12n
0718
(K12n
0718
)
A knot diagram
1
Linearized knot diagam
4 11 7 9 12 2 11 1 2 7 8 5
Solving Sequence
2,11 3,7
4 8 12 1 6 5 10 9
c
2
c
3
c
7
c
11
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h13u
5
− 14u
4
+ 83u
3
− 84u
2
+ 67b − 74u − 31, −24u
5
+ 31u
4
− 179u
3
+ 186u
2
+ 67a + 49u + 16,
u
6
+ 8u
4
+ 2u
3
+ 4u
2
+ u + 1i
I
u
2
= h−1569393106u
14
− 7670004252u
13
+ ··· + 10430913127b − 4860457910,
20548723543u
14
+ 25409181453u
13
+ ··· + 10430913127a − 34629938205,
u
15
+ u
14
+ 16u
13
+ 15u
12
+ 67u
11
+ 68u
10
− 6u
9
+ 55u
8
− 21u
7
+ 47u
6
− 22u
5
+ 20u
4
− 7u
3
+ 6u
2
− 2u + 1i
I
u
3
= h53383992u
13
− 54254216u
12
+ ··· + 162743197b + 4010822,
− 157493798u
13
+ 153482976u
12
+ ··· + 162743197a − 113034563,
u
14
− u
13
+ 2u
12
− u
11
− 23u
10
+ 20u
9
+ 63u
8
− 19u
7
− 48u
6
+ 20u
5
+ 26u
4
− 6u
3
− 5u
2
+ u + 1i
I
u
4
= h−1.12905 × 10
44
u
23
− 4.55305 × 10
43
u
22
+ ··· + 2.57192 × 10
47
b − 2.14246 × 10
47
,
6.26307 × 10
45
u
23
+ 9.22804 × 10
44
u
22
+ ··· + 5.24028 × 10
48
a − 1.07233 × 10
49
,
u
24
+ 23u
22
+ ··· − 507u + 163i
I
u
5
= hb + u − 1, a − u + 1, u
2
− u + 1i
I
u
6
= hb
2
− b + 1, a − 1, u + 1i
* 6 irreducible components of dim
C
= 0, with total 63 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
= h13u
5
− 14u
4
+ · · · + 67b − 31, −24u
5
+ 31u
4
+ · · · + 67a + 16, u
6
+
8u
4
+ 2u
3
+ 4u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.358209u
5
− 0.462687u
4
+ ··· − 0.731343u − 0.238806
−0.194030u
5
+ 0.208955u
4
+ ··· + 1.10448u + 0.462687
a
4
=
−0.462687u
5
− 0.194030u
4
+ ··· − 0.597015u + 0.641791
0.208955u
5
+ 0.313433u
4
+ ··· + 0.656716u + 0.194030
a
8
=
0.358209u
5
− 0.462687u
4
+ ··· − 0.731343u − 0.238806
u
a
12
=
−0.208955u
5
− 0.313433u
4
+ ··· − 1.65672u − 1.19403
−0.194030u
5
+ 0.208955u
4
+ ··· + 1.10448u + 0.462687
a
1
=
−0.671642u
5
− 0.507463u
4
+ ··· − 2.25373u + 0.447761
0.268657u
5
+ 0.402985u
4
+ ··· + 1.70149u + 0.820896
a
6
=
0.164179u
5
− 0.253731u
4
+ ··· + 0.373134u + 0.223881
−0.194030u
5
+ 0.208955u
4
+ ··· + 1.10448u + 0.462687
a
5
=
−0.402985u
5
− 0.104478u
4
+ ··· + 0.447761u + 1.26866
0.522388u
5
+ 0.283582u
4
+ ··· + 1.64179u − 0.0149254
a
10
=
0.208955u
5
+ 0.313433u
4
+ ··· + 1.65672u + 1.19403
0.164179u
5
− 0.253731u
4
+ ··· + 0.373134u − 0.776119
a
9
=
0.373134u
5
+ 0.0597015u
4
+ ··· + 2.02985u + 0.417910
0.164179u
5
− 0.253731u
4
+ ··· + 0.373134u − 0.776119
(ii) Obstruction class = −1
(iii) Cusp Shapes =
193
67
u
5
+
122
67
u
4
+
1526
67
u
3
+
1335
67
u
2
+
999
67
u +
720
67
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 4u
5
