12n
0201
(K12n
0201
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 11 3 12 5 8 6 10
Solving Sequence
3,5
2 1
4,10
9 6 12 8 7 11
c
2
c
1
c
4
c
9
c
5
c
12
c
8
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.14997 × 10
27
u
29
+ 1.82430 × 10
28
u
28
+ ··· + 1.93982 × 10
29
b + 5.49324 × 10
27
,
4.70210 × 10
29
u
29
+ 1.55178 × 10
30
u
28
+ ··· + 1.61005 × 10
31
a + 6.19868 × 10
31
,
u
30
+ 5u
29
+ ··· − 172u − 16i
I
u
2
= h−5u
4
a
3
− 6u
4
a
2
+ ··· − 20a + 39, 6u
4
a
2
+ 6u
4
a + ··· + 5a − 50, u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1i
I
u
3
= h−u
14
− 5u
13
− 6u
12
+ 9u
11
+ 26u
10
+ 10u
9
− 21u
8
− 15u
7
+ 6u
6
− 7u
5
− 19u
4
+ 2u
3
+ 15u
2
+ b + 3u − 3,
3u
14
+ 15u
13
+ ··· + a + 3,
u
15
+ 5u
14
+ 6u
13
− 9u
12
− 25u
11
− 7u
10
+ 22u
9
+ 10u
8
− 11u
7
+ 7u
6
+ 18u
5
− 6u
4
− 15u
3
+ 4u − 1i
I
u
4
= ha
2
+ 2b − a + 2, a
3
+ 2a + 1, u − 1i
I
u
5
= h−13u
5
a
3
− 13u
5
a
2
+ ··· + a + 2, u
5
a
3
− 3u
5
a
2
+ ··· − 31a + 33, u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1i
I
u
6
= h−a
3
+ b − 2a + 1, a
4
− a
3
+ 2a
2
− 2a + 1, u − 1i
* 6 irreducible components of dim
C
= 0, with total 96 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
=
h5.15×10
27
u
29
+1.82×10
28
u
28
+· · ·+1.94×10
29
b+5.49×10
27
, 4.70×10
29
u
29
+
1.55 × 10
30
u
28
+ · · · + 1.61 × 10
31
a + 6.20 × 10
31
, u
30
+ 5u
29
+ · · · − 172u − 16i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−0.0292047u
29
− 0.0963807u
28
+ ··· + 15.3253u − 3.84999
−0.0265487u
29
− 0.0940447u
28
+ ··· + 5.13027u − 0.0283182
a
9
=
−0.0292047u
29
− 0.0963807u
28
+ ··· + 15.3253u − 3.84999
0.0239871u
29
+ 0.113617u
28
+ ··· − 2.94099u − 0.822600
a
6
=
−0.0333701u
29
− 0.154719u
28
+ ··· + 4.11599u + 2.89975
−0.0107619u
29
− 0.0419176u
28
+ ··· + 0.102195u + 0.142700
a
12
=
0.0442756u
29
+ 0.200796u
28
+ ··· − 3.91736u − 2.44196
−0.00562573u
29
− 0.00670684u
28
+ ··· − 1.22478u − 0.441173
a
8
=
0.0525283u
29
+ 0.229276u
28
+ ··· + 1.10359u − 4.04234
0.0233792u
29
+ 0.0945798u
28
+ ··· + 0.173151u − 0.289600
a
7
=
0.0291491u
29
+ 0.134696u
28
+ ··· + 0.930435u − 3.75274
0.0233792u
29
+ 0.0945798u
28
+ ··· + 0.173151u − 0.289600
a
11
=
0.168494u
29
+ 0.707380u
28
+ ··· − 22.8757u − 5.50128
−0.00570701u
29
− 0.0157006u
28
+ ··· + 0.569930u − 0.316142
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.406284u
29
− 1.66706u
28
+ ··· + 56.3610u − 5.50399
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 27u
29
+ ··· + 35696u + 256
c
2
, c
4
u
30
− 5u
29
+ ··· + 172u − 16
c
3
, c
7
u
30
− 6u
29
