12a
0046
(K12a
0046
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 11 6 1 12 8 10
Solving Sequence
8,12
11
4,7
3 6 10 1 2 9 5
c
11
c
7
c
3
c
6
c
10
c
12
c
1
c
9
c
5
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.02752 × 10
30
u
93
+ 2.82962 × 10
30
u
92
+ ··· + 7.01285 × 10
29
b + 2.68128 × 10
30
,
1.33287 × 10
30
u
93
− 5.41849 × 10
30
u
92
+ ··· + 2.33762 × 10
29
a − 3.96691 × 10
30
, u
94
− 5u
93
+ ··· − 15u + 1i
I
u
2
= h2au − u
2
+ b + 2a, u
2
a + a
2
− au + u
2
+ u − 1, u
3
+ u
2
− 1i
I
u
3
= h−u
4
+ b − 2, 2u
4
− u
3
+ a + u + 3, u
5
− u
4
+ u
2
+ u − 1i
I
u
4
= hu
2
+ b − u, −u
2
+ a − u, u
3
+ u
2
− 1i
* 4 irreducible components of dim
C
= 0, with total 108 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
= h−1.03 × 10
30
u
93
+ 2.83 × 10
30
u
92
+ · · · + 7.01 × 10
29
b + 2.68 ×
10
30
, 1.33 × 10
30
u
93
− 5.42 × 10
30
u
92
+ · · · + 2.34 × 10
29
a − 3.97 ×
10
30
, u
94
− 5u
93
+ · · · − 15u + 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−5.70183u
93
+ 23.1795u
92
+ ··· − 124.011u + 16.9699
1.46519u
93
− 4.03491u
92
+ ··· + 39.3234u − 3.82338
a
7
=
−u
−u
3
+ u
a
3
=
−2.89290u
93
+ 5.89251u
92
+ ··· − 52.1238u + 11.9968
−12.2961u
93
+ 52.5426u
92
+ ··· − 84.0089u + 4.39211
a
6
=
−6.77410u
93
+ 35.7202u
92
+ ··· − 163.016u + 15.4696
20.9419u
93
− 88.1661u
92
+ ··· + 226.524u − 15.8512
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
2
=
5.35996u
93
− 24.6779u
92
+ ··· + 130.166u − 14.0247
−9.43706u
93
+ 37.3806u
92
+ ··· − 111.393u + 8.46972
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
5
=
−1.23353u
93
+ 0.892677u
92
+ ··· − 10.5212u + 5.01394
−6.25844u
93
+ 27.0384u
92
+ ··· − 59.6741u + 3.69409
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.58579u
93
− 34.2762u
92
+ ··· + 276.933u − 31.2371
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
94
+ 47u
93
+ ··· + 2083u + 1
c
2
, c
4
u
94
− 9u
93
+ ··· + 37u + 1
c
3
, c
6
u
94
− 4u
93
+ ··· + 320u − 32
c
5
, c
8
u
94
+ 2u
93
+ ··· − 2560u − 512
c
7
, c
11
u
94
− 5u
93
+ ··· − 15u + 1
c
9
, c
10
, c
12
u
94
− 23u
93
+ ··· − 185u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
94
+ 9y
93
+ ··· − 4301459y + 1
c
2
, c
4
y
94
− 47y
93
+ ··· − 2083y + 1
c
3
, c
6
y
94
+ 42y
93
+ ··· − 37376y + 1024
c
5
, c
8
y
94
+ 56y
93
+ ··· + 3801088y + 262144
c
7
, c
11
y
94
− 23y
93
+ ··· − 185y + 1
c
9
, c
10
, c
12
y
94
+ 101y
93
+ ··· − 28969y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.905451 + 0.437078I
a = −0.38908 − 2.12552I
b = −1.55661 + 2.03416I
−2.95530 − 3.62965I 0
u = −0.905451 − 0.437078I
a = −0.38908 + 2.12552I
b = −1.55661 − 2.03416I
−2.95530 + 3.62965I 0
u = 0.998868 + 0.153287I
a = −0.34700 − 1.43569I
b = 0.933069 + 0.889689I
3.69183 − 0.90668I 0
u = 0.998868 − 0.153287I
a = −0.34700 + 1.43569I
b = 0.933069 − 0.889689I
3.69183 + 0.90668I 0
u = 0.885560 + 0.419384I
a = 0.739482 + 1.067380I
b = −1.14651 − 1.15035I
