380 − 0.920134I
a = 0.155874 + 0.282788I
b = −0.05895 + 2.14310I
0.35506 − 1.51453I 0
u = −0.149078 + 1.079460I
a = 0.258697 − 0.239907I
b = −0.901395 − 0.136742I
2.39623 + 2.35738I 0
u = −0.149078 − 1.079460I
a = 0.258697 + 0.239907I
b = −0.901395 + 0.136742I
2.39623 − 2.35738I 0
u = −0.774685 + 0.781985I
a = 0.84572 − 1.50885I
b = 0.76174 − 1.41524I
−10.59630 − 3.65695I 0
u = −0.774685 − 0.781985I
a = 0.84572 + 1.50885I
b = 0.76174 + 1.41524I
−10.59630 + 3.65695I 0
u = −0.671146 + 0.874204I
a = −2.62474 + 2.99523I
b = −0.00887 + 3.26729I
−2.69730 + 2.59523I 0
u = −0.671146 − 0.874204I
a = −2.62474 − 2.99523I
b = −0.00887 − 3.26729I
−2.69730 − 2.59523I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733283 + 0.829346I
a = 1.52905 + 1.73070I
b = −0.037826 + 0.672568I
−5.24563 − 0.71971I 0
u = 0.733283 − 0.829346I
a = 1.52905 − 1.73070I
b = −0.037826 − 0.672568I
−5.24563 + 0.71971I 0
u = 0.860621 + 0.704440I
a = 1.234330 + 0.491055I
b = 0.871934 + 0.917474I
−4.58238 + 2.28560I 0
u = 0.860621 − 0.704440I
a = 1.234330 − 0.491055I
b = 0.871934 − 0.917474I
−4.58238 − 2.28560I 0
u = 0.813787 + 0.761771I
a = −2.63907 − 3.89564I
b = 0.00134 − 3.29415I
−6.47446 + 1.37228I 0
u = 0.813787 − 0.761771I
a = −2.63907 + 3.89564I
b = 0.00134 + 3.29415I
−6.47446 − 1.37228I 0
u = −0.735658 + 0.847408I
a = −1.26954 + 1.97061I
b = 0.736755 + 0.913449I
−4.87783 + 3.64446I 0
u = −0.735658 − 0.847408I
a = −1.26954 − 1.97061I
b = 0.736755 − 0.913449I
−4.87783 − 3.64446I 0
u = 0.916744 + 0.664952I
a = 0.92856 + 1.42190I
b = 0.84338 + 1.32703I
−6.64707 + 7.57494I 0
u = 0.916744 − 0.664952I
a = 0.92856 − 1.42190I
b = 0.84338 − 1.32703I
−6.64707 − 7.57494I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.303072 + 1.095470I
a = −1.114940 − 0.401261I
b = 0.787439 − 0.614349I
3.47785 − 6.81881I 0
u = 0.303072 − 1.095470I
a = −1.114940 + 0.401261I
b = 0.787439 + 0.614349I
3.47785 + 6.81881I 0
u = −0.810779 + 0.816732I
a = −0.29853 − 1.80929I
b = 0.041662 − 0.742708I
−8.95504 + 0.66716I 0
u = −0.810779 − 0.816732I
a = −0.29853 + 1.80929I
b = 0.041662 + 0.742708I
−8.95504 − 0.66716I 0
u = −0.644423 + 0.956924I
a = 0.322850 − 1.317380I
b = −0.963527 − 0.777985I
−0.60803 + 3.39602I 0
u = −0.644423 − 0.956924I
a = 0.322850 + 1.317380I
b = −0.963527 + 0.777985I
−0.60803 − 3.39602I 0
u = 0.198711 + 0.822369I
a = 2.17685 + 0.54412I
b = 0.054593 + 0.191928I
−2.78527 − 1.67495I −10.83994 + 4.29836I
u = 0.198711 − 0.822369I
a = 2.17685 − 0.54412I
b = 0.054593 − 0.191928I
−2.78527 + 1.67495I −10.83994 − 4.29836I
u = −0.727212 + 0.897879I
a = −0.286605 + 1.174070I
b = −0.694174 + 1.013200I
−4.72140 + 1.92715I 0
u = −0.727212 − 0.897879I
a = −0.286605 − 1.174070I
b = −0.694174 − 1.013200I