+ 9u
4
− 11u
3
+ 8u
2
− 3u + 1
c
2
, c
3
u
6
+ 8u
4
− 2u
3
+ 4u
2
− u + 1
c
4
, c
8
u
6
− 2u
3
+ 4u
2
− 3u + 1
c
5
, c
12
(u
3
− 2u
2
+ 3u − 1)
2
c
6
u
6
− u
5
+ 7u
4
+ 8u
2
− 5u + 1
c
7
, c
10
, c
11
u
6
− 3u
5
+ 5u
3
− u
2
− 2u + 1
c
9
u
6
− 5u
5
+ 13u
4
− 16u
3
+ 12u
2
− 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 2y
5
+ 9y
4
+ y
3
+ 16y
2
+ 7y + 1
c
2
, c
3
y
6
+ 16y
5
+ 72y
4
+ 62y
3
+ 28y
2
+ 7y + 1
c
4
, c
8
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
c
5
, c
12
(y
3
+ 2y
2
+ 5y −1)
2
c
6
y
6
+ 13y
5
+ 65y
4
+ 104y
3
+ 78y
2
− 9y + 1
c
7
, c
10
, c
11
y
6
− 9y
5
+ 28y
4
− 35y
3
+ 21y
2
− 6y + 1
c
9
y
6
+ y
5
+ 33y
4
+ 8y
3
+ 10y
2
− y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175218 + 0.614017I
a = 0.08270 − 1.43799I
b = 0.455994 + 1.129810I
1.18623 − 4.16039I 2.50198 + 9.24184I
u = 0.175218 − 0.614017I
a = 0.08270 + 1.43799I
b = 0.455994 − 1.129810I
1.18623 + 4.16039I 2.50198 − 9.24184I
u = −0.307599 + 0.479689I
a = 0.877439 + 0.479689I
b = −0.284920 + 0.155763I
1.134710 − 0.529643I 7.45884 + 1.83935I
u = −0.307599 − 0.479689I
a = 0.877439 − 0.479689I
b = −0.284920 − 0.155763I
1.134710 + 0.529643I 7.45884 − 1.83935I
u = 0.13238 + 2.74513I
a = 0.039862 + 0.693124I
b = −0.67107 − 2.43695I
14.1284 − 13.7510I 4.53918 + 6.26128I
u = 0.13238 − 2.74513I
a = 0.039862 − 0.693124I
b = −0.67107 + 2.43695I
14.1284 + 13.7510I 4.53918 − 6.26128I
5
II.
I
u
2
= h−1.57 × 10
9
u
14
− 7.67 × 10
9
u
13
+ · · · + 1.04 × 10
10
b − 4.86 × 10
9
, 2.05 ×
10
10
u
14
+2.54×10
10
u
13
+· · ·+1.04×10
10
a−3.46×10
10
, u
15
+u
14
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−1.96998u
14
− 2.43595u
13
+ ··· − 8.60582u + 3.31993
0.150456u
14
+ 0.735315u
13
+ ··· + 2.03805u + 0.465967
a
4
=
−0.465967u
14
− 0.315511u
13
+ ··· − 0.620033u + 2.96998
0.584859u
14
+ 0.726095u
13
+ ··· + 0.766879u − 0.150456
a
8
=
−1.96998u
14
− 2.43595u
13
+ ··· − 8.60582u + 3.31993
u
a
12
=
−1.55974u
14
− 0.980765u
13
+ ··· − 5.08122u + 3.74389
0.150456u
14
+ 0.735315u
13
+ ··· + 2.03805u + 0.465967
a
1
=
−2.12527u
14
− 2.81645u
13
+ ··· − 2.52477u + 1.85292
0.665898u
14
+ 0.835107u
13
+ ··· + 1.04529u + 0.832419
a
6
=
−1.81953u
14
− 1.70064u
13
+ ··· − 6.56777u + 3.78590
0.150456u
14
+ 0.735315u
13
+ ··· + 2.03805u + 0.465967
a
5
=
−2.60944u
14
− 4.20613u
13
+ ··· − 7.32190u + 1.21409
−0.774010u
14
− 0.545592u
13
+ ··· − 2.36170u + 2.98355
a
10
=
1.55974u
14
+ 0.980765u
13
+ ··· + 5.08122u − 3.74389
−0.552009u
14
− 1.50756u
13
+ ··· − 2.75574u + 0.113009
a
9
=
1.00773u
14
− 0.526796u
13
+ ··· + 2.32548u − 3.63089
−0.552009u
14