2.64492 + 6.49916I 0
u = 0.885560 − 0.419384I
a = 0.739482 − 1.067380I
b = −1.14651 + 1.15035I
2.64492 − 6.49916I 0
u = 0.913302 + 0.325477I
a = −0.70472 − 1.26351I
b = 1.10966 + 1.07964I
4.12929 + 1.39857I 0
u = 0.913302 − 0.325477I
a = −0.70472 + 1.26351I
b = 1.10966 − 1.07964I
4.12929 − 1.39857I 0
u = −0.954895 + 0.414756I
a = −0.025203 + 0.334361I
b = 1.332920 − 0.124333I
−2.18704 − 6.14689I 0
u = −0.954895 − 0.414756I
a = −0.025203 − 0.334361I
b = 1.332920 + 0.124333I
−2.18704 + 6.14689I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721866 + 0.754158I
a = 0.693424 − 0.277978I
b = −0.545353 − 0.989217I
−2.17526 − 1.45322I 0
u = −0.721866 − 0.754158I
a = 0.693424 + 0.277978I
b = −0.545353 + 0.989217I
−2.17526 + 1.45322I 0
u = 1.056890 + 0.104571I
a = 0.232763 + 1.345440I
b = −0.915683 − 0.763709I
1.69927 − 5.76809I 0
u = 1.056890 − 0.104571I
a = 0.232763 − 1.345440I
b = −0.915683 + 0.763709I
1.69927 + 5.76809I 0
u = −0.995318 + 0.375431I
a = 0.18189 + 1.71349I
b = 1.16693 − 1.59065I
2.38179 − 6.85574I 0
u = −0.995318 − 0.375431I
a = 0.18189 − 1.71349I
b = 1.16693 + 1.59065I
2.38179 + 6.85574I 0
u = −0.511330 + 0.782712I
a = −0.547011 + 0.562475I
b = 0.713250 + 0.726812I
−4.15606 − 4.95399I 0
u = −0.511330 − 0.782712I
a = −0.547011 − 0.562475I
b = 0.713250 − 0.726812I
−4.15606 + 4.95399I 0
u = 0.929009 + 0.068800I
a = −0.26626 − 1.43751I
b = −0.492725 + 0.646944I
−0.254266 − 0.867513I 0
u = 0.929009 − 0.068800I
a = −0.26626 + 1.43751I
b = −0.492725 − 0.646944I
−0.254266 + 0.867513I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823707 + 0.383516I
a = −0.041446 − 0.332414I
b = −1.142000 − 0.123519I
−0.67738 − 1.92321I 0
u = −0.823707 − 0.383516I
a = −0.041446 + 0.332414I
b = −1.142000 + 0.123519I
−0.67738 + 1.92321I 0
u = −1.036230 + 0.405152I
a = −0.04234 − 1.71265I
b = −1.23040 + 1.38676I
−0.10577 − 12.27470I 0
u = −1.036230 − 0.405152I
a = −0.04234 + 1.71265I
b = −1.23040 − 1.38676I
−0.10577 + 12.27470I 0
u = −0.859284 + 0.214626I
a = 0.548445 + 1.203540I
b = 0.64460 − 2.02449I
4.79944 − 3.38706I 0. + 9.66029I
u = −0.859284 − 0.214626I
a = 0.548445 − 1.203540I
b = 0.64460 + 2.02449I
4.79944 + 3.38706I 0. − 9.66029I
u = −0.878091 + 0.732966I
a = 2.13662 − 2.26977I
b = −4.27115 − 0.73401I
−4.29337 − 2.79203I 0
u = −0.878091 − 0.732966I
a = 2.13662 + 2.26977I
b = −4.27115 + 0.73401I
−4.29337 + 2.79203I 0
u = 0.792347 + 0.274736I
a = 0.600358 + 1.032710I
b = 0.263529 − 0.187085I
−0.12060 + 1.76624I 2.00000 − 5.30326I
u = 0.792347 − 0.274736I
a = 0.600358 − 1.032710I
b = 0.263529 + 0.187085I
−0.12060 − 1.76624I 2.00000 + 5.30326I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.995387 + 0.608742I
a = −0.063080 + 0.575346I
b = 1.46287 − 0.61224I
−2.64588 − 0.14652I 0
u = −0.995387 − 0.608742I
a = −0.063080 − 0.575346I
b = 1.46287 + 0.61224I
−2.64588 + 0.14652I 0
u = −0.844120 + 0.835558I
a = 1.108580 − 0.589162I
