11a
168
(K11a
168
)
A knot diagram
1
Linearized knot diagam
6 1 11 8 2 10 5 4 3 7 9
Solving Sequence
6,10
7
2,11
1 3 5 8 4 9
c
6
c
10
c
1
c
2
c
5
c
7
c
4
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.78806 × 10
130
u
65
− 3.53692 × 10
130
u
64
+ ··· + 1.19375 × 10
131
b − 9.79607 × 10
131
,
− 1.13631 × 10
131
u
65
+ 6.95957 × 10
131
u
64
+ ··· + 2.74563 × 10
132
a − 8.44042 × 10
133
,
u
66
+ 3u
65
+ ··· − 49u + 23i
I
u
2
= hu
13
+ u
12
− 7u
11
− 7u
10
+ 19u
9
+ 21u
8
− 26u
7
− 35u
6
+ 19u
5
+ 33u
4
− 4u
3
− 18u
2
+ b − u + 4,
u
13
+ 2u
12
− 5u
11
− 12u
10
+ 7u
9
+ 28u
8
+ 2u
7
− 33u
6
− 14u
5
+ 20u
4
+ 16u
3
− 5u
2
+ a − 5u,
u
14
+ 2u
13
− 5u
12
− 12u
11
+ 7u
10
+ 28u
9
+ 2u
8
− 33u
7
− 13u
6
+ 21u
5
+ 14u
4
− 7u
3
− 6u
2
+ u + 1i
I
u
3
= h−u
5
+ 2u
4
+ u
3
− 2u
2
+ b − u, −u
5
+ 2u
4
+ a − u,
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 9u
5
+ 4u
4
+ 5u
3
− u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 90 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−1.79 × 10
130
u
65
− 3.54 × 10
130
u
64
+ · · · + 1.19 × 10
131
b − 9.80 ×
10
131
, −1.14 × 10
131
u
65
+ 6.96 × 10
131
u
64
+ · · · + 2.75 × 10
132
a − 8.44 ×
10
133
, u
66
+ 3u
65
+ · · · − 49u + 23i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
2
=
0.0413863u
65
− 0.253478u
64
+ ··· − 71.6967u + 30.7413
0.149785u
65
+ 0.296286u
64
+ ··· − 25.4119u + 8.20610
a
11
=
−u
−u
3
+ u
a
1
=
−0.108398u
65
− 0.549764u
64
+ ··· − 46.2848u + 22.5351
0.149785u
65
+ 0.296286u
64
+ ··· − 25.4119u + 8.20610
a
3
=
−0.265019u
65
− 0.684530u
64
+ ··· + 16.5444u − 1.80031
0.0970785u
65
+ 0.246976u
64
+ ··· − 17.2639u + 5.68359
a
5
=
0.0633462u
65
+ 0.131815u
64
+ ··· + 22.7802u − 6.63331
0.0144495u
65
+ 0.0765866u
64
+ ··· + 23.6745u − 8.68302
a
8
=
0.241521u
65
+ 0.174805u
64
+ ··· − 90.4271u + 35.3903
0.0842047u
65
+ 0.187816u
64
+ ··· − 24.7015u + 6.71251
a
4
=
−0.352721u
65
− 0.894904u
64
+ ··· + 18.6230u − 2.09481
0.119566u
65
+ 0.307098u
64
+ ··· − 14.7416u + 4.76525
a
9
=
−0.204510u
65
− 0.292070u
64
+ ··· + 36.4550u − 17.5683
0.00530887u
65
+ 0.0353219u
64
+ ··· + 5.95418u − 2.01143
a
9
=
−0.204510u
65
− 0.292070u
64
+ ··· + 36.4550u − 17.5683
0.00530887u
65
+ 0.0353219u
64
+ ··· + 5.95418u − 2.01143
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.39895u
65
+ 3.59121u
64
+ ··· − 107.584u + 25.1145
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
66
+ 5u
65
+ ··· + 70u + 28
c
2
u
66
+ 27u
65
+ ··· + 5684u + 784
c
3
u
66
+ 7u
65
+ ··· − 293u + 131
c
4
, c
7
, c
8
u
66
− 2u
65
+ ··· − 20u + 1
c
6