−4.72140 − 1.92715I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.724796 + 0.910439I
a = −0.15404 + 1.86380I
b = −0.000985 + 0.833561I
−4.99704 − 4.83893I 0
u = 0.724796 − 0.910439I
a = −0.15404 − 1.86380I
b = −0.000985 − 0.833561I
−4.99704 + 4.83893I 0
u = −0.862419 + 0.782346I
a = 1.37781 − 1.98487I
b = −0.030325 − 0.784160I
−8.89092 − 3.50469I 0
u = −0.862419 − 0.782346I
a = 1.37781 + 1.98487I
b = −0.030325 + 0.784160I
−8.89092 + 3.50469I 0
u = −0.472880 + 1.066790I
a = −0.168184 + 0.711747I
b = 0.434418 − 0.055480I
2.15836 + 4.75591I 0
u = −0.472880 − 1.066790I
a = −0.168184 − 0.711747I
b = 0.434418 + 0.055480I
2.15836 − 4.75591I 0
u = −0.912938 + 0.730651I
a = −0.381024 + 0.994006I
b = −0.771448 + 0.900895I
−4.65732 − 6.45566I 0
u = −0.912938 − 0.730651I
a = −0.381024 − 0.994006I
b = −0.771448 − 0.900895I
−4.65732 + 6.45566I 0
u = −0.985084 + 0.643042I
a = 0.185249 + 0.910435I
b = 0.106274 + 0.813085I
−5.92496 + 1.10467I 0
u = −0.985084 − 0.643042I
a = 0.185249 − 0.910435I
b = 0.106274 − 0.813085I
−5.92496 − 1.10467I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776224 + 0.271739I
a = 0.098468 − 0.120546I
b = −0.334303 − 0.392446I
−0.309232 − 0.257103I −3.98318 + 1.23273I
u = −0.776224 − 0.271739I
a = 0.098468 + 0.120546I
b = −0.334303 + 0.392446I
−0.309232 + 0.257103I −3.98318 − 1.23273I
u = 0.711606 + 0.943046I
a = 1.135190 + 0.743815I
b = 0.85115 + 1.35114I
−4.23917 − 5.93059I 0
u = 0.711606 − 0.943046I
a = 1.135190 − 0.743815I
b = 0.85115 − 1.35114I
−4.23917 + 5.93059I 0
u = 0.794840 + 0.119506I
a = −0.093241 − 0.520824I
b = −0.552884 − 0.607003I
0.07573 + 2.96723I −4.49491 − 6.86660I
u = 0.794840 − 0.119506I
a = −0.093241 + 0.520824I
b = −0.552884 + 0.607003I
0.07573 − 2.96723I −4.49491 + 6.86660I
u = −0.733804 + 0.958544I
a = 1.16548 − 2.13975I
b = −0.87960 − 1.36956I
−10.05150 + 9.36822I 0
u = −0.733804 − 0.958544I
a = 1.16548 + 2.13975I
b = −0.87960 + 1.36956I
−10.05150 − 9.36822I 0
u = 0.699988 + 0.988293I
a = −1.05524 − 1.59575I
b = 0.808742 − 0.871999I
−0.57207 − 7.69896I 0
u = 0.699988 − 0.988293I
a = −1.05524 + 1.59575I
b = 0.808742 + 0.871999I
−0.57207 + 7.69896I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768945 + 0.945881I
a = 1.30420 − 1.61502I
b = −0.138008 − 0.677989I
−8.55225 + 5.26015I 0
u = −0.768945 − 0.945881I
a = 1.30420 + 1.61502I
b = −0.138008 + 0.677989I
−8.55225 − 5.26015I 0
u = −0.012968 + 0.778903I
a = 0.37988 − 1.44811I
b = −0.391327 − 1.002260I
−0.57888 + 1.37786I −5.42870 − 3.04988I
u = −0.012968 − 0.778903I
a = 0.37988 + 1.44811I
b = −0.391327 + 1.002260I
−0.57888 − 1.37786I −5.42870 + 3.04988I
u = 0.750545 + 0.978963I
a = −2.07453 − 3.15776I
b = 0.03855 − 3.28250I
−5.80691 − 7.24580I 0
u = 0.750545 − 0.978963I
