12n
0133
(K12n
0133
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 4 9 11 1 8 5 10
Solving Sequence
9,11
8
4,7
3 6 5 12 10 1 2
c
8
c
7
c
3
c
6
c
5
c
11
c
10
c
12
c
1
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
13
+ 5u
12
− 2u
11
− 16u
10
− 10u
9
+ 16u
8
+ 28u
7
+ 10u
6
− 19u
5
− 25u
4
− 7u
3
+ 6u
2
+ 2b + 5u,
− u
13
− 4u
12
− 3u
11
+ 8u
10
+ 14u
9
− 18u
7
− 21u
6
− 5u
5
+ 16u
4
+ 17u
3
+ 4u
2
+ 2a − 4u − 5,
u
14
+ 3u
13
− 9u
11
− 8u
10
+ 8u
9
+ 18u
8
+ 9u
7
− 10u
6
− 18u
5
− 6u
4
+ 6u
3
+ 6u
2
+ 2u − 1i
I
u
2
= h−1.17690 × 10
65
u
57
− 3.97295 × 10
65
u
56
+ ··· + 3.56133 × 10
64
b − 4.96718 × 10
63
,
− 6.29210 × 10
64
u
57
− 8.59795 × 10
64
u
56
+ ··· + 7.12266 × 10
64
a − 4.18226 × 10
65
, u
58
+ 4u
57
+ ··· − 5u + 1i
I
u
3
= hu
2
+ b + u − 1, a + u, u
3
+ u
2
− 1i
I
u
4
= h4u
2
a + 6au + b + 4a + 1, −2u
2
a + a
2
− au − 2u
2
+ 2a − u + 2, u
3
+ u
2
− 1i
I
u
5
= hb − u − 2, a + 2u + 3, u
2
+ u − 1i
I
u
6
= hb − 2a + 2, a
2
− a − 1, u − 1i
* 6 irreducible components of dim
C
= 0, with total 85 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
=
h2u
13
+5u
12
+· · ·+2b+5u, −u
13
−4u
12
+· · ·+2a−5, u
14
+3u
13
+· · ·+2u−1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
4
=
1
2
u
13
+ 2u
12
+ ··· + 2u +
5
2
−u
13
−
5
2
u
12
+ ··· − 3u
2
−
5
2
u
a
7
=
−u
2
+ 1
−u
2
a
3
=
1
2
u
13
+
3
2
u
12
+ ··· +
5
2
u + 2
−
1
2
u
13
− 2u
12
+ ··· − u −
1
2
a
6
=
1
2
u
13
+
3
2
u
12
+ ··· +
3
2
u + 2
−
1
2
u
12
−
3
2
u
11
+ ··· −
1
2
u −
1
2
a
5
=
1
2
u
13
+
3
2
u
12
+ ··· +
3
2
u + 2
−u
12
−
5
2
u
11
+ ··· − u −
1
2
a
12
=
−u
11
− u
10
+ 3u
9
+ 4u
8
− 3u
7
− 6u
6
− 2u
5
+ 3u
4
+ 5u
3
+ u
2
− 2u − 1
u
13
+
3
2
u
12
+ ··· + 3u
2
+
3
2
u
a
10
=
u
−u
3
+ u
a
1
=
1
2
u
13
+ u
12
+ ··· − u −
3
2
1
2
u
13
+ u
12
+ ··· +
7
2
u
2
+ u
a
2
=
−
1
2
u
13
−
3
2
u
12
+ ··· −
3
2
u −
3
2
−
1
2
u
13
−
1
2
u
12
+ ··· +
1
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 3u
13
+3u
12
−15u
11
−24u
10
+14u
9
+44u
8
+18u
7
−27u
6
−52u
5
−25u
4
+14u
3
+10u
2
+3u−11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
14
+ 9u
13
+ ··· + 16u + 1
c
2
, c
4
, c
8
c
10
u
14
− 3u
13
+ ··· − 2u − 1
c
3
, c
6
, c
9
c
12
u
14
− u
13
+ ··· − 4u − 1
c
5
, c
11
u
14
− 7u
13
+ ··· − 24u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
14
− 5y
13
+ ··· − 208y + 1
c
2
, c
4
, c
8
c
10
y
14
− 9y
13
+ ··· − 16y + 1
c
3
, c
6
, c
9
c
12
y
14
+ 3y
13
+ ··· − 8y + 1
c
5
, c
11
y
14
− 7y
13
+ ··· + 384y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.242991 + 0.933745I
a = −0.20291 + 1.67953I
b = −0.821533 + 0.270883I
1.33116 − 5.50874I −7.69545 + 3.70076I
u = −0.242991 − 0.933745I
a = −0.20291 − 1.67953I
b = −0.821533 − 0.270883I
1.33116 + 5.50874I −7.69545 − 3.70076I
u = 0.951606 + 0.107631I
a = −0.80680 + 1.21543I
b = 3.80232 + 0.74412I
−2.88995 − 0.46660I −33.6526 − 15.6404I