, c
10
u
66
+ 3u
65
+ ··· − 49u + 23
c
9
u
66
+ 2u
64
+ ··· + 24u + 1
c
11
u
66
+ 5u
65
+ ··· + 3276u + 667
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
66
+ 27y
65
+ ··· + 5684y + 784
c
2
y
66
+ 27y
65
+ ··· + 5306896y + 614656
c
3
y
66
− 15y
65
+ ··· − 380599y + 17161
c
4
, c
7
, c
8
y
66
+ 72y
65
+ ··· − 2y + 1
c
6
, c
10
y
66
− 33y
65
+ ··· − 12015y + 529
c
9
y
66
+ 4y
65
+ ··· − 30y + 1
c
11
y
66
− 15y
65
+ ··· − 11892756y + 444889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163567 + 0.974073I
a = 0.696136 − 0.268743I
b = −0.580597 − 1.004650I
1.17857 + 6.31445I 0. − 8.26296I
u = 0.163567 − 0.974073I
a = 0.696136 + 0.268743I
b = −0.580597 + 1.004650I
1.17857 − 6.31445I 0. + 8.26296I
u = −0.910079 + 0.369691I
a = 0.303793 − 0.056648I
b = −0.458628 + 0.318939I
−1.48654 + 0.69916I −4.61313 − 2.12935I
u = −0.910079 − 0.369691I
a = 0.303793 + 0.056648I
b = −0.458628 − 0.318939I
−1.48654 − 0.69916I −4.61313 + 2.12935I
u = 0.975903 + 0.320029I
a = −0.65293 − 2.09713I
b = 0.603233 − 1.184400I
−1.41728 − 5.05455I 0. + 12.20236I
u = 0.975903 − 0.320029I
a = −0.65293 + 2.09713I
b = 0.603233 + 1.184400I
−1.41728 + 5.05455I 0. − 12.20236I
u = −0.881923 + 0.307874I
a = −0.200444 + 0.477752I
b = 0.744898 − 0.630242I
0.032145 + 0.573668I 0. − 4.06060I
u = −0.881923 − 0.307874I
a = −0.200444 − 0.477752I
b = 0.744898 + 0.630242I
0.032145 − 0.573668I 0. + 4.06060I
u = −0.950720 + 0.502350I
a = −0.877967 + 0.026202I
b = −1.016380 + 0.270524I
6.72384 − 0.00894I 0
u = −0.950720 − 0.502350I
a = −0.877967 − 0.026202I
b = −1.016380 − 0.270524I
6.72384 + 0.00894I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.895747 + 0.113324I
a = −0.210467 − 0.615238I
b = 0.723006 − 0.613380I
0.35093 − 2.50495I 1.76854 + 6.87309I
u = 0.895747 − 0.113324I
a = −0.210467 + 0.615238I
b = 0.723006 + 0.613380I
0.35093 + 2.50495I 1.76854 − 6.87309I
u = 0.513355 + 0.969879I
a = −0.554489 − 0.295569I
b = 0.061422 + 0.772480I
3.81529 − 4.03349I 0
u = 0.513355 − 0.969879I
a = −0.554489 + 0.295569I
b = 0.061422 − 0.772480I
3.81529 + 4.03349I 0
u = −1.003490 + 0.462245I
a = −1.38592 + 1.18971I
b = 0.658324 + 1.027690I
−1.18063 + 5.94761I 0
u = −1.003490 − 0.462245I
a = −1.38592 − 1.18971I
b = 0.658324 − 1.027690I
−1.18063 − 5.94761I 0
u = 0.213343 + 0.781690I
a = 1.040630 + 0.205621I
b = −0.630515 + 0.547682I
2.50610 + 1.55549I 4.46271 − 2.30891I
u = 0.213343 − 0.781690I
a = 1.040630 − 0.205621I
b = −0.630515 − 0.547682I
2.50610 − 1.55549I 4.46271 + 2.30891I
u = −0.435912 + 0.662170I
a = 0.380983 + 0.238349I