a = −2.07453 + 3.15776I
b = 0.03855 + 3.28250I
−5.80691 + 7.24580I 0
u = −0.263851 + 1.206760I
a = 0.605867 − 0.435813I
b = −0.953748 − 0.946236I
1.35608 + 6.83479I 0
u = −0.263851 − 1.206760I
a = 0.605867 + 0.435813I
b = −0.953748 + 0.946236I
1.35608 − 6.83479I 0
u = 0.731217 + 1.003590I
a = −1.093900 − 0.586790I
b = −0.005942 − 0.817235I
−9.30286 − 0.82367I 0
u = 0.731217 − 1.003590I
a = −1.093900 + 0.586790I
b = −0.005942 + 0.817235I
−9.30286 + 0.82367I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001560 + 0.754879I
a = 0.99623 − 1.47644I
b = 0.91201 − 1.38050I
−9.7168 − 12.3498I 0
u = −1.001560 − 0.754879I
a = 0.99623 + 1.47644I
b = 0.91201 + 1.38050I
−9.7168 + 12.3498I 0
u = −0.782873 + 0.988188I
a = −0.11239 − 1.78523I
b = 0.058740 − 0.876478I
−8.24534 + 9.62498I 0
u = −0.782873 − 0.988188I
a = −0.11239 + 1.78523I
b = 0.058740 + 0.876478I
−8.24534 − 9.62498I 0
u = 0.748734 + 1.026430I
a = 0.05295 + 1.47708I
b = −1.11652 + 0.86908I
−3.58852 − 8.27941I 0
u = 0.748734 − 1.026430I
a = 0.05295 − 1.47708I
b = −1.11652 − 0.86908I
−3.58852 + 8.27941I 0
u = 0.417041 + 1.205090I
a = 0.697849 + 0.900322I
b = −1.00864 + 1.08129I
−0.01476 − 12.20380I 0
u = 0.417041 − 1.205090I
a = 0.697849 − 0.900322I
b = −1.00864 − 1.08129I
−0.01476 + 12.20380I 0
u = 1.038270 + 0.766425I
a = 0.031214 − 0.895863I
b = −0.050931 − 0.790657I
−8.92357 + 3.87422I 0
u = 1.038270 − 0.766425I
a = 0.031214 + 0.895863I
b = −0.050931 + 0.790657I
−8.92357 − 3.87422I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781779 + 1.035930I
a = −0.82707 + 1.67434I
b = 0.848359 + 0.911738I
−3.69576 + 12.71000I 0
u = −0.781779 − 1.035930I
a = −0.82707 − 1.67434I
b = 0.848359 − 0.911738I
−3.69576 − 12.71000I 0
u = 0.097281 + 1.296230I
a = −0.072148 + 0.145914I
b = −0.710978 − 0.546472I
2.08823 + 3.26218I 0
u = 0.097281 − 1.296230I
a = −0.072148 − 0.145914I
b = −0.710978 + 0.546472I
2.08823 − 3.26218I 0
u = 0.758282 + 1.060240I
a = 0.85871 + 2.01440I
b = −0.95522 + 1.37774I
−5.4260 − 13.7420I 0
u = 0.758282 − 1.060240I
a = 0.85871 − 2.01440I
b = −0.95522 − 1.37774I
−5.4260 + 13.7420I 0
u = 0.618650 + 0.289740I
a = 3.00042 + 3.23542I
b = 0.470090 + 0.832220I
−3.65232 + 1.86079I −14.7972 − 4.0060I
u = 0.618650 − 0.289740I
a = 3.00042 − 3.23542I
b = 0.470090 − 0.832220I
−3.65232 − 1.86079I −14.7972 + 4.0060I
u = −0.788712 + 1.087860I
a = −0.784033 + 0.707205I
b = 0.109225 + 0.734333I
−4.55475 + 5.33983I 0
u = −0.788712 − 1.087860I
a = −0.784033 − 0.707205I
b = 0.109225 − 0.734333I
−4.55475 − 5.33983I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826836 + 1.074140I
a = 0.71895 − 2.14852I
b = −0.97071 − 1.42794I
−8.6750 + 19.0243I 0
u = −0.826836 − 1.074140I
a = 0.71895 + 2.14852I
b = −0.97071 + 1.42794I