u = 0.951606 − 0.107631I
a = −0.80680 − 1.21543I
b = 3.80232 − 0.74412I
−2.88995 + 0.46660I −33.6526 + 15.6404I
u = −0.389011 + 0.665748I
a = 0.507976 + 0.255319I
b = 0.587054 + 0.784524I
3.75566 + 0.17244I −4.31674 − 1.33622I
u = −0.389011 − 0.665748I
a = 0.507976 − 0.255319I
b = 0.587054 − 0.784524I
3.75566 − 0.17244I −4.31674 + 1.33622I
u = −1.217360 + 0.433191I
a = −0.051195 + 0.233560I
b = 0.695133 + 0.745943I
−1.53918 + 8.57795I −13.9694 − 8.6920I
u = −1.217360 − 0.433191I
a = −0.051195 − 0.233560I
b = 0.695133 − 0.745943I
−1.53918 − 8.57795I −13.9694 + 8.6920I
u = 1.208510 + 0.461890I
a = 1.195780 − 0.437447I
b = 1.55260 − 0.60463I
−7.24910 − 2.92807I −16.0849 + 1.6852I
u = 1.208510 − 0.461890I
a = 1.195780 + 0.437447I
b = 1.55260 + 0.60463I
−7.24910 + 2.92807I −16.0849 − 1.6852I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31782
a = 0.941660
b = 0.882448
−10.4546 −24.6220
u = −1.28364 + 0.61767I
a = −1.46437 − 0.09958I
b = −2.38982 − 1.44096I
−4.9818 + 17.0516I −13.2441 − 9.4300I
u = −1.28364 − 0.61767I
a = −1.46437 + 0.09958I
b = −2.38982 + 1.44096I
−4.9818 − 17.0516I −13.2441 + 9.4300I
u = 0.263596
a = 2.70137
b = −0.733954
−0.942520 −9.45120
6
II.
I
u
2
= h−1.18×10
65
u
57
−3.97×10
65
u
56
+· · ·+3.56×10
64
b−4.97×10
63
, −6.29×
10
64
u
57
−8.60×10
64
u
56
+· · ·+7.12×10
64
a−4.18×10
65
, u
58
+4u
57
+· · ·−5u+1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
4
=
0.883391u
57
+ 1.20713u
56
+ ··· − 9.91542u + 5.87176
3.30467u
57
+ 11.1558u
56
+ ··· − 6.41751u + 0.139475
a
7
=
−u
2
+ 1
−u
2
a
3
=
0.793575u
57
+ 0.365747u
56
+ ··· − 3.89250u + 4.38523
1.32573u
57
+ 4.64753u
56
+ ··· + 4.91950u − 1.75010
a
6
=
1.70888u
57
+ 4.42480u
56
+ ··· − 6.68595u + 4.41639
2.56867u
57
+ 8.73466u
56
+ ··· − 12.4165u + 1.63075
a
5
=
1.70888u
57
+ 4.42480u
56
+ ··· − 6.68595u + 4.41639
0.322307u
57
+ 1.39608u
56
+ ··· + 1.34584u − 0.779945
a
12
=
1.31808u
57
+ 3.67421u
56
+ ··· + 1.92169u − 2.00892
0.489553u
57
+ 1.26691u
56
+ ··· − 0.411200u + 0.625023
a
10
=
u
−u
3
+ u
a
1
=
2.12433u
57
+ 5.66107u
56
+ ··· + 3.12772u − 2.10774
−0.0988242u
57
− 1.20154u
56
+ ··· + 7.79161u − 0.711908
a
2
=
−0.453494u
57
− 0.227312u
56
+ ··· + 6.41674u − 3.64552
−2.66084u
57
− 9.70894u
56
+ ··· + 11.5745u − 1.08534
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.86204u
57
+ 41.6548u
56
+ ··· + 50.2522u − 23.8526
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
58
+ 32u
57
+ ··· + 25u + 1
c
2
, c
4
, c
8
c
10
u
58
− 4u
57
+ ··· + 5u + 1
c
3
, c
6
, c
9
c
12
u
58
− 4u
57
+ ··· + 32u − 4
c
5
, c
11
(u
29
+ 2u
28
+ ··· − 28u − 8)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
58
− 8y
57
+ ··· + 195y + 1
c
2
, c
4
, c
8
c
10
y
58
− 32y
57
+ ··· − 25y + 1
c
3
, c
6
, c
9
c
12
y
58
+ 18y
57
+ ··· − 984y + 16
c
5
, c
11
(y
29
− 28y
28