+ ··· + 736u + 128
c
5
, c
6
, c
9
c
11
u
30
+ 10u
28
+ ··· + u − 1
c
8
u
30
+ 24u
29
+ ··· + 34816u + 2048
c
10
, c
12
u
30
− u
29
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 43y
29
+ ··· − 1144368896y + 65536
c
2
, c
4
y
30
− 27y
29
+ ··· − 35696y + 256
c
3
, c
7
y
30
+ 12y
29
+ ··· − 289792y + 16384
c
5
, c
6
, c
9
c
11
y
30
+ 20y
29
+ ··· − 5y + 1
c
8
y
30
+ 12y
29
+ ··· − 46137344y + 4194304
c
10
, c
12
y
30
− 23y
29
+ ··· − 40y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185580 + 0.944093I
a = −1.001730 + 0.055927I
b = −1.130640 − 0.094807I
−0.96646 − 3.13608I −4.74984 + 4.49793I
u = 0.185580 − 0.944093I
a = −1.001730 − 0.055927I
b = −1.130640 + 0.094807I
−0.96646 + 3.13608I −4.74984 − 4.49793I
u = 1.09059
a = −0.312198
b = −1.15451
−2.10768 1.10790
u = −0.640861 + 0.910736I
a = 0.987047 − 0.263529I
b = 0.763609 − 0.165945I
6.62408 + 4.56917I −5.77654 − 9.05645I
u = −0.640861 − 0.910736I
a = 0.987047 + 0.263529I
b = 0.763609 + 0.165945I
6.62408 − 4.56917I −5.77654 + 9.05645I
u = 0.412058 + 1.046100I
a = 1.320550 − 0.089510I
b = 1.142840 + 0.316503I
2.28381 − 11.34220I −5.85157 + 7.46971I
u = 0.412058 − 1.046100I
a = 1.320550 + 0.089510I
b = 1.142840 − 0.316503I
2.28381 + 11.34220I −5.85157 − 7.46971I
u = −0.858059 + 0.076225I
a = 0.40465 − 1.62711I
b = 0.221594 − 0.481448I
8.06685 + 5.26278I 9.69455 − 9.24591I
u = −0.858059 − 0.076225I
a = 0.40465 + 1.62711I
b = 0.221594 + 0.481448I
8.06685 − 5.26278I 9.69455 + 9.24591I
u = 0.697419 + 0.488961I
a = −0.219398 + 0.713511I
b = −0.189158 − 0.686223I
−3.18199 − 1.29456I −12.77780 − 2.70196I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697419 − 0.488961I
a = −0.219398 − 0.713511I
b = −0.189158 + 0.686223I
−3.18199 + 1.29456I −12.77780 + 2.70196I
u = −0.980322 + 0.821398I
a = −0.268522 + 0.673529I
b = −0.414628 + 0.219363I
5.73142 + 1.70454I −14.08727 − 0.46304I
u = −0.980322 − 0.821398I
a = −0.268522 − 0.673529I
b = −0.414628 − 0.219363I
5.73142 − 1.70454I −14.08727 + 0.46304I
u = 0.983080 + 0.840486I
a = −0.207226 − 0.993870I
b = −0.217086 − 0.194262I
0.63688 + 4.93892I −8.17431 − 4.19554I
u = 0.983080 − 0.840486I
a = −0.207226 + 0.993870I
b = −0.217086 + 0.194262I
0.63688 − 4.93892I −8.17431 + 4.19554I
u = 0.529897 + 0.387033I
a = 0.760579 + 0.099172I
b = 0.272048 − 0.498030I
−0.616430 − 1.153860I −7.46498 + 5.62168I
u = 0.529897 − 0.387033I
a = 0.760579 − 0.099172I
b = 0.272048 + 0.498030I
−0.616430 + 1.153860I −7.46498 − 5.62168I
u = 1.329220 + 0.243682I
a = 0.323500 + 0.469369I
b = 1.88537 − 0.37732I
