12a
0224
(K12a
0224
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 12 5 8 1 4 10
Solving Sequence
5,8
9
10,12
1 4 7 3 11 6 2
c
8
c
9
c
12
c
4
c
7
c
3
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.54139 × 10
211
u
118
− 1.77953 × 10
212
u
117
+ ··· + 1.16640 × 10
212
b + 2.45569 × 10
210
,
1.48602 × 10
212
u
118
− 2.52384 × 10
212
u
117
+ ··· + 1.16640 × 10
212
a − 2.66943 × 10
212
, u
119
− 2u
118
+ ··· + 4u − 1i
I
u
2
= h−2u
3
− 10u
2
+ 13b − 7u − 19, −7u
3
− 9u
2
+ 13a − 18u − 21, u
4
+ u
3
+ 3u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 123 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
= h5.54 × 10
211
u
118
− 1.78 × 10
212
u
117
+ · · · + 1.17 × 10
212
b + 2.46 ×
10
210
, 1.49 × 10
212
u
118
− 2.52 × 10
212
u
117
+ · · · + 1.17 × 10
212
a − 2.67 ×
10
212
, u
119
− 2u
118
+ · · · + 4u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
12
=
−1.27402u
118
+ 2.16379u
117
+ ··· + 3.90194u + 2.28861
−0.475087u
118
+ 1.52566u
117
+ ··· + 3.68582u − 0.0210536
a
1
=
−1.05425u
118
+ 1.73753u
117
+ ··· + 2.83349u + 1.51971
−0.511788u
118
+ 1.44255u
117
+ ··· + 3.26316u + 0.148729
a
4
=
u
u
3
+ u
a
7
=
5.78938u
118
− 9.05492u
117
+ ··· − 16.0766u + 1.50354
2.96804u
118
− 7.67244u
117
+ ··· − 18.0668u + 4.40843
a
3
=
0.800386u
118
− 0.654146u
117
+ ··· − 2.68625u + 1.50085
1.52874u
118
− 2.03781u
117
+ ··· − 4.20547u + 1.56993
a
11
=
−1.24679u
118
+ 2.17866u
117
+ ··· + 4.01135u + 2.22723
−0.409852u
118
+ 1.43273u
117
+ ··· + 3.54515u − 0.0131086
a
6
=
−4.27793u
118
+ 6.86729u
117
+ ··· + 26.0602u − 4.12891
−2.27112u
118
+ 6.74915u
117
+ ··· + 21.1757u − 5.07591
a
2
=
0.0164683u
118
+ 0.631381u
117
+ ··· + 3.64517u + 0.716005
−0.625567u
118
+ 1.59469u
117
+ ··· + 0.143061u + 0.960630
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.20464u
118
− 9.79230u
117
+ ··· − 12.0561u − 5.30921
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 60u
118
+ ··· − 4u − 1
c
2
, c
6
u
119
− 2u
118
+ ··· + 2u − 1
c
3
u
119
+ 2u
118
+ ··· − 391360u − 162248
c
4
, c
8
u
119
+ 2u
118
+ ··· + 4u + 1
c
5
13(13u
119
+ 45u
118
+ ··· − 9.53716 × 10
7
u + 8.13301 × 10
7
)
c
7
13(13u
119
+ 72u
118
+ ··· + 3.83586 × 10
7
u + 1.67631 × 10
7
)
c
9
u
119
− 48u
118
+ ··· − 4u + 1
c
10
, c
12
u
119
− 5u
118
+ ··· + 4638u + 169
c
11
u
119
− 5u
118
+ ··· − 3016u + 2704
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 120y
117
+ ··· + 8y −1
c
2
, c
6
y
119
+ 60y
118
+ ··· − 4y −1
c
3
y
119
− 60y
118
+ ··· − 1006938781552y −26324413504
c
4
, c
8
y
119
+ 48y
118
+ ··· − 4y −1
c
5
169(169y
119
+ 20465y
118
+ ··· − 3.94300 × 10
17
y −6.61458 × 10
15
)
c
7
169
· (169y
119
+ 1134y
118
+ ··· + 560619390409464y −281003063817316)