b = −1.15995 − 1.20057I
−3.06674 − 1.11761I 0
u = −0.844120 − 0.835558I
a = 1.108580 + 0.589162I
b = −1.15995 + 1.20057I
−3.06674 + 1.11761I 0
u = −0.964903 + 0.705690I
a = 0.079505 − 0.904415I
b = −1.75161 + 0.99325I
−1.44073 − 4.07182I 0
u = −0.964903 − 0.705690I
a = 0.079505 + 0.904415I
b = −1.75161 − 0.99325I
−1.44073 + 4.07182I 0
u = 0.884235 + 0.815291I
a = 0.997732 − 0.766176I
b = 1.20106 + 2.96128I
−1.221240 − 0.245856I 0
u = 0.884235 − 0.815291I
a = 0.997732 + 0.766176I
b = 1.20106 − 2.96128I
−1.221240 + 0.245856I 0
u = −0.227459 + 0.757503I
a = 1.90723 + 0.28691I
b = −1.249060 − 0.643882I
−2.75290 + 8.12923I −3.14725 − 5.96002I
u = −0.227459 − 0.757503I
a = 1.90723 − 0.28691I
b = −1.249060 + 0.643882I
−2.75290 − 8.12923I −3.14725 + 5.96002I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823780 + 0.888088I
a = 1.65148 − 0.04048I
b = −0.63909 + 2.70840I
−5.87040 − 4.86160I 0
u = 0.823780 − 0.888088I
a = 1.65148 + 0.04048I
b = −0.63909 − 2.70840I
−5.87040 + 4.86160I 0
u = −0.888709 + 0.828883I
a = −0.97034 + 1.31401I
b = 2.74854 − 0.53626I
−6.59016 − 1.87331I 0
u = −0.888709 − 0.828883I
a = −0.97034 − 1.31401I
b = 2.74854 + 0.53626I
−6.59016 + 1.87331I 0
u = −0.768651 + 0.153462I
a = −0.662957 − 0.821078I
b = −0.62346 + 2.12671I
4.22053 + 2.42602I 4.48189 + 9.29126I
u = −0.768651 − 0.153462I
a = −0.662957 + 0.821078I
b = −0.62346 − 2.12671I
4.22053 − 2.42602I 4.48189 − 9.29126I
u = 0.911045 + 0.807605I
a = −0.744831 + 1.036970I
b = −1.67892 − 2.96867I
−1.13789 + 6.32136I 0
u = 0.911045 − 0.807605I
a = −0.744831 − 1.036970I
b = −1.67892 + 2.96867I
−1.13789 − 6.32136I 0
u = 0.817206 + 0.911898I
a = −1.71283 − 0.11928I
b = 1.01533 − 2.55879I
−8.86590 − 10.56170I 0
u = 0.817206 − 0.911898I
a = −1.71283 + 0.11928I
b = 1.01533 + 2.55879I
−8.86590 + 10.56170I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845161 + 0.889434I
a = −0.288648 − 0.032497I
b = 0.104224 + 0.631601I
−10.59930 − 3.58899I 0
u = 0.845161 − 0.889434I
a = −0.288648 + 0.032497I
b = 0.104224 − 0.631601I
−10.59930 + 3.58899I 0
u = −0.913525 + 0.821468I
a = −1.23296 + 0.92411I
b = 1.62458 + 1.03417I
−6.51331 − 4.28654I 0
u = −0.913525 − 0.821468I
a = −1.23296 − 0.92411I
b = 1.62458 − 1.03417I
−6.51331 + 4.28654I 0
u = 0.873838 + 0.868456I
a = 0.240797 + 0.078349I
b = 0.061011 − 0.590277I
−8.40697 + 1.63722I 0
u = 0.873838 − 0.868456I
a = 0.240797 − 0.078349I
b = 0.061011 + 0.590277I
−8.40697 − 1.63722I 0
u = 0.860026 + 0.884880I
a = −1.88264 + 0.33095I
b = 0.51218 − 3.50291I
−11.31680 − 0.57038I 0
u = 0.860026 − 0.884880I
a = −1.88264 − 0.33095I
b = 0.51218 + 3.50291I
−11.31680 + 0.57038I 0
u = −0.865887 + 0.882160I
a = −0.996542 + 0.730783I
b = 1.20983 + 0.96608I
−5.55893 + 3.28453I 0
u = −0.865887 − 0.882160I
a = −0.996542 − 0.730783I
b = 1.20983 − 0.96608I
−5.55893 − 3.28453I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946485 + 0.806200I
a = 0.601050 − 1.153690I