−4.25514 − 1.03783I −6.94488 + 3.56711I
u = 1.329220 − 0.243682I
a = 0.323500 − 0.469369I
b = 1.88537 + 0.37732I
−4.25514 + 1.03783I −6.94488 − 3.56711I
u = −1.46779 + 0.42678I
a = 0.428034 − 0.659397I
b = 1.77991 − 0.18253I
−6.26616 + 8.18280I −7.69035 − 5.49765I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46779 − 0.42678I
a = 0.428034 + 0.659397I
b = 1.77991 + 0.18253I
−6.26616 − 8.18280I −7.69035 + 5.49765I
u = −1.57146 + 0.14677I
a = 0.578643 + 0.350914I
b = 2.02947 + 0.31224I
−10.76200 + 3.67525I −12.88309 − 1.54091I
u = −1.57146 − 0.14677I
a = 0.578643 − 0.350914I
b = 2.02947 − 0.31224I
−10.76200 − 3.67525I −12.88309 + 1.54091I
u = 1.56632 + 0.22150I
a = −0.528754 − 0.726360I
b = −1.94785 − 0.95867I
−0.77063 − 8.39049I −8.00000 + 5.59781I
u = 1.56632 − 0.22150I
a = −0.528754 + 0.726360I
b = −1.94785 + 0.95867I
−0.77063 + 8.39049I −8.00000 − 5.59781I
u = −1.54411 + 0.40410I
a = −0.646501 + 0.789954I
b = −2.35333 + 0.65826I
−3.9951 + 16.5974I −8.00000 − 7.96952I
u = −1.54411 − 0.40410I
a = −0.646501 − 0.789954I
b = −2.35333 − 0.65826I
−3.9951 − 16.5974I −8.00000 + 7.96952I
u = −1.64278 + 0.07145I
a = −0.548824 − 0.489947I
b = −1.50370 − 0.48413I
−9.12603 − 2.01137I −11.51571 + 3.04989I
u = −1.64278 − 0.07145I
a = −0.548824 + 0.489947I
b = −1.50370 + 0.48413I
−9.12603 + 2.01137I −11.51571 − 3.04989I
u = −0.0869836
a = −5.20191
b = −0.522412
−0.887138 −11.1170
7
II. I
u
2
= h−5u
4
a
3
− 6u
4
a
2
+ · · · − 20a + 39, 6u
4
a
2
+ 6u
4
a + · · · + 5a −
50, u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
a
0.172414a
3
u
4
+ 0.206897a
2
u
4
+ ··· + 0.689655a − 1.34483
a
9
=
a
0.172414a
3
u
4
+ 0.206897a
2
u
4
+ ··· + 0.689655a − 1.34483
a
6
=
−a
2
u
−0.448276a
3
u
4
− 1.13793a
2
u
4
+ ··· + 0.206897a + 0.896552
a
12
=
−0.206897a
3
u
4
− 0.448276a
2
u
4
+ ··· + 1.17241a + 4.41379
−0.551724a
3
u
4
− 0.862069a
2
u
4
+ ··· + 0.793103a + 3.10345
a
8
=
−1
−u
3
+ 2u − 1
a
7
=
u
3
− 2u
−u
3
+ 2u − 1
a
11
=
−0.172414a
3
u
4
− 0.206897a
2
u
4
+ ··· + 1.31034a + 1.34483
−0.310345a
3
u
4
− 0.172414a
2
u
4
+ ··· − 0.241379a − 1.37931
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
20
29
u
4
a
3
−
24
29
u
4
a
2
+ ··· +
36
29
a −
18
29
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
4
c
2
, c
4
(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
4
c
3
, c
7
(u
5
+ 3u
4
+ 6u
3
+ 7u
2
+ 4u + 2)
4
c
5
, c
6
, c
9
c
11
u
20
+ u
19
+ ··· − 88u + 43
c
8
(u
2
− u + 1)
10
c
10
, c
12
u
20
− 3u
19
+ ··· − 204u + 61
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y −1)
4
c
2
, c
4