c
9
y
119
+ 48y
118
+ ··· − 112y −1
c
10
, c
12
y
119
− 93y
118
+ ··· + 1876286y −28561
c
11
y
119
+ 27y
118
+ ··· − 531184576y −7311616
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.539418 + 0.840998I
a = −1.41285 − 3.92453I
b = 2.86930 − 3.88516I
−1.82418 − 1.97603I 0
u = 0.539418 − 0.840998I
a = −1.41285 + 3.92453I
b = 2.86930 + 3.88516I
−1.82418 + 1.97603I 0
u = 0.046971 + 1.018560I
a = −0.028457 − 0.767848I
b = −0.679310 + 1.026440I
0.75162 + 6.45433I 0
u = 0.046971 − 1.018560I
a = −0.028457 + 0.767848I
b = −0.679310 − 1.026440I
0.75162 − 6.45433I 0
u = −0.078413 + 1.020000I
a = 0.003241 + 0.649226I
b = −0.534367 − 0.951411I
3.26046 − 1.73121I 0
u = −0.078413 − 1.020000I
a = 0.003241 − 0.649226I
b = −0.534367 + 0.951411I
3.26046 + 1.73121I 0
u = −0.659946 + 0.783354I
a = 1.283510 − 0.311392I
b = 0.969241 + 0.277435I
−5.03562 + 0.41103I 0
u = −0.659946 − 0.783354I
a = 1.283510 + 0.311392I
b = 0.969241 − 0.277435I
−5.03562 − 0.41103I 0
u = 0.673685 + 0.775129I
a = 1.55336 + 0.38532I
b = 1.037470 − 0.181769I
−8.13975 + 3.86403I 0
u = 0.673685 − 0.775129I
a = 1.55336 − 0.38532I
b = 1.037470 + 0.181769I
−8.13975 − 3.86403I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671736 + 0.796619I
a = 1.240250 + 0.644710I
b = 0.855354 − 0.170542I
−8.40527 − 4.37677I 0
u = 0.671736 − 0.796619I
a = 1.240250 − 0.644710I
b = 0.855354 + 0.170542I
−8.40527 + 4.37677I 0
u = −0.608259 + 0.726692I
a = 1.55701 + 0.53379I
b = 1.251790 + 0.275028I
−3.42582 − 0.69701I 0
u = −0.608259 − 0.726692I
a = 1.55701 − 0.53379I
b = 1.251790 − 0.275028I
−3.42582 + 0.69701I 0
u = 0.559945 + 0.891958I
a = −2.93671 + 0.94418I
b = −1.96748 − 2.48153I
−1.62898 − 2.41378I 0
u = 0.559945 − 0.891958I
a = −2.93671 − 0.94418I
b = −1.96748 + 2.48153I
−1.62898 + 2.41378I 0
u = −0.633152 + 0.845568I
a = −0.148666 − 0.555779I
b = 0.252806 + 0.751615I
−4.67693 + 2.47706I 0
u = −0.633152 − 0.845568I
a = −0.148666 + 0.555779I
b = 0.252806 − 0.751615I
−4.67693 − 2.47706I 0
u = −0.446454 + 0.824660I
a = 5.44391 − 1.11040I
b = 1.60652 − 4.51876I
−4.00299 − 1.55704I 0
u = −0.446454 − 0.824660I
a = 5.44391 + 1.11040I
b = 1.60652 + 4.51876I
−4.00299 + 1.55704I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069950 + 0.934961I
a = 0.312469 − 0.726574I
b = −0.673000 + 0.632241I
−0.626086 − 1.186890I 0
u = 0.069950 − 0.934961I
a = 0.312469 + 0.726574I
b = −0.673000 − 0.632241I
−0.626086 + 1.186890I 0
u = 0.917495 + 0.542434I
a = −1.25859 + 0.96564I
b = −1.49694 + 0.80766I
−9.6630 + 13.1992I 0
u = 0.917495 − 0.542434I
a = −1.25859 − 0.96564I
b = −1.49694 − 0.80766I
−9.6630 − 13.1992I 0
u = −0.922448 + 0.546566I
a = −1.17166 − 0.90511I
b = −1.42673 − 0.77297I