− 1.50756u
13
+ ··· − 2.75574u + 0.113009
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
61025071082
10430913127
u
14
−
87492839805
10430913127
u
13
+ ···−
60233840046
10430913127
u +
63546445223
10430913127
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 8u
14
+ ··· − 26u + 4
c
2
, c
3
u
15
− u
14
+ ··· − 2u − 1
c
4
, c
8
u
15
+ u
12
+ ··· + 6u
2
− 1
c
5
, c
12
u
15
− 8u
14
+ ··· − 128u + 32
c
6
u
15
+ 4u
14
+ ··· + 14u + 1
c
7
, c
10
, c
11
u
15
− 6u
14
+ ··· + 28u − 16
c
9
u
15
+ 4u
14
+ ··· − 18u − 9
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 2y
13
+ ··· − 68y −16
c
2
, c
3
y
15
+ 31y
14
+ ··· − 8y −1
c
4
, c
8
y
15
+ 12y
13
+ ··· + 12y −1
c
5
, c
12
y
15
+ 2y
14
+ ··· − 3584y −1024
c
6
y
15
+ 26y
14
+ ··· + 34y −1
c
7
, c
10
, c
11
y
15
− 20y
14
+ ··· − 1232y −256
c
9
y
15
+ 14y
14
+ ··· − 288y −81
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358852 + 0.655382I
a = 0.37132 + 1.53080I
b = 0.249515 + 0.020338I
0.647850 + 0.593610I 0.397147 − 0.414996I
u = −0.358852 − 0.655382I
a = 0.37132 − 1.53080I
b = 0.249515 − 0.020338I
0.647850 − 0.593610I 0.397147 + 0.414996I
u = −0.362442 + 0.521099I
a = −1.62550 − 1.14103I
b = −0.565588 + 1.295060I
6.17652 − 3.16479I 8.46791 + 3.96283I
u = −0.362442 − 0.521099I
a = −1.62550 + 1.14103I
b = −0.565588 − 1.295060I
6.17652 + 3.16479I 8.46791 − 3.96283I
u = 0.495956 + 0.351454I
a = 0.594839 + 0.597610I
b = 0.360462 + 0.632001I
−1.23951 − 1.59759I −0.60489 + 4.37134I
u = 0.495956 − 0.351454I
a = 0.594839 − 0.597610I
b = 0.360462 − 0.632001I
−1.23951 + 1.59759I −0.60489 − 4.37134I
u = 0.177403 + 0.564115I
a = −1.56471 − 0.13961I
b = 0.654033 + 0.290971I
−2.12993 + 3.66119I 1.84247 − 2.75515I
u = 0.177403 − 0.564115I
a = −1.56471 + 0.13961I
b = 0.654033 − 0.290971I
−2.12993 − 3.66119I 1.84247 + 2.75515I
u = 0.361509 + 0.466401I
a = 2.32217 − 1.05813I
b = 0.51667 + 1.34137I
2.58286 + 9.32736I 5.11705 − 6.33212I
u = 0.361509 − 0.466401I
a = 2.32217 + 1.05813I
b = 0.51667 − 1.34137I
2.58286 − 9.32736I 5.11705 + 6.33212I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47475
a = 0.909455
b = 0.503214
2.65817 1.30990
u = 0.30799 + 2.79469I
a = −0.133260 + 0.638046I
b = 0.23778 − 2.35751I
16.9670 + 6.2281I 6.62700 − 4.47239I
u = 0.30799 − 2.79469I
a = −0.133260 − 0.638046I
b = 0.23778 + 2.35751I
16.9670 − 6.2281I 6.62700 + 4.47239I
u = −0.38419 + 2.88575I
a = 0.080416 + 0.603207I
b = 0.29553 − 2.22676I
11.03220 + 4.65884I 2.00000 − 4.62633I
u = −0.38419 − 2.88575I
a = 0.080416 − 0.603207I
b = 0.29553 + 2.22676I
11.03220 − 4.65884I 2.00000 + 4.62633I
10
III.