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
4
c
3
, c
7
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y −4)
4
c
5
, c
6
, c
9
c
11
y
20
+ 9y
19
+ ··· + 8424y + 1849
c
8
(y
2
+ y + 1)
10
c
10
, c
12
y
20
− 7y
19
+ ··· + 49640y + 3721
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331409 + 0.386277I
a = 1.34411 + 1.58943I
b = 1.46009 + 0.56077I
4.56162 + 0.89106I −2.71808 + 2.59039I
u = 0.331409 + 0.386277I
a = 2.21697 + 1.44611I
b = 1.55827 − 1.58798I
4.56162 − 3.16871I −2.71808 + 9.51860I
u = 0.331409 + 0.386277I
a = −2.71697 − 0.58008I
b = −0.264187 + 0.240329I
4.56162 − 3.16871I −2.71808 + 9.51860I
u = 0.331409 + 0.386277I
a = −1.84411 − 2.45545I
b = −0.94003 + 1.23377I
4.56162 + 0.89106I −2.71808 + 2.59039I
u = 0.331409 − 0.386277I
a = 1.34411 − 1.58943I
b = 1.46009 − 0.56077I
4.56162 − 0.89106I −2.71808 − 2.59039I
u = 0.331409 − 0.386277I
a = 2.21697 − 1.44611I
b = 1.55827 + 1.58798I
4.56162 + 3.16871I −2.71808 − 9.51860I
u = 0.331409 − 0.386277I
a = −2.71697 + 0.58008I
b = −0.264187 − 0.240329I
4.56162 + 3.16871I −2.71808 − 9.51860I
u = 0.331409 − 0.386277I
a = −1.84411 + 2.45545I
b = −0.94003 − 1.23377I
4.56162 − 0.89106I −2.71808 − 2.59039I
u = 1.49784
a = −0.736571 + 0.258832I
b = −2.15778 + 0.06792I
−3.58001 − 2.02988I −8.28576 + 3.46410I
u = 1.49784
a = −0.736571 − 0.258832I
b = −2.15778 − 0.06792I
−3.58001 + 2.02988I −8.28576 − 3.46410I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49784
a = 0.236571 + 0.607193I
b = 1.35362 + 1.32492I
−3.58001 − 2.02988I −8.28576 + 3.46410I
u = 1.49784
a = 0.236571 − 0.607193I
b = 1.35362 − 1.32492I
−3.58001 + 2.02988I −8.28576 − 3.46410I
u = −1.58033 + 0.28256I
a = −0.950991 − 0.218765I
b = −2.22328 − 0.39754I
−8.52888 + 9.02707I −9.13904 − 7.01094I
u = −1.58033 + 0.28256I
a = −0.723737 + 0.541697I
b = −2.02311 + 0.30398I
−8.52888 + 4.96731I −9.13904 − 0.08273I
u = −1.58033 + 0.28256I
a = 0.450991 − 0.647260I
b = 2.26931 − 0.79527I
−8.52888 + 9.02707I −9.13904 − 7.01094I
u = −1.58033 + 0.28256I
a = 0.223737 + 0.324328I
b = 0.967085 + 0.252556I
−8.52888 + 4.96731I −9.13904 − 0.08273I
u = −1.58033 − 0.28256I
a = −0.950991 + 0.218765I
b = −2.22328 + 0.39754I
−8.52888 − 9.02707I −9.13904 + 7.01094I
u = −1.58033 − 0.28256I
a = −0.723737 − 0.541697I
b = −2.02311 − 0.30398I
−8.52888 − 4.96731I −9.13904 + 0.08273I
u = −1.58033 − 0.28256I
a = 0.450991 + 0.647260I
b = 2.26931 + 0.79527I
−8.52888 − 9.02707I −9.13904 + 7.01094I
u = −1.58033 − 0.28256I
a = 0.223737 − 0.324328I
b = 0.967085 − 0.252556I
−8.52888 − 4.96731I −9.13904 + 0.08273I
12
III.