−6.80262 − 7.99479I 0
u = −0.922448 − 0.546566I
a = −1.17166 + 0.90511I
b = −1.42673 + 0.77297I
−6.80262 + 7.99479I 0
u = 0.930348 + 0.539182I
a = −1.22943 + 0.74279I
b = −1.45164 + 0.64689I
−11.52010 + 4.26179I 0
u = 0.930348 − 0.539182I
a = −1.22943 − 0.74279I
b = −1.45164 − 0.64689I
−11.52010 − 4.26179I 0
u = −0.974458 + 0.464052I
a = −0.767249 + 0.225407I
b = −1.016070 + 0.066000I
−9.08388 + 8.22471I 0
u = −0.974458 − 0.464052I
a = −0.767249 − 0.225407I
b = −1.016070 − 0.066000I
−9.08388 − 8.22471I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550074 + 0.933763I
a = 0.14546 − 1.56145I
b = −1.17975 − 0.97383I
−2.72220 − 1.73214I 0
u = −0.550074 − 0.933763I
a = 0.14546 + 1.56145I
b = −1.17975 + 0.97383I
−2.72220 + 1.73214I 0
u = −0.551834 + 0.943079I
a = −0.79925 − 2.16152I
b = −2.09153 − 0.35978I
−3.33941 + 5.68580I 0
u = −0.551834 − 0.943079I
a = −0.79925 + 2.16152I
b = −2.09153 + 0.35978I
−3.33941 − 5.68580I 0
u = 0.659514 + 0.622337I
a = 1.72648 − 0.86511I
b = 0.923703 − 0.477948I
−5.12870 − 0.71737I 0
u = 0.659514 − 0.622337I
a = 1.72648 + 0.86511I
b = 0.923703 + 0.477948I
−5.12870 + 0.71737I 0
u = 0.533310 + 0.955795I
a = −0.355768 + 1.171140I
b = −1.059370 + 0.421671I
−0.16207 − 2.47699I 0
u = 0.533310 − 0.955795I
a = −0.355768 − 1.171140I
b = −1.059370 − 0.421671I
−0.16207 + 2.47699I 0
u = −0.973549 + 0.502306I
a = −0.925732 − 0.061551I
b = −1.155010 − 0.152766I
−11.15970 − 0.90036I 0
u = −0.973549 − 0.502306I
a = −0.925732 + 0.061551I
b = −1.155010 + 0.152766I
−11.15970 + 0.90036I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130607 + 1.092120I
a = −0.134163 + 0.411423I
b = −0.144643 − 0.954492I
4.94213 − 0.22183I 0
u = −0.130607 − 1.092120I
a = −0.134163 − 0.411423I
b = −0.144643 + 0.954492I
4.94213 + 0.22183I 0
u = 0.682031 + 0.587060I
a = 1.59450 − 1.08081I
b = 0.774323 − 0.632613I
−4.10775 + 7.30854I 0
u = 0.682031 − 0.587060I
a = 1.59450 + 1.08081I
b = 0.774323 + 0.632613I
−4.10775 − 7.30854I 0
u = 0.994202 + 0.476764I
a = −0.713312 − 0.073664I
b = −0.978129 + 0.056427I
−6.20252 − 2.86568I 0
u = 0.994202 − 0.476764I
a = −0.713312 + 0.073664I
b = −0.978129 − 0.056427I
−6.20252 + 2.86568I 0
u = −0.948881 + 0.578795I
a = −0.737186 − 0.750921I
b = −1.083840 − 0.714353I
−3.26565 − 5.72258I 0
u = −0.948881 − 0.578795I
a = −0.737186 + 0.750921I
b = −1.083840 + 0.714353I
−3.26565 + 5.72258I 0
u = 0.663407 + 0.892584I
a = −0.70152 + 1.69641I
b = −0.523674 − 0.243591I
−8.11332 − 0.79069I 0
u = 0.663407 − 0.892584I
a = −0.70152 − 1.69641I
b = −0.523674 + 0.243591I
−8.11332 + 0.79069I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.653196 + 0.902505I
a = −0.96221 − 1.58214I
b = −0.673782 + 0.386392I