b = −2.39169 + 0.76305I
−2.75258 − 5.01184I 0
u = −0.946485 − 0.806200I
a = 0.601050 + 1.153690I
b = −2.39169 − 0.76305I
−2.75258 + 5.01184I 0
u = −0.536657 + 0.519170I
a = 0.199660 − 0.585956I
b = −0.726972 − 0.579075I
−1.58168 − 1.49511I −1.20774 + 4.62157I
u = −0.536657 − 0.519170I
a = 0.199660 + 0.585956I
b = −0.726972 + 0.579075I
−1.58168 + 1.49511I −1.20774 − 4.62157I
u = 0.945080 + 0.838821I
a = 0.142467 + 0.191244I
b = 0.447571 − 0.324800I
−8.18097 + 4.69776I 0
u = 0.945080 − 0.838821I
a = 0.142467 − 0.191244I
b = 0.447571 + 0.324800I
−8.18097 − 4.69776I 0
u = −0.391118 + 0.616467I
a = 2.19814 + 0.27289I
b = −1.22053 − 1.25849I
−4.57237 − 0.27043I −5.36990 − 0.41408I
u = −0.391118 − 0.616467I
a = 2.19814 − 0.27289I
b = −1.22053 + 1.25849I
−4.57237 + 0.27043I −5.36990 + 0.41408I
u = −0.958623 + 0.842313I
a = −0.725274 + 1.015570I
b = 2.36009 − 0.57501I
−5.26401 − 9.67296I 0
u = −0.958623 − 0.842313I
a = −0.725274 − 1.015570I
b = 2.36009 + 0.57501I
−5.26401 + 9.67296I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.963009 + 0.840863I
a = 0.36986 − 1.89136I
b = 3.04124 + 2.99193I
−10.99000 + 6.96104I 0
u = 0.963009 − 0.840863I
a = 0.36986 + 1.89136I
b = 3.04124 − 2.99193I
−10.99000 − 6.96104I 0
u = 0.984748 + 0.822057I
a = −0.07028 + 1.64656I
b = −2.82195 − 2.36983I
−5.36286 + 11.19750I 0
u = 0.984748 − 0.822057I
a = −0.07028 − 1.64656I
b = −2.82195 + 2.36983I
−5.36286 − 11.19750I 0
u = 0.974104 + 0.834723I
a = −0.113786 − 0.235277I
b = −0.526723 + 0.214120I
−10.1908 + 9.9724I 0
u = 0.974104 − 0.834723I
a = −0.113786 + 0.235277I
b = −0.526723 − 0.214120I
−10.1908 − 9.9724I 0
u = −0.308065 + 0.638255I
a = −0.510667 + 0.784027I
b = 0.745034 + 0.663909I
−4.22284 + 2.28384I −5.40942 − 1.60159I
u = −0.308065 − 0.638255I
a = −0.510667 − 0.784027I
b = 0.745034 − 0.663909I
−4.22284 − 2.28384I −5.40942 + 1.60159I
u = 0.911762 + 0.918432I
a = −0.149456 + 0.035449I
b = 0.118572 + 0.297180I
−13.05620 + 3.87938I 0
u = 0.911762 − 0.918432I
a = −0.149456 − 0.035449I
b = 0.118572 − 0.297180I
−13.05620 − 3.87938I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000930 + 0.829713I
a = −0.09785 − 1.69655I
b = 2.99495 + 2.10759I
−8.2816 + 16.9931I 0
u = 1.000930 − 0.829713I
a = −0.09785 + 1.69655I
b = 2.99495 − 2.10759I
−8.2816 − 16.9931I 0
u = 0.430117 + 0.545073I
a = 1.23174 + 0.88326I
b = −0.297726 + 0.130654I
1.21330 − 2.82397I 1.38406 + 2.73602I
u = 0.430117 − 0.545073I
a = 1.23174 − 0.88326I
b = −0.297726 − 0.130654I
1.21330 + 2.82397I 1.38406 − 2.73602I
u = −0.201484 + 0.659185I
a = −1.98860 − 0.38825I
b = 1.034070 + 0.728447I
−0.11479 + 3.13185I −0.06207 − 2.62342I
u = −0.201484 − 0.659185I
a = −1.98860 + 0.38825I
b = 1.034070 − 0.728447I
−0.11479 − 3.13185I −0.06207 + 2.62342I
u = 0.671898 + 0.151886I
a = 2.07226 + 2.12966I
b = −1.39171 − 1.41963I
−0.854990 + 0.184345I 6.5747 − 15.0325I
u = 0.671898 − 0.151886I
a = 2.07226 − 2.12966I
