12a
0737
(K12a
0737
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 12 10 2 1 6 7 5 4
Solving Sequence
5,12 6,9
10 7 11 4 1 3 8 2
c
5
c
9
c
6
c
11
c
4
c
12
c
3
c
8
c
2
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
34
− u
33
+ ··· + 8b − 7u, −u
34
+ u
33
+ ··· + 8a + 23u, u
35
− u
34
+ ··· + 5u
2
− 1i
I
u
2
= h3u
13
− u
12
− 22u
11
+ 11u
10
+ 49u
9
− 17u
8
− 35u
7
− 15u
6
− 4u
5
+ 45u
4
+ 8u
3
− 16u
2
+ 11b − 2u − 9,
5u
13
+ 2u
12
− 22u
11
− 11u
10
+ 34u
9
+ 23u
8
− 7u
7
− 25u
6
− 36u
5
+ 20u
4
+ 39u
3
− u
2
+ 11a − 7u − 15,
u
14
− 5u
12
+ 9u
10
+ u
9
− 5u
8
− 4u
7
− 3u
6
+ 6u
5
+ 4u
4
− 2u
3
− 2u − 1i
I
u
3
= h48312506401u
39
− 25481530594u
38
+ ··· + 43198696939b − 277160237401,
− 199007192694u
39
+ 322170993904u
38
+ ··· + 215993484695a + 1742428011421,
u
40
− u
39
+ ··· + 6u + 5i
I
u
4
= hb + a − 1, a
4
+ 2a
2
+ 2, u + 1i
I
u
5
= hb + a + 1, a
3
, u − 1i
* 5 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
=
hu
34
−u
33
+· · ·+8b − 7u, −u
34
+u
33
+· · ·+8a + 23u, u
35
−u
34
+· · ·+5u
2
−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
1
8
u
34
−
1
8
u
33
+ ··· −
5
2
u
3
−
23
8
u
−
1
8
u
34
+
1
8
u
33
+ ··· +
7
2
u
3
+
7
8
u
a
10
=
1
8
u
34
−
1
8
u
33
+ ··· −
5
2
u
3
−
15
8
u
−
1
8
u
34
+
1
8
u
33
+ ··· +
5
2
u
3
+
7
8
u
a
7
=
−
1
8
u
33
+
1
8
u
32
+ ··· +
5
2
u
2
+
7
8
1
8
u
33
−
1
8
u
32
+ ··· −
5
2
u
2
+
1
8
a
11
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
1
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
3
=
−
1
8
u
34
−
1
4
u
33
+ ··· −
1
8
u +
7
8
1
8
u
34
+
3
8
u
33
+ ··· +
1
8
u +
1
4
a
8
=
1
8
u
34
−
1
8
u
33
+ ··· −
13
2
u
3
−
23
8
u
u
13
− 5u
11
+ 7u
9
+ 2u
7
− 8u
5
− u
3
+ u
a
2
=
1
8
u
34
− u
33
+ ··· +
13
8
u −
7
8
1
4
u
34
+
7
8
u
33
+ ··· −
13
4
u
2
+
7
8
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3
4
u
34
+
1
4
u
33
+ ··· +
49
4
u +
15
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 17u
34
+ ··· + 4u + 4
c
2
, c
7
u
35
+ 3u
34
+ ··· + 6u + 2
c
3
u
35
− 3u
34
+ ··· + 72u + 296
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
35
− u
34
+ ··· + 5u
2
− 1
c
8
u
35
+ 9u
34
+ ··· − 70u − 46
c
12
u
35
+ 3u
34
+ ··· + 256u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 3y
34
+ ··· − 240y −16
c
2
, c
7
y
35
− 17y
34
+ ··· + 4y −4
c
3
y
35
− y
34
+ ··· + 704928y −87616
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
35
− 37y
34
+ ··· + 10y −1
c
8
y
35
+ 11y
34
+ ··· + 28820y −2116
c
12
y
35
+ 7y
34
+ ··· + 1441792y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167828 + 0.756763I