−4.67219 + 4.69161I 0
u = −0.653196 − 0.902505I
a = −0.96221 + 1.58214I
b = −0.673782 − 0.386392I
−4.67219 − 4.69161I 0
u = −0.613693 + 0.933505I
a = −1.46824 − 1.31363I
b = −1.142650 + 0.651183I
−2.79223 + 5.53654I 0
u = −0.613693 − 0.933505I
a = −1.46824 + 1.31363I
b = −1.142650 − 0.651183I
−2.79223 − 5.53654I 0
u = −0.658134 + 0.582283I
a = 1.52930 + 0.95183I
b = 0.732852 + 0.515230I
−1.37744 − 2.68961I 0
u = −0.658134 − 0.582283I
a = 1.52930 − 0.95183I
b = 0.732852 − 0.515230I
−1.37744 + 2.68961I 0
u = 0.662513 + 0.909459I
a = −1.03375 + 1.78951I
b = −0.765897 − 0.257992I
−7.73252 − 9.03670I 0
u = 0.662513 − 0.909459I
a = −1.03375 − 1.78951I
b = −0.765897 + 0.257992I
−7.73252 + 9.03670I 0
u = 0.987963 + 0.581470I
a = −0.596782 + 0.532091I
b = −0.940516 + 0.566068I
−2.98815 + 0.27290I 0
u = 0.987963 − 0.581470I
a = −0.596782 − 0.532091I
b = −0.940516 − 0.566068I
−2.98815 − 0.27290I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351471 + 0.773470I
a = 2.58714 − 1.56388I
b = −0.30248 − 2.06274I
−3.60723 + 5.96757I 0
u = −0.351471 − 0.773470I
a = 2.58714 + 1.56388I
b = −0.30248 + 2.06274I
−3.60723 − 5.96757I 0
u = 0.153792 + 1.146450I
a = −0.197319 − 0.303202I
b = 0.084898 + 0.871312I
4.36424 − 4.50432I 0
u = 0.153792 − 1.146450I
a = −0.197319 + 0.303202I
b = 0.084898 − 0.871312I
4.36424 + 4.50432I 0
u = 0.428182 + 0.707297I
a = 2.25893 + 0.55909I
b = 0.55178 + 1.36307I
−1.00838 − 1.74591I 0
u = 0.428182 − 0.707297I
a = 2.25893 − 0.55909I
b = 0.55178 − 1.36307I
−1.00838 + 1.74591I 0
u = 0.364581 + 0.735982I
a = 0.980469 + 0.160216I
b = −0.057859 + 0.579273I
0.01215 − 1.54922I 0
u = 0.364581 − 0.735982I
a = 0.980469 − 0.160216I
b = −0.057859 − 0.579273I
0.01215 + 1.54922I 0
u = 0.630700 + 0.997407I
a = −1.87823 + 0.89275I
b = −1.085260 − 0.620294I
−4.02362 − 4.33336I 0
u = 0.630700 − 0.997407I
a = −1.87823 − 0.89275I
b = −1.085260 + 0.620294I
−4.02362 + 4.33336I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570892 + 1.041270I
a = −1.090840 + 0.298866I
b = −0.607006 − 0.322725I
1.77634 − 2.48623I 0
u = 0.570892 − 1.041270I
a = −1.090840 − 0.298866I
b = −0.607006 + 0.322725I
1.77634 + 2.48623I 0
u = −0.626255 + 1.012710I
a = −1.85586 − 0.63971I
b = −0.977706 + 0.667269I
−0.12752 + 7.72535I 0
u = −0.626255 − 1.012710I
a = −1.85586 + 0.63971I
b = −0.977706 − 0.667269I
−0.12752 − 7.72535I 0
u = −0.599316 + 1.030510I
a = −1.45023 − 0.37860I
b = −0.747793 + 0.523187I
1.99991 + 6.77961I 0
u = −0.599316 − 1.030510I
a = −1.45023 + 0.37860I
b = −0.747793 − 0.523187I
1.99991 − 6.77961I 0
u = 0.635102 + 1.014540I
a = −2.01018 + 0.62700I
b = −1.012350 − 0.736958I
−2.86181 − 12.42930I 0
u = 0.635102 − 1.014540I
a = −2.01018 − 0.62700I