b = −1.39171 + 1.41963I
−0.854990 − 0.184345I 6.5747 + 15.0325I
u = 0.957675 + 0.896988I
a = −0.0122210 − 0.1384930I
b = −0.284882 + 0.043144I
−12.91010 + 2.80229I 0
u = 0.957675 − 0.896988I
a = −0.0122210 + 0.1384930I
b = −0.284882 − 0.043144I
−12.91010 − 2.80229I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668467
a = −0.668479
b = 0.148148
0.907840 11.5600
u = 0.194109 + 0.511596I
a = −1.65256 − 0.97107I
b = 0.476294 + 0.186820I
1.99178 + 1.65996I 2.30944 − 4.12201I
u = 0.194109 − 0.511596I
a = −1.65256 + 0.97107I
b = 0.476294 − 0.186820I
1.99178 − 1.65996I 2.30944 + 4.12201I
u = 0.0766424
a = 7.27869
b = −0.661524
−1.20372 −8.99890
14
II. I
u
2
= h2au − u
2
+ b + 2a, u
2
a + a
2
− au + u
2
+ u − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
a
−2au + u
2
− 2a
a
7
=
−u
u
2
+ u − 1
a
3
=
−au + u
2
+ u − 1
−au − u
2
− 2a + 1
a
6
=
0
−u
2
a − au − u
2
− 2u
a
10
=
−u
2
+ 1
u
2
a
1
=
u
−u
2
− u + 1
a
2
=
−au + u
2
+ u − 1
−3u
2
− a − 2u + 1
a
9
=
0
u
a
5
=
0
−u
2
a − au − u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
a − 7au − 6u
2
− 9a + u + 5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
11
(u
3
+ u
2
− 1)
2
c
4
, c
7
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
c
6
, c
9
, c
10
(u
3
+ u
2
+ 2u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
7
c
11
(y
3
− y
2
+ 2y −1)
2
c
5
, c
8
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.447279 + 0.744862I
b = 1.21508 − 2.15605I
− 5.65624I 3.29784 + 4.97572I
u = −0.877439 + 0.744862I
a = −1.53980 + 1.30714I
b = 2.53980 + 0.66632I
−4.13758 − 2.82812I 11.29331 + 8.29280I
u = −0.877439 − 0.744862I
a = 0.447279 − 0.744862I
b = 1.21508 + 2.15605I
5.65624I 3.29784 − 4.97572I
u = −0.877439 − 0.744862I
a = −1.53980 − 1.30714I
b = 2.53980 − 0.66632I
−4.13758 + 2.82812I 11.29331 − 8.29280I
u = 0.754878
a = 0.092519 + 0.562280I
b = 0.24512 − 1.97346I
4.13758 + 2.82812I 0.90884 − 8.67250I
u = 0.754878
a = 0.092519 − 0.562280I
b = 0.24512 + 1.97346I
4.13758 − 2.82812I 0.90884 + 8.67250I
18
III. I
u
3
= h−u
4
+ b − 2, 2u
4
− u
3
+ a + u + 3, u
5
− u
4
+ u
2
+ u − 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−2u
4
+ u
3
− u − 3
u
4
+ 2
a
7
=
−u
−u
3
+ u
a
3
=
−2u
4
+ u
3
− u − 3
u
4
+ 2
a
6
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
2
=
−u
4
+ u
3
− u
2
− u − 2
2
a
9
=
u
3
u
4
− u
3
− u
2
+ 1
a
5
=
−u
4
+ u
2
− 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 18u
4
− 7u
3
− 7u
2
+ 18u + 27
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
6
u
5
c
4
(u + 1)
5
c
5
, c
9
, c
10
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
7
u
5
+ u
4
− u
2
+ u + 1
c
8
, c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
11
u
5
− u
4
+ u
2
+ u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
, c
8
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
7
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758138 + 0.584034I