+ ··· + 2896y −64)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988988
a = −0.481132
b = −5.97136
−2.67255 −211.680
u = −0.852515 + 0.455377I
a = 0.096402 + 0.221595I
b = 1.14950 + 1.39220I
4.34822 + 5.30129I −10.14110 − 5.91971I
u = −0.852515 − 0.455377I
a = 0.096402 − 0.221595I
b = 1.14950 − 1.39220I
4.34822 − 5.30129I −10.14110 + 5.91971I
u = −0.875378 + 0.395680I
a = −1.17395 − 1.12502I
b = −0.55207 − 1.63441I
−1.15248 + 2.97907I −9.53425 − 4.84429I
u = −0.875378 − 0.395680I
a = −1.17395 + 1.12502I
b = −0.55207 + 1.63441I
−1.15248 − 2.97907I −9.53425 + 4.84429I
u = 0.382222 + 0.979860I
a = 0.37822 + 1.49048I
b = 0.968996 + 0.458325I
−4.05295 + 3.42058I −12.00000 − 4.03802I
u = 0.382222 − 0.979860I
a = 0.37822 − 1.49048I
b = 0.968996 − 0.458325I
−4.05295 − 3.42058I −12.00000 + 4.03802I
u = −1.06017
a = 1.48801
b = 1.19467
−10.6310 −48.5360
u = −0.216051 + 1.075610I
a = 0.49789 − 1.82352I
b = 0.930330 − 0.518578I
−1.66044 − 11.01250I −12.00000 + 0.I
u = −0.216051 − 1.075610I
a = 0.49789 + 1.82352I
b = 0.930330 + 0.518578I
−1.66044 + 11.01250I −12.00000 + 0.I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994844 + 0.502352I
a = −0.026325 − 0.357537I
b = −1.077780 − 0.102508I
−0.488787 + 0.370462I 0
u = 0.994844 − 0.502352I
a = −0.026325 + 0.357537I
b = −1.077780 + 0.102508I
−0.488787 − 0.370462I 0
u = −0.108845 + 0.869895I
a = 0.31064 + 1.79296I
b = 0.569231 + 0.371365I
−3.19564 − 4.35308I −12.04263 + 3.74313I
u = −0.108845 − 0.869895I
a = 0.31064 − 1.79296I
b = 0.569231 − 0.371365I
−3.19564 + 4.35308I −12.04263 − 3.74313I
u = −1.006590 + 0.537430I
a = 0.312868 + 0.518025I
b = −0.632775 − 0.100970I
2.03816 + 4.43643I 0
u = −1.006590 − 0.537430I
a = 0.312868 − 0.518025I
b = −0.632775 + 0.100970I
2.03816 − 4.43643I 0
u = −0.873306 + 0.762690I
a = 2.26083 + 2.71765I
b = 0.21388 + 2.77675I
1.81502 + 2.87998I 0
u = −0.873306 − 0.762690I
a = 2.26083 − 2.71765I
b = 0.21388 − 2.77675I
1.81502 − 2.87998I 0
u = 0.836851 + 0.036106I
a = 0.0838767 − 0.0224097I
b = 0.00910 − 4.38592I
1.81502 − 2.87998I −58.6220 + 17.5185I
u = 0.836851 − 0.036106I
a = 0.0838767 + 0.0224097I
b = 0.00910 + 4.38592I
1.81502 + 2.87998I −58.6220 − 17.5185I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654785 + 0.491061I
a = 0.267178 + 0.146980I
b = −0.936070 − 0.955868I
4.90257 − 1.34329I −7.80264 + 1.36225I
u = −0.654785 − 0.491061I
a = 0.267178 − 0.146980I
b = −0.936070 + 0.955868I
4.90257 + 1.34329I −7.80264 − 1.36225I
u = −1.141310 + 0.406924I
a = −1.042680 − 0.445981I
b = −1.124050 − 0.134041I
−4.05295 + 3.42058I 0
u = −1.141310 − 0.406924I
a = −1.042680 + 0.445981I
b = −1.124050 + 0.134041I
−4.05295 − 3.42058I 0
u = −0.787150 + 0.924733I
a = 1.205180 − 0.532327I
b = 1.38107 + 0.43654I
4.90257 + 1.34329I 0
u = −0.787150 − 0.924733I
a = 1.205180 + 0.532327I
b = 1.38107 − 0.43654I