I
u
3
= h−u
14
−5u
13
+· · ·+b−3, 3u
14
+15u
13
+· · ·+a+3, u
15
+5u
14
+· · ·+4u−1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−3u
14
− 15u
13
+ ··· + 10u − 3
u
14
+ 5u
13
+ ··· − 3u + 3
a
9
=
−3u
14
− 15u
13
+ ··· + 10u − 3
3u
14
+ 13u
13
+ ··· − 24u
2
+ 3
a
6
=
4u
14
+ 19u
13
+ ··· − 5u + 9
2u
14
+ 11u
13
+ ··· − 7u
2
− 7u
a
12
=
u
12
+ 4u
11
+ 3u
10
− 8u
9
− 14u
8
− u
7
+ 9u
6
− 2u
4
+ 9u
3
+ 6u
2
− 4u − 3
−2u
14
− 7u
13
+ ··· + 16u
2
− 3u
a
8
=
−u
12
− 3u
11
+ ··· + 4u − 1
2u
14
+ 8u
13
+ ··· − 8u
2
+ 3u
a
7
=
−2u
14
− 8u
13
+ ··· + u − 1
2u
14
+ 8u
13
+ ··· − 8u
2
+ 3u
a
11
=
−3u
14
− 15u
13
+ ··· + 10u − 2
2u
14
+ 9u
13
+ ··· − 3u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
14
+15u
13
+23u
12
−4u
11
−48u
10
−46u
9
−7u
8
−4u
7
−21u
6
+4u
5
+30u
4
+16u
3
−4u
2
−u−3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 13u
14
+ ··· + 16u − 1
c
2
u
15
+ 5u
14
+ ··· + 4u − 1
c
3
u
15
− u
14
+ ··· − 8u
2
− 1
c
4
u
15
− 5u
14
+ ··· + 4u + 1
c
5
, c
11
u
15
+ 7u
13
+ ··· − u + 1
c
6
, c
9
u
15
+ 7u
13
+ ··· − u − 1
c
7
u
15
+ u
14
+ ··· + 8u
2
+ 1
c
8
u
15
+ 5u
13
+ ··· + u − 1
c
10
, c
12
u
15
+ u
14
+ ··· + 5u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 17y
14
+ ··· − 8y −1
c
2
, c
4
y
15
− 13y
14
+ ··· + 16y −1
c
3
, c
7
y
15
+ 3y
14
+ ··· − 16y −1
c
5
, c
6
, c
9
c
11
y
15
+ 14y
14
+ ··· + 3y −1
c
8
y
15
+ 10y
14
+ ··· + y −1
c
10
, c
12
y
15
− y
14
+ ··· − 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796754 + 0.693348I
a = −0.847137 + 0.671365I
b = −0.497650 − 0.022952I
6.79252 + 3.72902I −3.12247 − 0.91109I
u = −0.796754 − 0.693348I
a = −0.847137 − 0.671365I
b = −0.497650 + 0.022952I
6.79252 − 3.72902I −3.12247 + 0.91109I
u = 0.930890 + 0.056485I
a = −0.285629 + 1.354480I
b = 4.78949 + 1.58588I
3.42636 + 1.92079I −18.2159 − 15.3647I
u = 0.930890 − 0.056485I
a = −0.285629 − 1.354480I
b = 4.78949 − 1.58588I
3.42636 − 1.92079I −18.2159 + 15.3647I
u = 0.401039 + 0.815529I
a = −0.507179 + 0.227656I
b = −0.692924 − 0.171185I
−2.12132 − 2.26307I −9.68770 + 3.58355I
u = 0.401039 − 0.815529I
a = −0.507179 − 0.227656I
b = −0.692924 + 0.171185I
−2.12132 + 2.26307I −9.68770 − 3.58355I
u = −0.989330 + 0.711734I
a = 0.287415 − 0.801453I
b = 0.343746 − 0.514545I
6.20548 + 1.67451I 3.16227 − 0.38526I
u = −0.989330 − 0.711734I
a = 0.287415 + 0.801453I
b = 0.343746 + 0.514545I
6.20548 − 1.67451I 3.16227 + 0.38526I
u = 1.36474
a = 0.285599
b = 1.95225
−4.46149 −9.01920
u = −1.46931 + 0.07528I
a = −0.353185 + 1.029040I
b = −1.57621 + 0.50876I
−1.37277 + 3.16303I −7.59589 − 1.64203I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46931 − 0.07528I
a = −0.353185 − 1.029040I
b = −1.57621 − 0.50876I
−1.37277 − 3.16303I −7.59589 + 1.64203I
u = −1.56575 + 0.31338I
a = 0.532385 − 0.260435I
b = 1.78333 − 0.18434I
−8.65053 + 6.60987I −9.62356 − 4.91898I
u = −1.56575 − 0.31338I
a = 0.532385 + 0.260435I
b = 1.78333 + 0.18434I
−8.65053 − 6.60987I −9.62356 + 4.91898I
u = 0.306844 + 0.131865I
a = 2.53053 + 3.22263I
b = 0.87409 − 1.42027I
4.53074 − 2.24627I −3.40718 + 0.47377I