I
u
3
= h5.34 × 10
7
u
13
− 5.43 × 10
7
u
12
+ · · · + 1.63 × 10
8
b + 4.01 × 10
6
, −1.57 ×
10
8
u
13
+ 1.53 × 10
8
u
12
+ · · · + 1.63 × 10
8
a − 1.13 × 10
8
, u
14
− u
13
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.967744u
13
− 0.943099u
12
+ ··· − 7.60104u + 0.694558
−0.328026u
13
+ 0.333373u
12
+ ··· − 1.99239u − 0.0246451
a
4
=
−0.0246451u
13
+ 0.352671u
12
+ ··· + 0.273186u + 1.96774
−0.00534722u
13
+ 0.173641u
12
+ ··· − 0.303381u − 0.328026
a
8
=
0.967744u
13
− 0.943099u
12
+ ··· − 7.60104u + 0.694558
−u
a
12
=
−1.00142u
13
+ 1.17112u
12
+ ··· + 10.0376u − 0.867819
0.328026u
13
− 0.333373u
12
+ ··· + 1.99239u + 0.0246451
a
1
=
−0.115338u
13
− 0.488695u
12
+ ··· + 1.49454u + 2.39877
0.127699u
13
− 0.330520u
12
+ ··· + 0.882317u + 0.772326
a
6
=
0.639718u
13
− 0.609726u
12
+ ··· − 9.59343u + 0.669913
−0.328026u
13
+ 0.333373u
12
+ ··· − 1.99239u − 0.0246451
a
5
=
0.495091u
13
+ 0.698721u
12
+ ··· − 12.6713u − 2.60480
−0.333373u
13
+ 0.507014u
12
+ ··· − 2.29577u − 1.35267
a
10
=
1.00142u
13
− 1.17112u
12
+ ··· − 10.0376u + 0.867819
−0.742720u
13
+ 0.616688u
12
+ ··· − 0.824103u + 0.145057
a
9
=
0.258696u
13
− 0.554431u
12
+ ··· − 10.8617u + 1.01288
−0.742720u
13
+ 0.616688u
12
+ ··· − 0.824103u + 0.145057
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
585676500
162743197
u
13
+
980281103
162743197
u
12
+ ··· +
608482609
162743197
u −
380597444
162743197
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 9u
13
+ ··· − 39u + 9
c
2
u
14
− u
13
+ ··· + u + 1
c
3
u
14
+ u
13
+ ··· − u + 1
c
4
, c
8
u
14
+ 2u
12
+ ··· − u + 1
c
5
u
14
+ 5u
13
+ ··· + 4u + 5
c
6
u
14
+ u
13
+ ··· − u + 1
c
7
u
14
− 4u
13
+ ··· + 4u + 1
c
9
u
14
− u
13
+ ··· + 3u + 5
c
10
, c
11
u
14
+ 4u
13
+ ··· − 4u + 1
c
12
u
14
− 5u
13
+ ··· − 4u + 5
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− y
13
+ ··· + 441y + 81
c
2
, c
3
y
14
+ 3y
13
+ ··· − 11y + 1
c
4
, c
8
y
14
+ 4y
13
+ ··· + 9y + 1
c
5
, c
12
y
14
+ 5y
13
+ ··· + 194y + 25
c
6
y
14
+ 7y
13
+ ··· − 9y + 1
c
7
, c
10
, c
11
y
14
− 20y
13
+ ··· + 8y + 1
c
9
y
14
+ 7y
13
+ ··· − 159y + 25
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790557 + 0.311356I
a = 0.222610 − 0.126329I
b = 0.845913 − 0.487651I
−2.48510 + 1.52387I −12.05484 − 4.31807I
u = −0.790557 − 0.311356I
a = 0.222610 + 0.126329I
b = 0.845913 + 0.487651I
−2.48510 − 1.52387I −12.05484 + 4.31807I
u = 0.651265 + 0.441006I
a = 0.654355 + 0.591336I
b = −0.840663 + 0.070677I
−3.27577 − 5.02886I −3.36805 + 4.35249I
u = 0.651265 − 0.441006I
a = 0.654355 − 0.591336I
b = −0.840663 − 0.070677I