b = −0.160229 + 0.802581I
−1.40850 + 1.04300I −5.70485 − 4.49521I
u = −0.435912 − 0.662170I
a = 0.380983 − 0.238349I
b = −0.160229 − 0.802581I
−1.40850 − 1.04300I −5.70485 + 4.49521I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.142840 + 0.408088I
a = 0.12099 − 2.00122I
b = −0.017416 − 1.388480I
−0.42442 + 7.17415I 0
u = −1.142840 − 0.408088I
a = 0.12099 + 2.00122I
b = −0.017416 + 1.388480I
−0.42442 − 7.17415I 0
u = 1.120610 + 0.507476I
a = −0.213239 + 0.187929I
b = −0.870327 − 0.488823I
−0.11868 − 6.20190I 0
u = 1.120610 − 0.507476I
a = −0.213239 − 0.187929I
b = −0.870327 + 0.488823I
−0.11868 + 6.20190I 0
u = 0.348013 + 0.685297I
a = 0.385405 + 0.184638I
b = −0.782208 + 0.911468I
8.00774 − 2.72139I 5.67340 + 3.59670I
u = 0.348013 − 0.685297I
a = 0.385405 − 0.184638I
b = −0.782208 − 0.911468I
8.00774 + 2.72139I 5.67340 − 3.59670I
u = 1.174490 + 0.439061I
a = 0.55437 + 2.35095I
b = −0.581613 + 0.937637I
5.38489 − 7.07352I 0
u = 1.174490 − 0.439061I
a = 0.55437 − 2.35095I
b = −0.581613 − 0.937637I
5.38489 + 7.07352I 0
u = 1.082830 + 0.650499I
a = −0.763412 − 0.125255I
b = −0.584235 − 0.734442I
6.02312 − 2.42646I 0
u = 1.082830 − 0.650499I
a = −0.763412 + 0.125255I
b = −0.584235 + 0.734442I
6.02312 + 2.42646I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.240570 + 0.249436I
a = −0.25707 − 1.89384I
b = −0.025398 − 1.232230I
−6.29461 − 3.96507I 0
u = 1.240570 − 0.249436I
a = −0.25707 + 1.89384I
b = −0.025398 + 1.232230I
−6.29461 + 3.96507I 0
u = −0.456533 + 1.193620I
a = −0.479732 + 0.721690I
b = 0.787442 + 0.623044I
9.11482 − 3.60155I 0
u = −0.456533 − 1.193620I
a = −0.479732 − 0.721690I
b = 0.787442 − 0.623044I
9.11482 + 3.60155I 0
u = 0.970943 + 0.846933I
a = −0.110406 − 0.251793I
b = 0.601898 + 0.133589I
3.63388 − 3.20673I 0
u = 0.970943 − 0.846933I
a = −0.110406 + 0.251793I
b = 0.601898 − 0.133589I
3.63388 + 3.20673I 0
u = −1.233540 + 0.392626I
a = 0.21257 − 2.00569I
b = −0.71720 − 1.24384I
3.82726 + 6.26660I 0
u = −1.233540 − 0.392626I
a = 0.21257 + 2.00569I
b = −0.71720 + 1.24384I
3.82726 − 6.26660I 0
u = −1.317410 + 0.143765I
a = 0.58844 − 1.71642I
b = 0.100771 − 0.992542I
−4.86658 + 0.02437I 0
u = −1.317410 − 0.143765I
a = 0.58844 + 1.71642I
b = 0.100771 + 0.992542I
−4.86658 − 0.02437I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599634 + 0.293642I
a = −0.360866 − 1.059790I
b = −1.107300 − 0.801620I
7.97540 + 3.77535I 12.7373 − 9.7511I
u = −0.599634 − 0.293642I
a = −0.360866 + 1.059790I
b = −1.107300 + 0.801620I
7.97540 − 3.77535I 12.7373 + 9.7511I