a = −0.442614 + 1.051550I
b = 1.270390 − 0.413868I
−3.46474 − 2.21397I −3.79538 + 3.60694I
u = −0.758138 − 0.584034I
a = −0.442614 − 1.051550I
b = 1.270390 + 0.413868I
−3.46474 + 2.21397I −3.79538 − 3.60694I
u = 0.935538 + 0.903908I
a = 0.304213 + 0.337334I
b = −0.857040 + 0.196802I
−12.60320 + 3.33174I 2.32599 − 3.47010I
u = 0.935538 − 0.903908I
a = 0.304213 − 0.337334I
b = −0.857040 − 0.196802I
−12.60320 − 3.33174I 2.32599 + 3.47010I
u = 0.645200
a = −3.72320
b = 2.17329
−0.762751 36.9390
22
IV. I
u
4
= hu
2
+ b − u, −u
2
+ a − u, u
3
+ u
2
− 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
u
2
+ u
−u
2
+ u
a
7
=
−u
u
2
+ u − 1
a
3
=
u + 1
0
a
6
=
0
−u
2
+ 1
a
10
=
−u
2
+ 1
u
2
a
1
=
u
−u
2
− u + 1
a
2
=
u + 1
−u
2
− u + 1
a
9
=
0
u
a
5
=
0
−u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
− 3u + 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
u
3
− u
2
+ 2u − 1
c
2
, c
11
u
3
+ u
2
− 1
c
4
, c
7
u
3
− u
2
+ 1
c
5
, c
8
u
3
c
6
, c
9
, c
10
u
3
+ u
2
+ 2u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
7
c
11
y
3
− y
2
+ 2y −1
c
5
, c
8
y
3
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.662359 − 0.562280I
b = −1.09252 + 2.05200I
0 4.20216 + 0.37970I
u = −0.877439 − 0.744862I
a = −0.662359 + 0.562280I
b = −1.09252 − 2.05200I
0 4.20216 − 0.37970I
u = 0.754878
a = 1.32472
b = 0.185037
0 −1.40430
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)
3
(u
94
+ 47u
93
+ ··· + 2083u + 1)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)
3
(u
94
− 9u
93
+ ··· + 37u + 1)
c
3
u
5
(u
3
− u
2
+ 2u − 1)
3
(u
94
− 4u
93
+ ··· + 320u − 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)
3
(u
94
− 9u
93
+ ··· + 37u + 1)
c
5
u
9
(u
5
+ u
4
+ ··· + 3u + 1)(u
94
+ 2u
93
+ ··· − 2560u − 512)
c
6
u
5
(u
3
+ u
2
+ 2u + 1)
3
(u
94
− 4u
93
+ ··· + 320u − 32)
c
7
((u
3
− u
2
+ 1)
3
)(u
5
+ u
4
− u
2
+ u + 1)(u
94
− 5u
93
+ ··· − 15u + 1)
c
8
u
9
(u
5
− u
4
+ ··· + 3u − 1)(u
94
+ 2u
93
+ ··· − 2560u − 512)
c
9
, c
10
(u
3
+ u
2
+ 2u + 1)
3
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
94
− 23u
93
+ ··· − 185u + 1)
c
11
((u
3
+ u
2
− 1)
3
)(u
5
− u
4
+ u
2
+ u − 1)(u
94
− 5u
93
+ ··· − 15u + 1)
c
12
(u
3
− u
2
+ 2u − 1)
3
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
94
− 23u
93
+ ··· − 185u + 1)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
3
+ 3y
2
+ 2y −1)
3
(y
94
+ 9y
93
+ ··· − 4301459y + 1)
c
2
, c
4
((y −1)
5
)(y
3
− y
2
+ 2y −1)
3
(y
94
− 47y
93
+ ··· − 2083y + 1)
c
3
, c
6
y
5
(y
3
+ 3y
2
+ 2y −1)
3
(y
94
+ 42y
93
+ ··· − 37376y + 1024)
c
5
, c
8
y
9
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
94
+ 56y
93
+ ··· + 3801088y + 262144)
c
7
, c
11
(y
3
− y
2
+ 2y −1)
3
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
94
− 23y
93
+ ··· − 185y + 1)
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
3
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
94
+ 101y
93
+ ··· − 28969y + 1)
28