4.90257 − 1.34329I 0
u = 0.000304 + 0.780908I
a = −0.24339 − 2.24468I
b = 0.267868 − 0.277636I
−3.74876 − 1.54341I −12.07483 + 3.03548I
u = 0.000304 − 0.780908I
a = −0.24339 + 2.24468I
b = 0.267868 + 0.277636I
−3.74876 + 1.54341I −12.07483 − 3.03548I
u = 1.120680 + 0.529353I
a = 1.175230 − 0.118199I
b = 1.86181 − 1.77127I
−3.19564 − 4.35308I 0
u = 1.120680 − 0.529353I
a = 1.175230 + 0.118199I
b = 1.86181 + 1.77127I
−3.19564 + 4.35308I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665448 + 0.320577I
a = −1.75785 − 0.27970I
b = −0.427413 − 0.048282I
−0.488787 + 0.370462I −8.36692 − 2.50640I
u = −0.665448 − 0.320577I
a = −1.75785 + 0.27970I
b = −0.427413 + 0.048282I
−0.488787 − 0.370462I −8.36692 + 2.50640I
u = −1.209970 + 0.458074I
a = −1.109810 − 0.614505I
b = −2.00916 − 2.00839I
−7.27243 + 6.00653I 0
u = −1.209970 − 0.458074I
a = −1.109810 + 0.614505I
b = −2.00916 + 2.00839I
−7.27243 − 6.00653I 0
u = 1.264110 + 0.277934I
a = −0.094671 − 0.217784I
b = 0.589009 + 0.036358I
−1.15248 − 2.97907I 0
u = 1.264110 − 0.277934I
a = −0.094671 + 0.217784I
b = 0.589009 − 0.036358I
−1.15248 + 2.97907I 0
u = 1.278760 + 0.279605I
a = −0.874635 + 0.506037I
b = −1.179270 + 0.382768I
−3.74876 + 1.54341I 0
u = 1.278760 − 0.279605I
a = −0.874635 − 0.506037I
b = −1.179270 − 0.382768I
−3.74876 − 1.54341I 0
u = 0.689587
a = 6.16946
b = −5.31315
−2.67255 −211.680
u = 1.251940 + 0.396137I
a = −1.204600 + 0.452476I
b = −2.28308 + 2.02996I
−7.39364 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.251940 − 0.396137I
a = −1.204600 − 0.452476I
b = −2.28308 − 2.02996I
−7.39364 0
u = 0.027420 + 0.672723I
a = 0.367381 + 0.017368I
b = −0.180737 − 0.719838I
2.03816 − 4.43643I −7.12586 + 5.70665I
u = 0.027420 − 0.672723I
a = 0.367381 − 0.017368I
b = −0.180737 + 0.719838I
2.03816 + 4.43643I −7.12586 − 5.70665I
u = −1.227590 + 0.512752I
a = 1.029830 + 0.433526I
b = 1.235900 + 0.213650I
−6.56035 + 9.36152I 0
u = −1.227590 − 0.512752I
a = 1.029830 − 0.433526I
b = 1.235900 − 0.213650I
−6.56035 − 9.36152I 0
u = −0.984255 + 0.909262I
a = −1.077810 + 0.708898I
b = −1.52408 − 0.24363I
4.34822 + 5.30129I 0
u = −0.984255 − 0.909262I
a = −1.077810 − 0.708898I
b = −1.52408 + 0.24363I
4.34822 − 5.30129I 0
u = −1.220950 + 0.580073I
a = 1.236460 + 0.202005I
b = 2.15316 + 1.56889I
−1.66044 + 11.01250I 0
u = −1.220950 − 0.580073I
a = 1.236460 − 0.202005I
b = 2.15316 − 1.56889I
−1.66044 − 11.01250I 0
u = 1.196500 + 0.654445I
a = −1.393060 + 0.026552I
b = −2.02586 + 1.44130I
−6.56035 − 9.36152I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.196500 − 0.654445I
a = −1.393060 − 0.026552I
b = −2.02586 − 1.44130I
−6.56035 + 9.36152I 0
u = 1.44823 + 0.32172I
a = 0.885882 − 0.795017I
b = 0.993193 − 0.775693I
−7.27243 + 6.00653I 0
u = 1.44823 − 0.32172I
a = 0.885882 + 0.795017I