b = −1.012350 + 0.736958I
−2.86181 + 12.42930I 0
u = −0.608097 + 0.485373I
a = 1.122160 + 0.734555I
b = 0.347130 + 0.332291I
0.49419 − 1.95496I 0
u = −0.608097 − 0.485373I
a = 1.122160 − 0.734555I
b = 0.347130 − 0.332291I
0.49419 + 1.95496I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071841 + 1.265180I
a = −0.355437 + 0.135357I
b = 0.886169 − 0.725281I
−2.70501 + 11.17610I 0
u = −0.071841 − 1.265180I
a = −0.355437 − 0.135357I
b = 0.886169 + 0.725281I
−2.70501 − 11.17610I 0
u = 0.087038 + 1.275070I
a = −0.327605 − 0.135550I
b = 0.780458 + 0.645595I
0.26047 − 5.97490I 0
u = 0.087038 − 1.275070I
a = −0.327605 + 0.135550I
b = 0.780458 − 0.645595I
0.26047 + 5.97490I 0
u = −0.067606 + 1.303270I
a = −0.321966 + 0.090369I
b = 0.870196 − 0.448726I
−4.44384 + 2.05586I 0
u = −0.067606 − 1.303270I
a = −0.321966 − 0.090369I
b = 0.870196 + 0.448726I
−4.44384 − 2.05586I 0
u = 0.701980 + 1.107930I
a = 1.65747 − 0.94084I
b = 1.55337 + 1.05580I
−7.9282 − 19.1536I 0
u = 0.701980 − 1.107930I
a = 1.65747 + 0.94084I
b = 1.55337 − 1.05580I
−7.9282 + 19.1536I 0
u = −0.430980 + 0.536340I
a = 2.05565 − 1.34242I
b = 0.327938 − 1.261390I
−3.62566 + 6.02987I −6.64015 − 6.08277I
u = −0.430980 − 0.536340I
a = 2.05565 + 1.34242I
b = 0.327938 + 1.261390I
−3.62566 − 6.02987I −6.64015 + 6.08277I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705292 + 1.107790I
a = 1.58262 + 0.88581I
b = 1.47278 − 1.03154I
−5.0786 + 13.9740I 0
u = −0.705292 − 1.107790I
a = 1.58262 − 0.88581I
b = 1.47278 + 1.03154I
−5.0786 − 13.9740I 0
u = 0.604663 + 0.318299I
a = 0.757036 − 0.480378I
b = 0.020954 − 0.223471I
−0.04814 − 2.08809I −0.78344 + 4.16869I
u = 0.604663 − 0.318299I
a = 0.757036 + 0.480378I
b = 0.020954 + 0.223471I
−0.04814 + 2.08809I −0.78344 − 4.16869I
u = −0.722645 + 1.101000I
a = 1.36579 + 0.56182I
b = 1.12117 − 1.04638I
−1.64257 + 11.82940I 0
u = −0.722645 − 1.101000I
a = 1.36579 − 0.56182I
b = 1.12117 + 1.04638I
−1.64257 − 11.82940I 0
u = 0.706409 + 1.113310I
a = 1.46286 − 0.98081I
b = 1.47651 + 0.89383I
−9.7571 − 10.2648I 0
u = 0.706409 − 1.113310I
a = 1.46286 + 0.98081I
b = 1.47651 − 0.89383I
−9.7571 + 10.2648I 0
u = 0.738011 + 1.104240I
a = 1.162980 − 0.466020I
b = 0.945749 + 0.947625I
−1.36081 − 6.52452I 0
u = 0.738011 − 1.104240I
a = 1.162980 + 0.466020I
b = 0.945749 − 0.947625I
−1.36081 + 6.52452I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.037590 + 0.666994I
a = 1.34528 + 0.72369I
b = −0.355360 + 0.201184I
0.22453 − 1.54530I 1.17875 + 5.54371I
u = 0.037590 − 0.666994I
a = 1.34528 − 0.72369I
b = −0.355360 − 0.201184I
0.22453 + 1.54530I 1.17875 − 5.54371I
u = −0.723615 + 1.144220I
a = 0.758451 + 0.855169I
b = 1.019340 − 0.459558I