a = 0.22251 − 1.74569I
b = 0.396759 − 0.137285I
−4.21898 − 7.81840I 0.96471 + 7.49925I
u = −0.167828 − 0.756763I
a = 0.22251 + 1.74569I
b = 0.396759 + 0.137285I
−4.21898 + 7.81840I 0.96471 − 7.49925I
u = −0.086793 + 0.752466I
a = 0.11704 − 1.72052I
b = 0.203323 − 0.193454I
−5.93777 − 0.09592I −2.21151 + 0.44008I
u = −0.086793 − 0.752466I
a = 0.11704 + 1.72052I
b = 0.203323 + 0.193454I
−5.93777 + 0.09592I −2.21151 − 0.44008I
u = 0.152216 + 0.717373I
a = −0.21415 − 1.68842I
b = −0.321763 − 0.065640I
−1.80618 + 3.02164I 3.90973 − 3.95401I
u = 0.152216 − 0.717373I
a = −0.21415 + 1.68842I
b = −0.321763 + 0.065640I
−1.80618 − 3.02164I 3.90973 + 3.95401I
u = −1.300490 + 0.187880I
a = −1.52389 − 1.71909I
b = 2.06311 + 2.28997I
2.41004 + 1.41249I 9.47570 + 0.I
u = −1.300490 − 0.187880I
a = −1.52389 + 1.71909I
b = 2.06311 − 2.28997I
2.41004 − 1.41249I 9.47570 + 0.I
u = −1.311970 + 0.248425I
a = −1.07722 − 1.85643I
b = 1.68583 + 2.62705I
1.60231 − 6.99533I 7.54634 + 6.51965I
u = −1.311970 − 0.248425I
a = −1.07722 + 1.85643I
b = 1.68583 − 2.62705I
1.60231 + 6.99533I 7.54634 − 6.51965I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.331990 + 0.208218I
a = 1.25521 − 1.60201I
b = −1.72921 + 2.28481I
5.46888 + 3.18024I 12.51891 − 3.03421I
u = 1.331990 − 0.208218I
a = 1.25521 + 1.60201I
b = −1.72921 − 2.28481I
5.46888 − 3.18024I 12.51891 + 3.03421I
u = 0.161198 + 0.551221I
a = −0.29100 − 1.43200I
b = −0.174142 + 0.205041I
−0.34475 + 1.77362I 4.56578 − 5.89788I
u = 0.161198 − 0.551221I
a = −0.29100 + 1.43200I
b = −0.174142 − 0.205041I
−0.34475 − 1.77362I 4.56578 + 5.89788I
u = 1.38810 + 0.33957I
a = 0.48176 − 1.67486I
b = −1.06352 + 2.91942I
3.48171 + 8.10374I 6.00000 − 4.49399I
u = 1.38810 − 0.33957I
a = 0.48176 + 1.67486I
b = −1.06352 − 2.91942I
3.48171 − 8.10374I 6.00000 + 4.49399I
u = 1.43331
a = 1.28549
b = −1.20757
8.30021 10.1560
u = 1.43493 + 0.26536I
a = 0.64645 − 1.33183I
b = −0.86486 + 2.42158I
9.31625 + 3.51006I 13.29415 + 0.I
u = 1.43493 − 0.26536I
a = 0.64645 + 1.33183I
b = −0.86486 − 2.42158I
9.31625 − 3.51006I 13.29415 + 0.I
u = −1.41859 + 0.34725I
a = −0.40165 − 1.57935I
b = 0.89723 + 2.93938I
8.28583 − 11.00080I 12.8696 + 5.9885I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41859 − 0.34725I
a = −0.40165 + 1.57935I
b = 0.89723 − 2.93938I
8.28583 + 11.00080I 12.8696 − 5.9885I
u = 1.41768 + 0.36311I
a = 0.35041 − 1.60931I
b = −0.89725 + 3.02458I
5.9000 + 16.1532I 9.74356 − 9.72712I