u = 1.189390 + 0.620718I
a = −0.11891 + 1.45206I
b = 0.333461 + 1.110410I
0.1230110 + 0.0150349I 0
u = 1.189390 − 0.620718I
a = −0.11891 − 1.45206I
b = 0.333461 − 1.110410I
0.1230110 − 0.0150349I 0
u = 1.229960 + 0.588843I
a = 0.98305 + 1.56765I
b = −0.665256 + 1.110210I
−1.99580 − 11.89200I 0
u = 1.229960 − 0.588843I
a = 0.98305 − 1.56765I
b = −0.665256 − 1.110210I
−1.99580 + 11.89200I 0
u = 0.626363 + 0.088665I
a = 2.69216 − 3.52949I
b = −0.309304 − 0.848107I
3.63938 − 2.52827I −1.147337 − 0.754292I
u = 0.626363 − 0.088665I
a = 2.69216 + 3.52949I
b = −0.309304 + 0.848107I
3.63938 + 2.52827I −1.147337 + 0.754292I
u = −1.218200 + 0.688747I
a = 0.95882 − 1.32677I
b = −0.514831 − 1.018630I
−3.18756 + 4.76965I 0
u = −1.218200 − 0.688747I
a = 0.95882 + 1.32677I
b = −0.514831 + 1.018630I
−3.18756 − 4.76965I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582346 + 0.119440I
a = 0.65201 + 3.57882I
b = −0.423495 + 1.216100I
2.04523 − 4.42740I 0.06553 + 3.55579I
u = −0.582346 − 0.119440I
a = 0.65201 − 3.57882I
b = −0.423495 − 1.216100I
2.04523 + 4.42740I 0.06553 − 3.55579I
u = −1.214820 + 0.714561I
a = 0.338561 + 0.013564I
b = 0.986535 − 0.471169I
6.64257 + 10.26800I 0
u = −1.214820 − 0.714561I
a = 0.338561 − 0.013564I
b = 0.986535 + 0.471169I
6.64257 − 10.26800I 0
u = −0.29930 + 1.39073I
a = −0.274401 − 0.646909I
b = 0.664803 − 1.023810I
7.89254 − 9.07916I 0
u = −0.29930 − 1.39073I
a = −0.274401 + 0.646909I
b = 0.664803 + 1.023810I
7.89254 + 9.07916I 0
u = 0.477375 + 0.237133I
a = 1.096490 − 0.505493I
b = 0.681358 + 0.179083I
1.48045 + 0.06659I 8.57715 + 1.33589I
u = 0.477375 − 0.237133I
a = 1.096490 + 0.505493I
b = 0.681358 − 0.179083I
1.48045 − 0.06659I 8.57715 − 1.33589I
u = −1.51195 + 0.21374I
a = 0.104633 + 1.369450I
b = −0.342184 + 0.961816I
−4.43757 − 1.23820I 0
u = −1.51195 − 0.21374I
a = 0.104633 − 1.369450I
b = −0.342184 − 0.961816I
−4.43757 + 1.23820I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34952 + 0.73556I
a = −0.72074 + 1.63019I
b = 0.695108 + 1.158380I
4.5173 + 16.3689I 0
u = −1.34952 − 0.73556I
a = −0.72074 − 1.63019I
b = 0.695108 − 1.158380I
4.5173 − 16.3689I 0
u = 1.13836 + 1.03918I
a = −0.99274 − 1.43051I
b = 0.496265 − 1.089620I
1.16169 − 7.37354I 0
u = 1.13836 − 1.03918I
a = −0.99274 + 1.43051I
b = 0.496265 + 1.089620I
1.16169 + 7.37354I 0
u = 0.247407 + 0.342006I
a = 1.23861 − 0.86436I
b = −0.851416 − 0.882734I
8.18428 + 3.39136I 6.60752 + 1.70089I
u = 0.247407 − 0.342006I
a = 1.23861 + 0.86436I
b = −0.851416 + 0.882734I
8.18428 − 3.39136I 6.60752 − 1.70089I
11
II.