−9.20080 + 7.07762I 0
u = −0.723615 − 1.144220I
a = 0.758451 − 0.855169I
b = 1.019340 + 0.459558I
−9.20080 − 7.07762I 0
u = 0.291072 + 0.557749I
a = 2.10548 + 1.04899I
b = 0.170539 + 0.954018I
−0.99783 − 1.71399I −3.04526 + 3.23022I
u = 0.291072 − 0.557749I
a = 2.10548 − 1.04899I
b = 0.170539 − 0.954018I
−0.99783 + 1.71399I −3.04526 − 3.23022I
u = 0.742996 + 1.167790I
a = 0.551376 − 0.625292I
b = 0.755847 + 0.427035I
−4.10574 − 3.43456I 0
u = 0.742996 − 1.167790I
a = 0.551376 + 0.625292I
b = 0.755847 − 0.427035I
−4.10574 + 3.43456I 0
u = −0.719081 + 1.183370I
a = 0.364011 + 0.735086I
b = 0.743183 − 0.244699I
−6.89898 − 2.04706I 0
u = −0.719081 − 1.183370I
a = 0.364011 − 0.735086I
b = 0.743183 + 0.244699I
−6.89898 + 2.04706I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.359766 + 0.405439I
a = 2.54808 − 1.18763I
b = 0.664409 − 1.001360I
−4.28515 − 1.65584I −8.74963 + 1.62245I
u = −0.359766 − 0.405439I
a = 2.54808 + 1.18763I
b = 0.664409 + 1.001360I
−4.28515 + 1.65584I −8.74963 − 1.62245I
u = 0.08688 + 1.57899I
a = −0.159136 − 0.031227I
b = 0.409318 + 0.066953I
5.08219 − 3.21414I 0
u = 0.08688 − 1.57899I
a = −0.159136 + 0.031227I
b = 0.409318 − 0.066953I
5.08219 + 3.21414I 0
u = −0.377517 + 0.035731I
a = 3.80534 − 0.17960I
b = 1.63596 − 0.13954I
−5.66161 + 3.95732I −6.96836 − 3.31121I
u = −0.377517 − 0.035731I
a = 3.80534 + 0.17960I
b = 1.63596 + 0.13954I
−5.66161 − 3.95732I −6.96836 + 3.31121I
u = 0.321909
a = 3.57094
b = 1.45256
−2.65593 −2.13400
u = 0.233250 + 0.182366I
a = 3.07453 + 0.43541I
b = 1.062060 + 0.348490I
−2.08724 − 0.78753I −7.27534 − 2.81901I
u = 0.233250 − 0.182366I
a = 3.07453 − 0.43541I
b = 1.062060 − 0.348490I
−2.08724 + 0.78753I −7.27534 + 2.81901I
16
II. I
u
2
=
h−2u
3
−10u
2
+13b−7u−19, −7u
3
−9u
2
+13a−18u−21, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
12
=
0.538462u
3
+ 0.692308u
2
+ 1.38462u + 1.61538
0.153846u
3
+ 0.769231u
2
+ 0.538462u + 1.46154
a
1
=
0.538462u
3
− 0.307692u
2
+ 1.38462u + 0.615385
0.153846u
3
− 0.230769u
2
+ 0.538462u + 1.46154
a
4
=
u
u
3
+ u
a
7
=
−0.644970u
3
− 0.994083u
2
− 1.75740u − 1.01183
−0.118343u
3
− 0.668639u
2
− 0.414201u − 1.66272
a
3
=
0.449704u
3
− 0.0591716u
2
+ 0.573964u + 0.118343
0.183432u
3
− 0.313609u
2
− 0.857988u − 0.372781
a
11
=
0.538462u
3
+ 0.692308u
2
+ 1.38462u + 1.61538
0.153846u
3
+ 0.769231u
2
+ 0.538462u + 1.46154
a
6
=
−0.0473373u
3
− 0.467456u
2
− 0.165680u − 1.06509
0.349112u
3
− 0.177515u
2
+ 1.72189u − 0.644970
a
2
=
1.04734u
3
+ 0.467456u
2
+ 2.16568u + 1.06509
0.650888u
3
+ 1.17751u
2
+ 1.27811u + 1.64497
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2907
169
u
3
−
3927
169
u
2
−
4682
169
u −
1948
169