u = 0.306844 − 0.131865I
a = 2.53053 − 3.22263I
b = 0.87409 + 1.42027I
4.53074 + 2.24627I −3.40718 − 0.47377I
17
IV. I
u
4
= ha
2
+ 2b − a + 2, a
3
+ 2a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
−
1
2
a
2
+
1
2
a − 1
a
9
=
a
−
1
2
a
2
−
1
2
a − 1
a
6
=
−a
2
1
2
a
2
+
1
2
a
12
=
−a
2
−
1
2
a
2
−
3
2
a
8
=
a
2
− a − 1
0
a
7
=
a
2
− a − 1
0
a
11
=
−a
2
− 2a − 1
−
1
2
a
2
+
1
2
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
17
4
a
2
+
1
2
a −
97
4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
u
3
+ 2u − 1
c
8
u
3
− 3u
2
+ 5u − 2
c
9
, c
10
, c
11
c
12
u
3
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
8
y
3
+ y
2
+ 13y −4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.22670 + 1.46771I
b = 0.164742 + 0.401127I
7.79580 − 5.13794I −15.1998 − 2.0943I
u = 1.00000
a = 0.22670 − 1.46771I
b = 0.164742 − 0.401127I
7.79580 + 5.13794I −15.1998 + 2.0943I
u = 1.00000
a = −0.453398
b = −1.32948
−2.43213 −25.3500
21
V. I
u
5
= h−13u
5
a
3
− 13u
5
a
2
+ · · · + a + 2, u
5
a
3
− 3u
5
a
2
+ · · · − 31a +
33, u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
a
1.18182a
3
u
5
+ 1.18182a
2
u
5
+ ··· − 0.0909091a − 0.181818
a
9
=
a
1.18182a
3
u
5
+ 1.18182a
2
u
5
+ ··· − 0.0909091a − 0.181818
a
6
=
−a
2
u
0.909091a
3
u
5
− 1.09091a
2
u
5
+ ··· − 0.454545a + 1.09091
a
12
=
1.09091a
3
u
5
− 0.909091a
2
u
5
+ ··· − 0.545455a + 2.90909
−2.45455a
3
u
5
− 2.45455a
2
u
5
+ ··· + 0.727273a − 0.545455
a
8
=
−u
5
+ 2u
3
− 2u
2
− u + 3
u
5
− u
3
+ u
2
− u
a
7
=
−2u
5
+ 3u
3
− 3u
2
+ 3
u
5
− u
3
+ u
2
− u
a
11
=
0.454545a
3
u
5
− 0.545455a
2
u
5
+ ··· − 2.72727a + 5.54545
−0.181818a
3
u
5
+ 0.818182a
2
u
5
+ ··· + 0.0909091a + 0.181818
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4
11
u
5
a
3
+
48
11
u
5
a
2
+ ··· +
20
11
a −
70
11
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1)
4
c
2
, c
4
(u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
4
c
3
, c
7
(u
3
− u
2
+ 2u − 1)
8
c
5
, c
6
, c
9
c
11
u
24
+ u
23
+ ··· − 14u + 67
c
8
(u
2
− u + 1)
12
c
10
, c
12
u
24
− 7u
23
+ ··· − 122u + 61
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
4
c
2
, c
4
(y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1)
4
c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
8
c
5
, c
6
, c
9
c
11
y
24
+ 21y
23
+ ··· + 24192y + 4489
c
8
(y
2
+ y + 1)
12
c
10
, c
12
y
24
+ 5y
23
+ ··· − 37820y + 3721
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592989 + 0.847544I
a = 0.929183 − 0.410221I
b = 0.885713 − 0.329153I
−1.37919 − 0.79824I −7.50976 − 0.48465I
u = 0.592989 + 0.847544I
a = −1.026620 − 0.271921I
b = −0.997939 − 0.570659I
−1.37919 − 4.85801I −7.50976 + 6.44355I
u = 0.592989 + 0.847544I
a = 0.515331 − 1.058190I
b = 0.1116080 − 0.0764541I
−1.37919 − 4.85801I −7.50976 + 6.44355I
u = 0.592989 + 0.847544I
a = 0.478377 + 0.632485I
b = 0.117869 − 0.114876I
−1.37919 − 0.79824I −7.50976 − 0.48465I
u = 0.592989 − 0.847544I
a = 0.929183 + 0.410221I
b = 0.885713 + 0.329153I
−1.37919 + 0.79824I −7.50976 + 0.48465I
u = 0.592989 − 0.847544I