b = 0.993193 + 0.775693I
−7.27243 − 6.00653I 0
u = −1.57371
a = 0.372440
b = 0.379153
−10.6310 0
u = 0.242019 + 0.246574I
a = 1.39952 − 1.87926I
b = −0.768573 − 0.066926I
−0.942618 −9.31087 + 0.I
u = 0.242019 − 0.246574I
a = 1.39952 + 1.87926I
b = −0.768573 + 0.066926I
−0.942618 −9.31087 + 0.I
u = 0.257910 + 0.127141I
a = 2.21702 − 1.31285I
b = −0.746774 − 0.028572I
−0.942376 −9.38299 + 0.I
u = 0.257910 − 0.127141I
a = 2.21702 + 1.31285I
b = −0.746774 + 0.028572I
−0.942376 −9.38299 + 0.I
15
III. I
u
3
= hu
2
+ b + u − 1, a + u, u
3
+ u
2
− 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
4
=
−u
−u
2
− u + 1
a
7
=
−u
2
+ 1
−u
2
a
3
=
−1
0
a
6
=
0
−u
a
5
=
0
−u
a
12
=
0
u
a
10
=
u
u
2
+ u − 1
a
1
=
u
2
− 1
u
2
a
2
=
−1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 12
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
3
− u
2
+ 2u − 1
c
2
, c
8
u
3
+ u
2
− 1
c
4
, c
10
u
3
− u
2
+ 1
c
5
, c
11
u
3
c
6
, c
12
u
3
+ u
2
+ 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
9
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
8
c
10
y
3
− y
2
+ 2y −1
c
5
, c
11
y
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.877439 − 0.744862I
b = 1.66236 + 0.56228I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = −0.877439 − 0.744862I
a = 0.877439 + 0.744862I
b = 1.66236 − 0.56228I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.754878
a = −0.754878
b = −0.324718
−2.22691 −18.0390
19
IV.
I
u
4
= h4u
2
a + 6au + b + 4a + 1, −2u
2
a + a
2
−au −2u
2
+2a −u +2, u
3
+u
2
−1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
4
=
a
−4u
2
a − 6au − 4a − 1
a
7
=
−u
2
+ 1
−u
2
a
3
=
−au + u
2
− u
−3u
2
a − 5au − 3a − u
a
6
=
0
−u
2
a − 2au + 2u
2
− 2a + 2u + 1
a
5
=
0
−u
2
a − 2au + 2u
2
− 2a + 2u + 1
a
12
=
0
u
a
10
=
u
u
2
+ u − 1
a
1
=
u
2
− 1
u
2
a
2
=
−au + u
2
− u
−u
2
a − 2au + 2u
2
− a + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16u
2
a − 21au − 21a + 11u − 1
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
(u
3
+ u
2
− 1)
2
c
4
, c
10
(u
3
− u
2
+ 1)
2
c
5
, c
11
u
6
c
6
, c
12
(u
3
+ u
2
+ 2u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
9
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
8
c
10
(y
3
− y
2
+ 2y −1)
2
c
5
, c
11
y
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −1.069840 + 0.424452I
b = −1.75488 − 0.64082I
6.04826 −6.45445 + 0.I
u = −0.877439 + 0.744862I
a = −1.37744 − 2.29387I
b = 0.18504 − 1.97346I
1.91067 + 2.82812I 9.7272 + 14.7292I
u = −0.877439 − 0.744862I
a = −1.069840 − 0.424452I
b = −1.75488 + 0.64082I
6.04826 −6.45445 + 0.I
u = −0.877439 − 0.744862I
a = −1.37744 + 2.29387I
b = 0.18504 + 1.97346I
1.91067 − 2.82812I 9.7272 − 14.7292I
u = 0.754878
a = −0.052721 + 0.320410I
b = −0.43016 − 3.46319I
1.91067 − 2.82812I 9.7272 − 14.7292I
u = 0.754878
a = −0.052721 − 0.320410I
b = −0.43016 + 3.46319I