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
+ u
3
+ 5u
2
− u + 2
c
5
13(13u
4
− 16u
3
+ 7u
2
− u + 1)
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
13(13u
4
− 23u
3
+ 9u + 2)
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
10
(u − 1)
4
c
11
u
4
c
12
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
5
169(169y
4
− 74y
3
+ 43y
2
+ 13y + 1)
c
7
169(169y
4
− 529y
3
+ 466y
2
− 81y + 4)
c
9
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
10
, c
12
(y −1)
4
c
11
y
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 1.129280 + 0.482208I
b = 1.208620 − 0.018695I
−1.85594 + 1.41510I −2.41540 − 6.57837I
u = −0.395123 − 0.506844I
a = 1.129280 − 0.482208I
b = 1.208620 + 0.018695I
−1.85594 − 1.41510I −2.41540 + 6.57837I
u = −0.10488 + 1.55249I
a = 0.216875 − 0.063104I
b = −0.324008 + 0.017675I
5.14581 + 3.16396I 34.1047 + 28.0396I
u = −0.10488 − 1.55249I
a = 0.216875 + 0.063104I
b = −0.324008 − 0.017675I
5.14581 − 3.16396I 34.1047 − 28.0396I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
119
+ 60u
118
+ ··· − 4u − 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
119
− 2u
118
+ ··· + 2u − 1)
c
3
(u
4
+ u
3
+ 5u
2
− u + 2)(u
119
+ 2u
118
+ ··· − 391360u − 162248)
c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
119
+ 2u
118
+ ··· + 4u + 1)
c
5
169(13u
4
− 16u
3
+ 7u
2
− u + 1)
· (13u
119
+ 45u
118
+ ··· − 95371633u + 81330053)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
119
− 2u
118
+ ··· + 2u − 1)
c
7
169(13u
4
− 23u
3
+ 9u + 2)
· (13u
119
+ 72u
118
+ ··· + 38358566u + 16763146)
c
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
119
+ 2u
118
+ ··· + 4u + 1)
c
9
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
119
− 48u
118
+ ··· − 4u + 1)
c
10
((u − 1)
4
)(u
119
− 5u
118
+ ··· + 4638u + 169)
c
11
u
4
(u
119
− 5u
118
+ ··· − 3016u + 2704)
c
12
((u + 1)
4
)(u
119
− 5u
118
+ ··· + 4638u + 169)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
119
+ 120y
117
+ ··· + 8y −1)
c
2
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
119
+ 60y
118
+ ··· − 4y −1)
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
119
− 60y
118
+ ··· − 1006938781552y −26324413504)
c
4
, c
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
119
+ 48y
118
+ ··· − 4y −1)
c
5
28561(169y
4
− 74y
3
+ 43y
2
+ 13y + 1)
· (169y
119
+ 2.05 × 10
4
y
118
+ ··· − 3.94 × 10
17
y −6.61 × 10
15
)
c
7
28561(169y
4
− 529y
3
+ 466y
2
− 81y + 4)
· (169y
119
+ 1134y
118
+ ··· + 560619390409464y −281003063817316)
c
9
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)(y
119
+ 48y
118
+ ··· − 112y −1)
c
10
, c
12
((y −1)
4
)(y
119
− 93y
118
+ ··· + 1876286y −28561)
c
11
y
4
(y
119
+ 27y
118
+ ··· − 5.31185 × 10
8
y −7311616)
22