I
u
2
= hu
13
+ u
12
+ · · · + b + 4, u
13
+ 2u
12
+ · · · + a − 5u, u
14
+ 2u
13
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
2
=
−u
13
− 2u
12
+ ··· + 5u
2
+ 5u
−u
13
− u
12
+ ··· + u − 4
a
11
=
−u
−u
3
+ u
a
1
=
−u
12
− 2u
11
+ ··· + 4u + 4
−u
13
− u
12
+ ··· + u − 4
a
3
=
u
13
+ u
12
+ ··· + 5u + 4
−4u
13
− 4u
12
+ ··· + 51u
2
− 10
a
5
=
2u
13
+ 4u
12
+ ··· − 8u
2
+ 3
4u
13
+ 7u
12
+ ··· − 6u + 4
a
8
=
2u
13
+ 3u
12
+ ··· − 4u + 2
−u
12
− u
11
+ ··· + 5u − 1
a
4
=
u
11
+ 2u
10
+ ··· + 6u + 1
−3u
13
− 3u
12
+ ··· − u − 8
a
9
=
u
12
+ 2u
11
+ ··· − 6u − 5
u
13
+ u
12
+ ··· − 20u
2
+ 5
a
9
=
u
12
+ 2u
11
+ ··· − 6u − 5
u
13
+ u
12
+ ··· − 20u
2
+ 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
13
− 9u
12
+ 20u
11
+ 56u
10
− 28u
9
− 137u
8
− 11u
7
+ 169u
6
+
61u
5
− 113u
4
− 60u
3
+ 42u
2
+ 22u − 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· + 4u
2
+ 1
c
2
u
14
+ 7u
13
+ ··· + 8u + 1
c
3
u
14
+ 2u
11
− 2u
10
− u
9
− u
8
− 2u
7
+ 4u
6
+ 2u
5
− 2u
3
− u + 1
c
4
u
14
− u
13
+ ··· + 4u
2
+ 1
c
5
u
14
+ u
13
+ ··· + 4u
2
+ 1
c
6
u
14
+ 2u
13
+ ··· + u + 1
c
7
, c
8
u
14
+ u
13
+ ··· + 4u
2
+ 1
c
9
u
14
+ u
13
+ 2u
11
− 2u
9
+ 4u
8
+ 2u
7
− u
6
+ u
5
− 2u
4
− 2u
3
+ 1
c
10
u
14
− 2u
13
+ ··· − u + 1
c
11
u
14
− 4u
12
+ ··· − 6u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 8y + 1
c
2
y
14
+ 7y
13
+ ··· + 4y + 1
c
3
y
14
− 4y
12
+ ··· − y + 1
c
4
, c
7
, c
8
y
14
+ 15y
13
+ ··· + 8y + 1
c
6
, c
10
y
14
− 14y
13
+ ··· − 13y + 1
c
9
y
14
− y
13
+ ··· − 4y
2
+ 1
c
11
y
14
− 8y
13
+ ··· − 6y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.893293 + 0.330555I
a = −1.15727 − 1.80484I
b = 0.592535 − 1.077080I
−1.31269 − 4.25298I −1.95653 + 2.08128I
u = 0.893293 − 0.330555I
a = −1.15727 + 1.80484I
b = 0.592535 + 1.077080I
−1.31269 + 4.25298I −1.95653 − 2.08128I
u = −0.647670 + 0.662108I
a = −0.510220 − 1.279880I
b = −0.233748 + 0.627547I
4.41438 + 3.29645I 4.47890 − 2.20670I
u = −0.647670 − 0.662108I
a = −0.510220 + 1.279880I
b = −0.233748 − 0.627547I
4.41438 − 3.29645I 4.47890 + 2.20670I
u = −1.004110 + 0.573368I
a = 0.83903 − 2.27992I
b = −0.459822 − 1.169450I
2.10465 + 6.34173I 0.34884 − 6.28453I
u = −1.004110 − 0.573368I
a = 0.83903 + 2.27992I
b = −0.459822 + 1.169450I
2.10465 − 6.34173I 0.34884 + 6.28453I
u = 0.630522 + 0.153615I
a = 0.851195 − 1.013010I
b = 0.557304 + 0.531416I
0.482214 + 0.495105I 1.13492 − 1.08750I
u = 0.630522 − 0.153615I
a = 0.851195 + 1.013010I
b = 0.557304 − 0.531416I
0.482214 − 0.495105I 1.13492 + 1.08750I
u = −0.599098 + 0.137170I
a = −0.253842 − 0.494489I
b = −1.007620 − 0.852501I
7.61522 + 3.62847I −8.05550 − 2.25038I
u = −0.599098 − 0.137170I
a = −0.253842 + 0.494489I
b = −1.007620 + 0.852501I
7.61522 − 3.62847I −8.05550 + 2.25038I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43294 + 0.11177I
a = 0.13928 + 1.45428I
b = 0.336823 + 0.911322I
−3.87634 + 1.39907I 1.20170 − 5.22268I
u = 1.43294 − 0.11177I
a = 0.13928 − 1.45428I
b = 0.336823 − 0.911322I
−3.87634 − 1.39907I 1.20170 + 5.22268I
u = −1.70588 + 0.11918I
a = 0.591819 + 1.217770I
b = −0.285468 + 0.936375I
−1.20276 − 1.17534I −6.65232 + 0.40861I
u = −1.70588 − 0.11918I
a = 0.591819 − 1.217770I
b = −0.285468 − 0.936375I
−1.20276 + 1.17534I −6.65232 − 0.40861I
16
III.