−3.27577 + 5.02886I −3.36805 − 4.35249I
u = −1.286040 + 0.174398I
a = −0.962915 − 0.327892I
b = −0.424318 − 0.274794I
0.42007 + 8.20640I 2.95833 − 6.07795I
u = −1.286040 − 0.174398I
a = −0.962915 + 0.327892I
b = −0.424318 + 0.274794I
0.42007 − 8.20640I 2.95833 + 6.07795I
u = 0.449003 + 0.276873I
a = −2.83110 + 0.52067I
b = −0.932191 − 0.915727I
1.86269 − 0.47837I 4.00892 + 2.29799I
u = 0.449003 − 0.276873I
a = −2.83110 − 0.52067I
b = −0.932191 + 0.915727I
1.86269 + 0.47837I 4.00892 − 2.29799I
u = −0.365580 + 0.259701I
a = 2.22502 + 1.59201I
b = 0.815180 − 0.576796I
1.08385 + 2.12480I 2.10872 − 3.90851I
u = −0.365580 − 0.259701I
a = 2.22502 − 1.59201I
b = 0.815180 + 0.576796I
1.08385 − 2.12480I 2.10872 + 3.90851I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75681 + 0.66656I
a = 0.711754 − 0.230141I
b = 0.662699 + 0.392339I
2.71530 − 0.58653I −0.31767 + 11.02629I
u = 1.75681 − 0.66656I
a = 0.711754 + 0.230141I
b = 0.662699 − 0.392339I
2.71530 + 0.58653I −0.31767 − 11.02629I
u = 0.08510 + 2.59262I
a = −0.019722 − 0.738947I
b = 0.37338 + 2.36028I
14.4834 − 3.0320I 4.66457 + 0.35258I
u = 0.08510 − 2.59262I
a = −0.019722 + 0.738947I
b = 0.37338 − 2.36028I
14.4834 + 3.0320I 4.66457 − 0.35258I
15
IV. I
u
4
= h−1.13 × 10
44
u
23
− 4.55 × 10
43
u
22
+ · · · + 2.57 × 10
47
b − 2.14 ×
10
47
, 6.26 × 10
45
u
23
+ 9.23 × 10
44
u
22
+ · · · + 5.24 × 10
48
a − 1.07 ×
10
49
, u
24
+ 23u
22
+ · · · − 507u + 163i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−0.00119518u
23
− 0.000176098u
22
+ ··· − 4.63707u + 2.04632
0.000438993u
23
+ 0.000177030u
22
+ ··· + 2.63368u + 0.833021
a
4
=
−0.000916187u
23
− 0.000184171u
22
+ ··· − 0.122354u + 3.09669
0.000590316u
23
+ 0.000590123u
22
+ ··· + 4.74285u + 0.522808
a
8
=
−0.00119518u
23
− 0.000176098u
22
+ ··· − 4.63707u + 2.04632
0.000297902u
23
+ 0.0000128219u
22
+ ··· + 2.52815u + 0.804317
a
12
=
−0.000437714u
23
+ 0.000247445u
22
+ ··· + 1.38888u + 0.570111
−0.000184171u
23
+ 0.000425432u
22
+ ··· + 2.63218u + 0.149338
a
1
=
−0.00343719u
23
− 0.000380507u
22
+ ··· − 11.7851u − 1.62097
−0.00160994u
23
− 0.000560518u
22
+ ··· − 7.70778u + 0.658868
a
6
=
−0.000756187u
23
+ 9.31402 × 10
−7
u
22
+ ··· − 2.00339u + 2.87935
0.000438993u
23
+ 0.000177030u
22
+ ··· + 2.63368u + 0.833021
a
5
=
0.00118185u
23
− 0.000522705u
22
+ ··· + 0.0140662u + 3.34301
0.000423989u
23
+ 0.000706459u
22
+ ··· + 5.79076u + 0.302312
a
10
=
0.000437714u
23
− 0.000247445u
22
+ ··· − 1.38888u − 0.570111
1.47188 × 10
−6
u
23
− 0.000188058u
22
+ ··· − 0.828986u − 0.109005
a
9
=
0.000439185u
23
− 0.000435503u