u = 1.41768 − 0.36311I
a = 0.35041 + 1.60931I
b = −0.89725 − 3.02458I
5.9000 − 16.1532I 9.74356 + 9.72712I
u = −1.43323 + 0.29831I
a = −0.53750 − 1.42612I
b = 0.84249 + 2.64127I
10.04470 − 8.52981I 14.2743 + 6.4652I
u = −1.43323 − 0.29831I
a = −0.53750 + 1.42612I
b = 0.84249 − 2.64127I
10.04470 + 8.52981I 14.2743 − 6.4652I
u = −0.314010 + 0.390794I
a = 0.71540 − 1.22571I
b = 0.025527 + 0.500038I
−1.48480 + 2.02330I 2.63866 + 1.25082I
u = −0.314010 − 0.390794I
a = 0.71540 + 1.22571I
b = 0.025527 − 0.500038I
−1.48480 − 2.02330I 2.63866 − 1.25082I
u = −1.50324 + 0.03422I
a = −0.874162 − 0.174169I
b = 0.489019 + 0.337659I
13.70520 − 1.40021I 16.4192 + 0.I
u = −1.50324 − 0.03422I
a = −0.874162 + 0.174169I
b = 0.489019 − 0.337659I
13.70520 + 1.40021I 16.4192 + 0.I
u = −0.450369 + 0.202730I
a = 1.37562 − 0.88797I
b = −0.510703 + 0.597542I
−1.04042 − 4.50619I 4.53729 + 8.22316I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450369 − 0.202730I
a = 1.37562 + 0.88797I
b = −0.510703 − 0.597542I
−1.04042 + 4.50619I 4.53729 − 8.22316I
u = 1.50640 + 0.06553I
a = 0.834503 − 0.327285I
b = −0.448322 + 0.642057I
12.03530 + 6.55130I 13.7606 − 5.2864I
u = 1.50640 − 0.06553I
a = 0.834503 + 0.327285I
b = −0.448322 − 0.642057I
12.03530 − 6.55130I 13.7606 + 5.2864I
u = 0.377334 + 0.098062I
a = −1.222090 − 0.396295I
b = 0.510257 + 0.241115I
0.940032 + 0.385042I 10.54272 − 2.65749I
u = 0.377334 − 0.098062I
a = −1.222090 + 0.396295I
b = 0.510257 − 0.241115I
0.940032 − 0.385042I 10.54272 + 2.65749I
8
II. I
u
2
=
h3u
13
−u
12
+· · ·+11b−9, 5u
13
+2u
12
+· · ·+11a−15, u
14
−5u
12
+· · ·−2u−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
−0.454545u
13
− 0.181818u
12
+ ··· + 0.636364u + 1.36364
−0.272727u
13
+ 0.0909091u
12
+ ··· + 0.181818u + 0.818182
a
10
=
−u
13
+ 5u
11
− 9u
9
− u
8
+ 5u
7
+ 4u
6
+ 3u
5
− 6u
4
− 4u
3
+ 2u
2
+ 2
−0.545455u
13
+ 0.181818u
12
+ ··· + 0.363636u + 0.636364
a
7
=
0.636364u
13
− 0.545455u
12
+ ··· + 1.90909u − 0.909091
−1
a
11
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
1
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
3
=
−0.818182u
13
+ 0.272727u
12
+ ··· + 0.545455u + 1.45455
u
8
− 2u
6
+ u
3
+ 2u
2
− u
a
8
=
−0.454545u
13
− 0.181818u
12
+ ··· + 0.636364u + 1.36364
−0.272727u
13
+ 0.0909091u
12
+ ··· + 0.181818u + 0.818182
a
2
=
−0.727273u
13
− 0.0909091u
12
+ ··· + 2.81818u + 1.18182
0.0909091u
13
− 0.363636u
12
+ ··· + 0.272727u − 0.272727
(ii) Obstruction class = −1
(iii) Cusp Shapes =
16
11
u
13
−