1.91067 + 2.82812I 9.7272 + 14.7292I
23
V. I
u
5
= hb − u − 2, a + 2u + 3, u
2
+ u − 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
8
=
1
u − 1
a
4
=
−2u − 3
u + 2
a
7
=
u
u − 1
a
3
=
−2u − 3
u + 2
a
6
=
u
u − 1
a
5
=
u
−u
a
12
=
−2u + 1
3u − 1
a
10
=
u
−u + 1
a
1
=
−u
u
a
2
=
−3u − 3
2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 29
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
u
2
c
4
(u + 1)
2
c
5
, c
7
u
2
− 3u + 1
c
8
, c
9
u
2
+ u − 1
c
10
, c
12
u
2
− u − 1
c
11
u
2
+ 3u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
2
c
3
, c
6
y
2
c
5
, c
7
, c
11
y
2
− 7y + 1
c
8
, c
9
, c
10
c
12
y
2
− 3y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −4.23607
b = 2.61803
−2.63189 29.0000
u = −1.61803
a = 0.236068
b = 0.381966
−10.5276 29.0000
27
VI. I
u
6
= hb − 2a + 2, a
2
− a − 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
1
a
8
=
1
−1
a
4
=
a
2a − 2
a
7
=
0
−1
a
3
=
a
a − 2
a
6
=
−a − 1
−3
a
5
=
−a − 1
a − 2
a
12
=
−3a − 2
0
a
10
=
1
0
a
1
=
−3a − 2
0
a
2
=
−a − 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 29
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
+ 3u + 1
c
7
, c
8
(u − 1)
2
c
9
, c
12
u
2
c
10
(u + 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
7
, c
8
, c
10
(y −1)
2
c
9
, c
12
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = −3.23607
−2.63189 29.0000
u = 1.00000
a = 1.61803
b = 1.23607
−10.5276 29.0000
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
((u − 1)
2
)(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
3
(u
14
+ 9u
13
+ ··· + 16u + 1)
· (u
58
+ 32u
57
+ ··· + 25u + 1)
c
2
, c
8
((u − 1)
2
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
3
(u
14
− 3u
13
+ ··· − 2u − 1)
· (u
58
− 4u
57
+ ··· + 5u + 1)
c
3
, c
9
u
2
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
14
− u
13
+ ··· − 4u − 1)
· (u
58
− 4u
57
+ ··· + 32u − 4)
c
4
, c
10
((u + 1)
2
)(u
2
− u − 1)(u
3
− u
2
+ 1)
3
(u
14
− 3u
13
+ ··· − 2u − 1)
· (u
58
− 4u
57
+ ··· + 5u + 1)
c
5
, c
11
u
9
(u
2
− 3u + 1)(u
2
+ 3u + 1)(u
14
− 7u
13
+ ··· − 24u + 8)
· (u
29
+ 2u
28
+ ··· − 28u − 8)
2
c
6
, c
12
u
2
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
3
(u
14
− u
13
+ ··· − 4u − 1)
· (u
58
− 4u
57
+ ··· + 32u − 4)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y −1)
2
)(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y −1)
3
(y
14
− 5y
13
+ ··· − 208y + 1)
· (y
58
− 8y
57
+ ··· + 195y + 1)
c
2
, c
4
, c
8
c
10
((y −1)
2
)(y
2
− 3y + 1)(y
3
− y
2
+ 2y −1)
3
(y
14
− 9y
13
+ ··· − 16y + 1)
· (y
58
− 32y
57
+ ··· − 25y + 1)
c
3
, c
6
, c
9
c
12
y
2
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
3
(y
14
+ 3y
13
+ ··· − 8y + 1)
· (y
58
+ 18y
57
+ ··· − 984y + 16)
c
5
, c
11
y
9
(y
2
− 7y + 1)
2
(y
14
− 7y
13
+ ··· + 384y + 64)
· (y
29
− 28y
28
+ ··· + 2896y −64)
2
33