22
+ ··· − 2.21787u − 0.679116
1.47188 × 10
−6
u
23
− 0.000188058u
22
+ ··· − 0.828986u − 0.109005
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00110204u
23
− 0.000567243u
22
+ ··· − 7.49840u + 5.00882
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ u
5
+ 2u
4
+ u
3
+ 3u
2
+ u + 2)
4
c
2
, c
3
u
24
+ 23u
22
+ ··· + 507u + 163
c
4
, c
8
u
24
+ 2u
23
+ ··· + 7u + 1
c
5
, c
12
(u
2
+ u + 1)
12
c
6
u
24
− 3u
23
+ ··· − 412u + 2467
c
7
, c
10
, c
11
(u
6
+ 2u
5
− 3u
4
− 5u
3
+ 4u
2
+ 4u + 1)
4
c
9
u
24
+ 11u
22
+ ··· − 5445u + 1525
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
4
c
2
, c
3
y
24
+ 46y
23
+ ··· + 573599y + 26569
c
4
, c
8
y
24
+ 2y
23
+ ··· − 29y + 1
c
5
, c
12
(y
2
+ y + 1)
12
c
6
y
24
+ 41y
23
+ ··· + 45336538y + 6086089
c
7
, c
10
, c
11
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
4
c
9
y
24
+ 22y
23
+ ··· + 10441175y + 2325625
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257453 + 1.064070I
a = 0.247709 − 0.266585I
b = −1.45282 + 0.06524I
−1.92892 − 5.38658I 4.19329 + 5.73346I
u = 0.257453 − 1.064070I
a = 0.247709 + 0.266585I
b = −1.45282 − 0.06524I
−1.92892 + 5.38658I 4.19329 − 5.73346I
u = 0.261438 + 0.846267I
a = 0.06541 + 1.48893I
b = 0.662123 − 0.986027I
2.96813 + 2.91160I 7.96296 − 5.29088I
u = 0.261438 − 0.846267I
a = 0.06541 − 1.48893I
b = 0.662123 + 0.986027I
2.96813 − 2.91160I 7.96296 + 5.29088I
u = 1.055090 + 0.407250I
a = 0.348669 + 0.050187I
b = 0.385166 + 0.518251I
−1.92892 − 1.32681I 4.19329 − 1.19474I
u = 1.055090 − 0.407250I
a = 0.348669 − 0.050187I
b = 0.385166 − 0.518251I
−1.92892 + 1.32681I 4.19329 + 1.19474I
u = −0.973308 + 0.878078I
a = 0.931219 + 0.383298I
b = 0.29104 − 1.39305I
2.96813 − 1.14816I 7.96296 + 1.63733I
u = −0.973308 − 0.878078I
a = 0.931219 − 0.383298I
b = 0.29104 + 1.39305I
2.96813 + 1.14816I 7.96296 − 1.63733I
u = 1.363340 + 0.050417I
a = −0.922481 − 0.292010I
b = −1.41068 − 1.51509I
2.96813 − 2.91160I 7.96296 + 5.29088I
u = 1.363340 − 0.050417I
a = −0.922481 + 0.292010I
b = −1.41068 + 1.51509I
2.96813 + 2.91160I 7.96296 − 5.29088I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.334830 + 0.354644I
a = −0.279369 + 0.071822I
b = −0.137180 − 0.680632I
−1.92892 + 5.38658I 4.19329 − 5.73346I
u = −1.334830 − 0.354644I
a = −0.279369 − 0.071822I
b = −0.137180 + 0.680632I
−1.92892 − 5.38658I 4.19329 + 5.73346I
u = −0.528305 + 0.131092I
a = 2.41293 − 0.24285I
b = −0.374948 + 0.480247I
2.96813 − 1.14816I 7.96296 + 1.63733I
u = −0.528305 − 0.131092I
a = 2.41293 + 0.24285I
b = −0.374948 − 0.480247I
2.96813 + 1.14816I 7.96296 − 1.63733I