a = −1.026620 + 0.271921I
b = −0.997939 + 0.570659I
−1.37919 + 4.85801I −7.50976 − 6.44355I
u = 0.592989 − 0.847544I
a = 0.515331 + 1.058190I
b = 0.1116080 + 0.0764541I
−1.37919 + 4.85801I −7.50976 − 6.44355I
u = 0.592989 − 0.847544I
a = 0.478377 − 0.632485I
b = 0.117869 + 0.114876I
−1.37919 + 0.79824I −7.50976 + 0.48465I
u = 1.13416
a = 0.385031 + 0.931825I
b = −0.34379 + 5.37612I
2.75839 − 2.02988I −0.98049 + 3.46410I
u = 1.13416
a = 0.385031 − 0.931825I
b = −0.34379 − 5.37612I
2.75839 + 2.02988I −0.98049 − 3.46410I
25
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13416
a = −0.217824 + 1.221440I
b = −2.14651 + 1.06279I
2.75839 + 2.02988I −0.98049 − 3.46410I
u = 1.13416
a = −0.217824 − 1.221440I
b = −2.14651 − 1.06279I
2.75839 − 2.02988I −0.98049 + 3.46410I
u = −1.47043 + 0.10268I
a = −0.155430 + 0.985327I
b = −0.719608 − 0.619193I
−1.37919 + 4.85801I −7.50976 − 6.44355I
u = −1.47043 + 0.10268I
a = 0.848595 − 0.875871I
b = 2.24219 − 1.17501I
−1.37919 + 4.85801I −7.50976 − 6.44355I
u = −1.47043 + 0.10268I
a = −0.074026 − 1.295000I
b = −0.039244 − 1.020410I
−1.37919 + 0.79824I −7.50976 + 0.48465I
u = −1.47043 + 0.10268I
a = −0.177765 + 0.639970I
b = −2.27588 + 0.59891I
−1.37919 + 0.79824I −7.50976 + 0.48465I
u = −1.47043 − 0.10268I
a = −0.155430 − 0.985327I
b = −0.719608 + 0.619193I
−1.37919 − 4.85801I −7.50976 + 6.44355I
u = −1.47043 − 0.10268I
a = 0.848595 + 0.875871I
b = 2.24219 + 1.17501I
−1.37919 − 4.85801I −7.50976 + 6.44355I
u = −1.47043 − 0.10268I
a = −0.074026 + 1.295000I
b = −0.039244 + 1.020410I
−1.37919 − 0.79824I −7.50976 − 0.48465I
u = −1.47043 − 0.10268I
a = −0.177765 − 0.639970I
b = −2.27588 − 0.59891I
−1.37919 − 0.79824I −7.50976 − 0.48465I
26
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379278
a = 1.80591 + 0.63475I
b = 0.436714 + 0.501880I
2.75839 − 2.02988I −0.98049 + 3.46410I
u = −0.379278
a = 1.80591 − 0.63475I
b = 0.436714 − 0.501880I
2.75839 + 2.02988I −0.98049 − 3.46410I
u = −0.379278
a = −0.31076 + 3.22443I
b = −0.271129 + 0.788683I
2.75839 + 2.02988I −0.98049 − 3.46410I
u = −0.379278
a = −0.31076 − 3.22443I
b = −0.271129 − 0.788683I
2.75839 − 2.02988I −0.98049 + 3.46410I
27
VI. I
u
6
= h−a
3
+ b − 2a + 1, a
4
− a
3
+ 2a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
10
=
a
a
3
+ 2a − 1
a
9
=
a
a
3
+ a − 1
a
6
=
−a
2
−a
3
+ a
2
− a + 2
a
12
=
−a
2
−a
3
− a
a
8
=
1
0
a
7
=
1
0
a
11
=
−a
3
− a + 1
a
3
+ 2a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
3
+ 4a − 12
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
8
(u
2
+ u + 1)
2
c
9
, c
10
, c
11
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
(y
2
+ y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.621744 + 0.440597I
b = 0.121744 + 1.306620I
1.64493 − 2.02988I −10.00000 + 3.46410I
u = 1.00000
a = 0.621744 − 0.440597I
b = 0.121744 − 1.306620I
1.64493 + 2.02988I −10.00000 − 3.46410I
u = 1.00000
a = −0.121744 + 1.306620I
b = −0.621744 + 0.440597I
1.64493 + 2.02988I −10.00000 − 3.46410I
u = 1.00000
a = −0.121744 − 1.306620I
b = −0.621744 − 0.440597I