I
u
3
= h−u
5
+ 2u
4
+ u
3
− 2u
2
+ b − u, −u
5
+ 2u
4
+ a − u, u
10
− 4u
9
+ · · · − u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
2
=
u
5
− 2u
4
+ u
u
5
− 2u
4
− u
3
+ 2u
2
+ u
a
11
=
−u
−u
3
+ u
a
1
=
u
3
− 2u
2
u
5
− 2u
4
− u
3
+ 2u
2
+ u
a
3
=
u
8
− 4u
7
+ 3u
6
+ 5u
5
− 5u
4
− 3u
3
+ 2u
2
+ u
u
5
− 2u
4
− u
3
+ 2u
2
+ u − 1
a
5
=
u
8
− 4u
7
+ 3u
6
+ 5u
5
− 5u
4
− 3u
3
+ 2u
2
+ u
u
5
− 2u
4
− u
3
+ 2u
2
+ u − 1
a
8
=
u
u
3
− u
a
4
=
−u
9
+ 4u
8
− 4u
7
− 2u
6
+ 5u
5
− 2u
4
− 2u
3
+ 2u
2
+ u
−u
9
+ 2u
8
+ 3u
7
− 6u
6
− 3u
5
+ 4u
4
+ 2u
3
+ u
a
9
=
u
2
− 2u + 1
u
4
− 2u
3
+ 2u
a
9
=
u
2
− 2u + 1
u
4
− 2u
3
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
5
+ 8u
4
+ 4u
3
− 8u
2
− 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
4
, c
7
c
8
u
10
+ 2u
8
− u
6
− u
5
− 2u
4
− u
3
+ u
2
+ u + 1
c
6
, c
10
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 9u
5
+ 4u
4
+ 5u
3
− u
2
− u + 1
c
9
u
10
− 2u
8
− 4u
7
+ u
6
+ 5u
5
+ 16u
4
+ 11u
3
+ 7u
2
+ 3u + 1
c
11
u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 9u
5
+ 4u
4
− 5u
3
− u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
5
c
3
, c
4
, c
7
c
8
y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 9y
5
+ 4y
4
− 5y
3
− y
2
+ y + 1
c
6
, c
10
, c
11
y
10
− 12y
9
+ ··· − 3y + 1
c
9
y
10
− 4y
9
+ 6y
8
+ 12y
7
− 9y
6
+ 69y
5
+ 180y
4
+ 75y
3
+ 15y
2
+ 5y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904891 + 0.285000I
a = −1.49566 + 2.57455I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = −0.904891 − 0.285000I
a = −1.49566 − 2.57455I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = −0.628015 + 0.487800I
a = 0.387710 + 0.820455I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = −0.628015 − 0.487800I
a = 0.387710 − 0.820455I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 1.313160 + 0.316773I
a = −0.878996 − 0.922989I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = 1.313160 − 0.316773I
a = −0.878996 + 0.922989I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 0.338512 + 0.395352I
a = 0.463484 + 0.404816I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 0.338512 − 0.395352I
a = 0.463484 − 0.404816I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = 1.88124 + 0.12422I
a = 0.023461 + 1.248230I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 1.88124 − 0.12422I