u = 0.097980 + 0.171071I
a = 1.73398 − 1.03783I
b = 1.055780 + 0.485788I
−1.92892 − 1.32681I 4.19329 − 1.19474I
u = 0.097980 − 0.171071I
a = 1.73398 + 1.03783I
b = 1.055780 − 0.485788I
−1.92892 + 1.32681I 4.19329 + 1.19474I
u = 0.31655 + 2.39342I
a = 0.164927 − 0.770147I
b = 0.15146 + 1.82908I
14.5877 + 0.3793I 5.34374 + 0.53819I
u = 0.31655 − 2.39342I
a = 0.164927 + 0.770147I
b = 0.15146 − 1.82908I
14.5877 − 0.3793I 5.34374 − 0.53819I
u = −0.08751 + 2.56563I
a = −0.083936 − 0.735940I
b = −0.11921 + 2.32826I
14.5877 − 4.4391I 5.34374 + 6.39001I
u = −0.08751 − 2.56563I
a = −0.083936 + 0.735940I
b = −0.11921 − 2.32826I
14.5877 + 4.4391I 5.34374 − 6.39001I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34061 + 2.54807I
a = −0.039494 − 0.738614I
b = −1.11776 + 2.21280I
14.5877 + 4.4391I 5.34374 − 6.39001I
u = −0.34061 − 2.54807I
a = −0.039494 + 0.738614I
b = −1.11776 − 2.21280I
14.5877 − 4.4391I 5.34374 + 6.39001I
u = −0.08729 + 2.75540I
a = −0.076498 − 0.685495I
b = 0.56702 + 2.84260I
14.5877 − 0.3793I 5.34374 + 0.I
u = −0.08729 − 2.75540I
a = −0.076498 + 0.685495I
b = 0.56702 − 2.84260I
14.5877 + 0.3793I 5.34374 + 0.I
21
V. I
u
5
= hb + u − 1, a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u − 1
a
7
=
u − 1
−u + 1
a
4
=
u
0
a
8
=
u − 1
1
a
12
=
−u + 1
u − 1
a
1
=
1
0
a
6
=
0
−u + 1
a
5
=
1
−u
a
10
=
u − 1
1
a
9
=
u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 5
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
, c
4
, c
5
u
2
− u + 1
c
3
, c
10
, c
11
(u − 1)
2
c
6
, c
12
u
2
+ u + 1
c
7
, c
8
, c
9
(u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
4
, c
5
c
6
, c
12
y
2
+ y + 1
c
3
, c
7
, c
8
c
9
, c
10
, c
11
(y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
25
VI. I
u
6
= hb
2
− b + 1, a − 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
−1
a
3
=
1
1
a
7
=
1
b
a
4
=
b
0
a
8
=
1
b − 1
a
12
=
−1
−b
a
1
=
1
0
a
6
=
b + 1
b
a
5
=
2b
b − 1
a
10
=
1
b − 1
a
9
=
b
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b + 1
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
, c
4
, c
7
(u + 1)
2
c
3
, c
6
, c
12
u
2
+ u + 1
c
5
, c
8
, c
9
u
2
− u + 1
c
10
, c
11
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
4
, c
7
c
10
, c
11
(y −1)
2
c
3
, c
5
, c
6
c
8
, c
9
, c
12
y
2
+ y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
u = −1.00000
a = 1.00000
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u
6
− 4u
5
+ 9u
4
− 11u
3
+ 8u
2
− 3u + 1)
· ((u
6
+ u
5
+ 2u
4
+ u
3
+ 3u
2
+ u + 2)
4
)(u
14
− 9u
13
+ ··· − 39u + 9)
· (u
15
− 8u
14
+ ··· − 26u + 4)
c
2
(u + 1)