1.64493 − 2.02988I −10.00000 + 3.46410I
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
4
· ((u
6
+ 5u
5
+ ··· + 8u + 1)
4
)(u
15
− 13u
14
+ ··· + 16u − 1)
· (u
30
+ 27u
29
+ ··· + 35696u + 256)
c
2
(u − 1)
7
(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
4
· ((u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
4
)(u
15
+ 5u
14
+ ··· + 4u − 1)
· (u
30
− 5u
29
+ ··· + 172u − 16)
c
3
u
7
(u
3
− u
2
+ 2u − 1)
8
(u
5
+ 3u
4
+ 6u
3
+ 7u
2
+ 4u + 2)
4
· (u
15
− u
14
+ ··· − 8u
2
− 1)(u
30
− 6u
29
+ ··· + 736u + 128)
c
4
(u + 1)
7
(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
4
· ((u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
4
)(u
15
− 5u
14
+ ··· + 4u + 1)
· (u
30
− 5u
29
+ ··· + 172u − 16)
c
5
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
15
+ 7u
13
+ ··· − u + 1)
· (u
20
+ u
19
+ ··· − 88u + 43)(u
24
+ u
23
+ ··· − 14u + 67)
· (u
30
+ 10u
28
+ ··· + u − 1)
c
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
15
+ 7u
13
+ ··· − u − 1)
· (u
20
+ u
19
+ ··· − 88u + 43)(u
24
+ u
23
+ ··· − 14u + 67)
· (u
30
+ 10u
28
+ ··· + u − 1)
c
7
u
7
(u
3
− u
2
+ 2u − 1)
8
(u
5
+ 3u
4
+ 6u
3
+ 7u
2
+ 4u + 2)
4
· (u
15
+ u
14
+ ··· + 8u
2
+ 1)(u
30
− 6u
29
+ ··· + 736u + 128)
c
8
((u
2
− u + 1)
22
)(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
15
+ 5u
13
+ ··· + u − 1)
· (u
30
+ 24u
29
+ ··· + 34816u + 2048)
c
9
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
15
+ 7u
13
+ ··· − u − 1)
· (u
20
+ u
19
+ ··· − 88u + 43)(u
24
+ u
23
+ ··· − 14u + 67)
· (u
30
+ 10u
28
+ ··· + u − 1)
c
10
, c
12
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
15
+ u
14
+ ··· + 5u
2
+ 1)
· (u
20
− 3u
19
+ ··· − 204u + 61)(u
24
− 7u
23
+ ··· − 122u + 61)
· (u
30
− u
29
+ ··· − 2u + 1)
c
11
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
15
+ 7u
13
+ ··· − u + 1)
· (u
20
+ u
19
+ ··· − 88u + 43)(u
24
+ u
23
+ ··· − 14u + 67)
· (u
30
+ 10u
28
+ ··· + u − 1)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
7
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y −1)
4
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
4
· (y
15
− 17y
14
+ ··· − 8y −1)
· (y
30
− 43y
29
+ ··· − 1144368896y + 65536)
c
2
, c
4
(y −1)
7
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
4
· ((y
6
− 5y
5
+ ··· − 8y + 1)
4
)(y
15
− 13y
14
+ ··· + 16y −1)
· (y
30
− 27y
29
+ ··· − 35696y + 256)
c
3
, c
7
y
7
(y
3
+ 3y
2
+ 2y −1)
8
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y −4)
4
· (y
15
+ 3y
14
+ ··· − 16y −1)(y
30
+ 12y
29
+ ··· − 289792y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
15
+ 14y
14
+ ··· + 3y −1)
· (y
20
+ 9y
19
+ ··· + 8424y + 1849)
· (y
24
+ 21y
23
+ ··· + 24192y + 4489)(y
30
+ 20y
29
+ ··· − 5y + 1)
c
8
((y
2
+ y + 1)
24
)(y
3
+ y
2
+ 13y −4)(y
15
+ 10y
14
+ ··· + y −1)
· (y
30
+ 12y
29
+ ··· − 46137344y + 4194304)
c
10
, c
12
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
15
− y
14
+ ··· − 10y −1)
· (y
20
− 7y
19
+ ··· + 49640y + 3721)
· (y
24
+ 5y
23
+ ··· − 37820y + 3721)(y
30
− 23y
29
+ ··· − 40y + 1)
33