20
11
u
12
− 4u
11
+ 4u
10
+
12
11
u
9
+
56
11
u
8
+
48
11
u
7
−
212
11
u
6
−
36
11
u
5
+
108
11
u
4
+
28
11
u
3
+
76
11
u
2
−
40
11
u +
18
11
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 4u
6
+ 8u
5
+ 8u
4
+ 4u
3
+ u
2
+ 2u + 1)
2
c
2
, c
7
(u
7
− 2u
5
+ 2u
3
+ u
2
− 1)
2
c
3
(u
7
+ 5u
6
+ 12u
5
+ 17u
4
+ 15u
3
+ 5u
2
− 4u − 4)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
14
− 5u
12
+ 9u
10
+ u
9
− 5u
8
− 4u
7
− 3u
6
+ 6u
5
+ 4u
4
− 2u
3
− 2u − 1
c
8
(u
7
+ 2u
5
+ 2u
4
+ 4u
3
+ u
2
+ 2u − 1)
2
c
12
(u
7
+ 2u
5
− 2u
4
+ 4u
3
− u
2
+ 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 8y
5
− 4y
4
+ 24y
3
− y
2
+ 2y −1)
2
c
2
, c
7
(y
7
− 4y
6
+ 8y
5
− 8y
4
+ 4y
3
− y
2
+ 2y −1)
2
c
3
(y
7
− y
6
+ 4y
5
+ 13y
4
− y
3
− 9y
2
+ 56y −16)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
14
− 10y
13
+ ··· − 4y + 1
c
8
, c
12
(y
7
+ 4y
6
+ 12y
5
+ 16y
4
+ 20y
3
+ 19y
2
+ 6y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957061 + 0.519308I
a = 0.514399 + 0.255510I
b = −1.40007 − 0.49397I
5.11553 − 1.84683I 13.12815 + 1.09324I
u = 0.957061 − 0.519308I
a = 0.514399 − 0.255510I
b = −1.40007 + 0.49397I
5.11553 + 1.84683I 13.12815 − 1.09324I
u = −0.239949 + 0.878713I
a = −1.07659 + 1.37148I
b = 0.018151 + 0.213597I
0.63279 − 11.68630I 6.29693 + 8.84509I
u = −0.239949 − 0.878713I
a = −1.07659 − 1.37148I
b = 0.018151 − 0.213597I
0.63279 + 11.68630I 6.29693 − 8.84509I
u = 1.14029
a = −0.464314
b = 0.191074
2.04041 4.35900
u = −1.168590 + 0.306255I
a = 0.757257 + 0.859295I
b = −1.53466 − 1.20028I
−2.65620 − 3.76357I 1.39540 + 4.24459I
u = −1.168590 − 0.306255I
a = 0.757257 − 0.859295I
b = −1.53466 + 1.20028I
−2.65620 + 3.76357I 1.39540 − 4.24459I
u = −1.321610 + 0.182486I
a = −0.214561 − 0.416784I
b = 1.52571 + 1.12991I
5.11553 − 1.84683I 13.12815 + 1.09324I
u = −1.321610 − 0.182486I
a = −0.214561 + 0.416784I
b = 1.52571 − 1.12991I
5.11553 + 1.84683I 13.12815 − 1.09324I
u = 0.043481 + 0.649444I
a = 1.06596 + 1.83916I
b = −0.617135 + 0.405783I
−2.65620 + 3.76357I 1.39540 − 4.24459I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043481 − 0.649444I
a = 1.06596 − 1.83916I
b = −0.617135 − 0.405783I
−2.65620 − 3.76357I 1.39540 + 4.24459I
u = 1.365780 + 0.312423I
a = −0.455826 + 1.037870I
b = 1.45156 − 2.32441I
0.63279 + 11.68630I 6.29693 − 8.84509I
u = 1.365780 − 0.312423I
a = −0.455826 − 1.037870I
b = 1.45156 + 2.32441I
0.63279 − 11.68630I 6.29693 + 8.84509I
u = −0.412656
a = 1.28304
b = 0.921809
2.04041 4.35900
13
III.