2
(u
2
− u + 1)(u
6
+ 8u
4
− 2u
3
+ 4u
2
− u + 1)
· (u
14
− u
13
+ ··· + u + 1)(u
15
− u
14
+ ··· − 2u − 1)
· (u
24
+ 23u
22
+ ··· + 507u + 163)
c
3
(u − 1)
2
(u
2
+ u + 1)(u
6
+ 8u
4
− 2u
3
+ 4u
2
− u + 1)
· (u
14
+ u
13
+ ··· − u + 1)(u
15
− u
14
+ ··· − 2u − 1)
· (u
24
+ 23u
22
+ ··· + 507u + 163)
c
4
, c
8
((u + 1)
2
)(u
2
− u + 1)(u
6
− 2u
3
+ ··· − 3u + 1)(u
14
+ 2u
12
+ ··· − u + 1)
· (u
15
+ u
12
+ ··· + 6u
2
− 1)(u
24
+ 2u
23
+ ··· + 7u + 1)
c
5
(u
2
− u + 1)
2
(u
2
+ u + 1)
12
(u
3
− 2u
2
+ 3u − 1)
2
· (u
14
+ 5u
13
+ ··· + 4u + 5)(u
15
− 8u
14
+ ··· − 128u + 32)
c
6
((u
2
+ u + 1)
2
)(u
6
− u
5
+ ··· − 5u + 1)(u
14
+ u
13
+ ··· − u + 1)
· (u
15
+ 4u
14
+ ··· + 14u + 1)(u
24
− 3u
23
+ ··· − 412u + 2467)
c
7
(u + 1)
4
(u
6
− 3u
5
+ 5u
3
− u
2
− 2u + 1)
· ((u
6
+ 2u
5
+ ··· + 4u + 1)
4
)(u
14
− 4u
13
+ ··· + 4u + 1)
· (u
15
− 6u
14
+ ··· + 28u − 16)
c
9
(u + 1)
2
(u
2
− u + 1)(u
6
− 5u
5
+ 13u
4
− 16u
3
+ 12u
2
− 5u + 1)
· (u
14
− u
13
+ ··· + 3u + 5)(u
15
+ 4u
14
+ ··· − 18u − 9)
· (u
24
+ 11u
22
+ ··· − 5445u + 1525)
c
10
, c
11
(u − 1)
4
(u
6
− 3u
5
+ 5u
3
− u
2
− 2u + 1)
· ((u
6
+ 2u
5
+ ··· + 4u + 1)
4
)(u
14
+ 4u
13
+ ··· − 4u + 1)
· (u
15
− 6u
14
+ ··· + 28u − 16)
c
12
((u
2
+ u + 1)
14
)(u
3
− 2u
2
+ 3u − 1)
2
(u
14
− 5u
13
+ ··· − 4u + 5)
· (u
15
− 8u
14
+ ··· − 128u + 32)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
4
(y
6
+ 2y
5
+ 9y
4
+ y
3
+ 16y
2
+ 7y + 1)
· (y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
4
· (y
14
− y
13
+ ··· + 441y + 81)(y
15
+ 2y
13
+ ··· − 68y −16)
c
2
, c
3
(y −1)
2
(y
2
+ y + 1)(y
6
+ 16y
5
+ 72y
4
+ 62y
3
+ 28y
2
+ 7y + 1)
· (y
14
+ 3y
13
+ ··· − 11y + 1)(y
15
+ 31y
14
+ ··· − 8y −1)
· (y
24
+ 46y
23
+ ··· + 573599y + 26569)
c
4
, c
8
(y −1)
2
(y
2
+ y + 1)(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
14
+ 4y
13
+ ··· + 9y + 1)(y
15
+ 12y
13
+ ··· + 12y −1)
· (y
24
+ 2y
23
+ ··· − 29y + 1)
c
5
, c
12
((y
2
+ y + 1)
14
)(y
3
+ 2y
2
+ 5y −1)
2
(y
14
+ 5y
13
+ ··· + 194y + 25)
· (y
15
+ 2y
14
+ ··· − 3584y −1024)
c
6
(y
2
+ y + 1)
2
(y
6
+ 13y
5
+ 65y
4
+ 104y
3
+ 78y
2
− 9y + 1)
· (y
14
+ 7y
13
+ ··· − 9y + 1)(y
15
+ 26y
14
+ ··· + 34y −1)
· (y
24
+ 41y
23
+ ··· + 45336538y + 6086089)
c
7
, c
10
, c
11
(y −1)
4
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
4
· (y
6
− 9y
5
+ ··· − 6y + 1)(y
14
− 20y
13
+ ··· + 8y + 1)
· (y
15
− 20y
14
+ ··· − 1232y −256)
c
9
(y −1)
2
(y
2
+ y + 1)(y
6
+ y
5
+ 33y
4
+ 8y
3
+ 10y
2
− y + 1)
· (y
14
+ 7y
13
+ ··· − 159y + 25)(y
15
+ 14y
14
+ ··· − 288y −81)
· (y
24
+ 22y
23
+ ··· + 10441175y + 2325625)
31