−8.6750 − 19.0243I 0
u = −0.069434 + 0.626267I
a = −1.37279 + 2.93741I
b = 0.383474 − 0.599280I
−1.32642 − 1.43233I 0.36847 + 1.82515I
u = −0.069434 − 0.626267I
a = −1.37279 − 2.93741I
b = 0.383474 + 0.599280I
−1.32642 + 1.43233I 0.36847 − 1.82515I
u = 0.847758 + 1.083770I
a = −0.757329 − 0.892513I
b = 0.189209 − 0.788907I
−7.87653 − 10.72040I 0
u = 0.847758 − 1.083770I
a = −0.757329 + 0.892513I
b = 0.189209 + 0.788907I
−7.87653 + 10.72040I 0
u = −0.315350 + 1.371310I
a = −0.305158 − 0.089656I
b = −0.437376 + 0.435733I
1.32897 + 2.54365I 0
u = −0.315350 − 1.371310I
a = −0.305158 + 0.089656I
b = −0.437376 − 0.435733I
1.32897 − 2.54365I 0
u = −0.560432
a = 1.03456
b = 0.310159
−1.12206 −9.21340
u = −0.551319 + 0.060131I
a = 5.68240 + 10.93550I
b = 1.80179 + 2.16150I
−2.75296 − 0.06291I −75.7664 + 36.6206I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.551319 − 0.060131I
a = 5.68240 − 10.93550I
b = 1.80179 − 2.16150I
−2.75296 + 0.06291I −75.7664 − 36.6206I
u = −0.092826 + 0.524249I
a = 0.651210 − 1.004270I
b = −0.333802 − 0.973972I
−0.66149 + 1.45734I −4.35229 − 4.44056I
u = −0.092826 − 0.524249I
a = 0.651210 + 1.004270I
b = −0.333802 + 0.973972I
−0.66149 − 1.45734I −4.35229 + 4.44056I
u = 0.283170 + 0.423021I
a = 1.75968 + 5.23956I
b = −0.659894 + 0.543547I
−4.15362 − 0.40167I −9.52783 + 9.14652I
u = 0.283170 − 0.423021I
a = 1.75968 − 5.23956I
b = −0.659894 − 0.543547I
−4.15362 + 0.40167I −9.52783 − 9.14652I
u = 0.022040 + 0.452263I
a = 0.51540 + 1.35269I
b = 0.429943 + 1.261700I
−7.21260 + 4.35579I 4.39844 − 1.29194I
u = 0.022040 − 0.452263I
a = 0.51540 − 1.35269I
b = 0.429943 − 1.261700I
−7.21260 − 4.35579I 4.39844 + 1.29194I
u = −0.287194
a = 5.64059
b = 1.00048
−2.30286 −1.96350
16
II. I
u
2
= h2u
2
+ b + u + 3, 7u
2
+ a + 3u + 12, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
3
=
u
−u
2
− u − 1
a
12
=
−7u
2
− 3u − 12
−2u
2
− u − 3
a
6
=
21u
2
+ 9u + 38
5u
2
+ 2u + 9
a
10
=
−7u
2
− 3u − 11
−u
2
− u − 3
a
1
=
−1
−u
2
a
11
=
−7u
2
− 3u − 12
−2u
2
− u − 3
a
5
=
1
0
a
2
=
−u
2
− 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −53u
2
− 32u − 104
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
u
3
+ 2u
2
− 3u + 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
u
3
− 3u
2
+ 2u + 1
c
10
(u − 1)
3
c
11
u
3
c
12
(u + 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
y
3
− 10y
2
+ 5y −1
c
8
, c
9
y
3
− 5y
2
+ 10y −1
c
10
, c
12
(y −1)
3
c
11
y
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.281752 + 0.014533I
b = 0.539798 − 0.182582I
1.37919 + 2.82812I −9.0124 − 12.0277I
u = −0.215080 − 1.307140I
a = 0.281752 − 0.014533I
b = 0.539798 + 0.182582I
1.37919 − 2.82812I −9.0124 + 12.0277I
u = −0.569840
a = −12.5635
b = −3.07960
−2.75839 −102.980
20
III.