a = 0.023461 − 1.248230I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
14
− u
13
+ ··· + 4u
2
+ 1)(u
66
+ 5u
65
+ ··· + 70u + 28)
c
2
((u
2
+ u + 1)
5
)(u
14
+ 7u
13
+ ··· + 8u + 1)
· (u
66
+ 27u
65
+ ··· + 5684u + 784)
c
3
(u
10
+ 2u
8
− u
6
− u
5
− 2u
4
− u
3
+ u
2
+ u + 1)
· (u
14
+ 2u
11
− 2u
10
− u
9
− u
8
− 2u
7
+ 4u
6
+ 2u
5
− 2u
3
− u + 1)
· (u
66
+ 7u
65
+ ··· − 293u + 131)
c
4
(u
10
+ 2u
8
+ ··· + u + 1)(u
14
− u
13
+ ··· + 4u
2
+ 1)
· (u
66
− 2u
65
+ ··· − 20u + 1)
c
5
((u
2
− u + 1)
5
)(u
14
+ u
13
+ ··· + 4u
2
+ 1)(u
66
+ 5u
65
+ ··· + 70u + 28)
c
6
(u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 9u
5
+ 4u
4
+ 5u
3
− u
2
− u + 1)
· (u
14
+ 2u
13
+ ··· + u + 1)(u
66
+ 3u
65
+ ··· − 49u + 23)
c
7
, c
8
(u
10
+ 2u
8
+ ··· + u + 1)(u
14
+ u
13
+ ··· + 4u
2
+ 1)
· (u
66
− 2u
65
+ ··· − 20u + 1)
c
9
(u
10
− 2u
8
− 4u
7
+ u
6
+ 5u
5
+ 16u
4
+ 11u
3
+ 7u
2
+ 3u + 1)
· (u
14
+ u
13
+ 2u
11
− 2u
9
+ 4u
8
+ 2u
7
− u
6
+ u
5
− 2u
4
− 2u
3
+ 1)
· (u
66
+ 2u
64
+ ··· + 24u + 1)
c
10
(u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 9u
5
+ 4u
4
+ 5u
3
− u
2
− u + 1)
· (u
14
− 2u
13
+ ··· − u + 1)(u
66
+ 3u
65
+ ··· − 49u + 23)
c
11
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 9u
5
+ 4u
4
− 5u
3
− u
2
+ u + 1)
· (u
14
− 4u
12
+ ··· − 6u + 1)(u
66
+ 5u
65
+ ··· + 3276u + 667)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
5
)(y
14
+ 7y
13
+ ··· + 8y + 1)
· (y
66
+ 27y
65
+ ··· + 5684y + 784)
c
2
((y
2
+ y + 1)
5
)(y
14
+ 7y
13
+ ··· + 4y + 1)
· (y
66
+ 27y
65
+ ··· + 5306896y + 614656)
c
3
(y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 9y
5
+ 4y
4
− 5y
3
− y
2
+ y + 1)
· (y
14
− 4y
12
+ ··· − y + 1)(y
66
− 15y
65
+ ··· − 380599y + 17161)
c
4
, c
7
, c
8
(y
10
+ 4y
9
+ 2y
8
− 8y
7
− 5y
6
+ 9y
5
+ 4y
4
− 5y
3
− y
2
+ y + 1)
· (y
14
+ 15y
13
+ ··· + 8y + 1)(y
66
+ 72y
65
+ ··· − 2y + 1)
c
6
, c
10
(y
10
− 12y
9
+ ··· − 3y + 1)(y
14
− 14y
13
+ ··· − 13y + 1)
· (y
66
− 33y
65
+ ··· − 12015y + 529)
c
9
(y
10
− 4y
9
+ 6y
8
+ 12y
7
− 9y
6
+ 69y
5
+ 180y
4
+ 75y
3
+ 15y
2
+ 5y + 1)
· (y
14
− y
13
+ ··· − 4y
2
+ 1)(y
66
+ 4y
65
+ ··· − 30y + 1)
c
11
(y
10
− 12y
9
+ ··· − 3y + 1)(y
14
− 8y
13
+ ··· − 6y + 1)
· (y
66
− 15y
65
+ ··· − 11892756y + 444889)
22