I
v
1
= ha, 16v
4
+ 47v
3
+ 36v
2
+ 29b + 104v − 5, v
5
+ 3v
4
+ 3v
3
+ 8v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
12
=
0
−0.551724v
4
− 1.62069v
3
+ ··· − 3.58621v + 0.172414
a
6
=
1
−0.344828v
4
− 1.13793v
3
+ ··· − 3.24138v − 1.51724
a
10
=
−0.344828v
4
− 1.13793v
3
+ ··· − 3.24138v − 0.517241
v
4
+ 3v
3
+ 3v
2
+ 8v + 1
a
1
=
−0.655172v
4
− 1.86207v
3
+ ··· − 4.75862v − 0.482759
v
4
+ 3v
3
+ 3v
2
+ 8v + 1
a
11
=
0.551724v
4
+ 1.62069v
3
+ ··· + 3.58621v − 0.172414
−0.551724v
4
− 1.62069v
3
+ ··· − 3.58621v + 0.172414
a
5
=
0.655172v
4
+ 1.86207v
3
+ ··· + 4.75862v + 0.482759
−v
4
− 3v
3
− 3v
2
− 8v − 1
a
2
=
−0.655172v
4
− 1.86207v
3
+ ··· − 3.75862v − 0.482759
v
4
+ 3v
3
+ 3v
2
+ 8v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
65
29
v
4
+
142
29
v
3
+
81
29
v
2
+
437
29
v −
613
29
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
6
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
9
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
5
c
3
, c
7
, c
8
y
5
c
5
, c
10
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
6
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.01014 + 1.59703I
a = 0
b = −0.339110 + 0.822375I
−1.97403 − 1.53058I −13.4575 + 4.4032I
v = −0.01014 − 1.59703I
a = 0
b = −0.339110 − 0.822375I
−1.97403 + 1.53058I −13.4575 − 4.4032I
v = −0.043806 + 0.365575I
a = 0
b = 0.455697 − 1.200150I
−7.51750 − 4.40083I −22.0438 + 5.2094I
v = −0.043806 − 0.365575I
a = 0
b = 0.455697 + 1.200150I
−7.51750 + 4.40083I −22.0438 − 5.2094I
v = −2.89210
a = 0
b = 0.766826
−4.04602 −2.99730
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)(u
118
+ 65u
117
+ ··· + 172u + 1)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)(u
118
− 7u
117
+ ··· − 2u + 1)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
118
+ 2u
117
+ ··· + 160u + 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)(u
118
− 7u
117
+ ··· − 2u + 1)
c
5
(u
3
+ 2u
2
− 3u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
118
+ 4u
117
+ ··· + 8634757u + 591517)
c
6
(u
3
+ 2u
2
− 3u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
118
+ 67u
116
+ ··· + 196401u + 29189)
c
7
u
5
(u
3
+ u
2
+ 2u + 1)(u
118
+ 2u
117
+ ··· + 160u + 32)
c
8
u
5
(u
3
− 3u
2
+ 2u + 1)(u
118
− 36u
117
+ ··· − 20992u + 1024)
c
9
(u
3
− 3u
2
+ 2u + 1)(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
118
− 9u
117
+ ··· + 2u − 1)
c
10
((u − 1)
3
)(u
5
+ u
4
+ ··· + u − 1)(u
118
− 5u
117
+ ··· + 143u − 1)
c
11
u
3
(u
5
+ u
4
+ ··· + u + 1)(u
118
+ 20u
117
+ ··· + 156u + 8)
c
12
((u + 1)
3
)(u
5
− u
4
+ ··· + u + 1)(u
118
− 5u
117
+ ··· + 143u − 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
5
)(y
3
+ 3y
2
+ 2y − 1)(y
118
− 17y
117
+ ··· − 21024y + 1)
c
2
, c
4
((y − 1)
5
)(y
3
− y
2
+ 2y − 1)(y
118
− 65y
117
+ ··· − 172y + 1)
c
3
, c
7
y
5
(y
3
+ 3y
2
+ 2y − 1)(y
118
+ 36y
117
+ ··· + 20992y + 1024)
c
5
(y
3
− 10y
2
+ 5y − 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
118
+ 46y
117
+ ··· − 9372454336793y + 349892361289)
c
6
(y
3
− 10y
2
+ 5y − 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
· (y
118
+ 134y
117
+ ··· + 56845137931y + 851997721)
c
8
y
5
(y
3
− 5y
2
+ 10y − 1)(y
118
+ 84y
117
+ ··· − 2.37634 × 10
8
y + 1048576)
c
9
(y
3
− 5y
2
+ 10y − 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
118
− 25y
117
+ ··· − 26y + 1)
c
10
, c
12
(y − 1)
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
118
− 91y
117
+ ··· − 21455y + 1)
c
11
y
3
(y
5
+ 3y
4
+ ··· − y − 1)(y
118
+ 24y
117
+ ··· − 6288y + 64)
26