I
u
3
= h4.83×10
10
u
39
−2.55×10
10
u
38
+· · ·+4.32×10
10
b−2.77×10
11
, −1.99×
10
11
u
39
+3.22×10
11
u
38
+· · ·+2.16×10
11
a+1.74×10
12
, u
40
−u
39
+· · ·+6u+5i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
0.921357u
39
− 1.49158u
38
+ ··· + 14.4435u − 8.06704
−1.11838u
39
+ 0.589868u
38
+ ··· − 8.45803u + 6.41594
a
10
=
1
5
u
39
−
1
5
u
38
+ ··· +
24
5
u +
6
5
−0.721357u
39
+ 1.29158u
38
+ ··· − 8.64350u + 9.26704
a
7
=
−1.85341u
39
+ 1.13205u
38
+ ··· − 56.5699u − 19.7639
−1
a
11
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
1
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
3
=
−0.141219u
39
+ 0.286734u
38
+ ··· + 12.4150u + 9.11906
0.874874u
39
− 1.11047u
38
+ ··· + 30.2577u + 9.75078
a
8
=
0.125054u
39
− 0.909866u
38
+ ··· + 16.1112u + 2.54657
−0.585648u
39
+ 1.51958u
38
+ ··· − 12.9285u + 8.73631
a
2
=
−1.29679u
39
− 0.118839u
38
+ ··· + 35.8131u + 24.9355
4.70549u
39
− 0.173819u
38
+ ··· − 4.96586u − 15.7106
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
241664643308
43198696939
u
39
+
123235657656
43198696939
u
38
+ ··· −
438305923412
43198696939
u +
1059211366526
43198696939
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 9u
19
+ ··· + 2u
2
+ 1)
2
c
2
, c
7
(u
20
− u
19
+ ··· − 2u + 1)
2
c
3
(u
10
− 2u
9
+ u
8
+ 4u
6
− 6u
5
+ u
4
+ 6u
3
− 5u
2
+ 1)
4
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
40
− u
39
+ ··· + 6u + 5
c
8
(u
20
− 3u
19
+ ··· − 16u + 5)
2
c
12
(u
20
+ 3u
19
+ ··· + 16u + 5)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 3y
19
+ ··· + 4y + 1)
2
c
2
, c
7
(y
20
− 9y
19
+ ··· + 2y
2
+ 1)
2
c
3
(y
10
− 2y
9
+ ··· − 10y + 1)
4
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
40
− 31y
39
+ ··· + 204y + 25
c
8
, c
12
(y
20
+ 3y
19
+ ··· + 204y + 25)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805245 + 0.548498I
a = 0.484950 + 0.496101I
b = −1.063550 − 0.519102I
5.84675 14.3672 + 0.I
u = 0.805245 − 0.548498I
a = 0.484950 − 0.496101I
b = −1.063550 + 0.519102I
5.84675 14.3672 + 0.I
u = −0.729774 + 0.602283I
a = −0.541328 + 0.641388I
b = 0.884543 − 0.553467I
4.40946 − 4.65452I 11.20346 + 6.04247I
u = −0.729774 − 0.602283I
a = −0.541328 − 0.641388I
b = 0.884543 + 0.553467I
4.40946 + 4.65452I 11.20346 − 6.04247I
u = −1.066160 + 0.285066I
a = 0.937984 + 0.759238I
b = −1.51409 − 0.75635I
−1.54326 + 3.92983I 2.95600 − 3.21471I
u = −1.066160 − 0.285066I
a = 0.937984 − 0.759238I
b = −1.51409 + 0.75635I
−1.54326 − 3.92983I 2.95600 + 3.21471I
u = 0.254311 + 0.850232I
a = 1.03350 + 1.37276I
b = −0.082493 + 0.163450I
2.96491 + 6.68616I 9.50669 − 5.21994I
u = 0.254311 − 0.850232I
a = 1.03350 − 1.37276I
b = −0.082493 − 0.163450I
2.96491 − 6.68616I 9.50669 + 5.21994I
u = −1.041820 + 0.410831I
a = −0.406675 + 0.084930I
b = 1.53742 − 0.18333I
1.016470 − 0.519983I 6.28339 + 0.77505I
u = −1.041820 − 0.410831I
a = −0.406675 − 0.084930I
b = 1.53742 + 0.18333I
1.016470 + 0.519983I 6.28339 − 0.77505I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006990 + 0.539596I
a = −0.566442 + 0.194865I
b = 1.53566 − 0.53787I
2.96491 + 6.68616I 9.50669 − 5.21994I
u = −1.006990 − 0.539596I
a = −0.566442 − 0.194865I
b = 1.53566 + 0.53787I
2.96491 − 6.68616I 9.50669 + 5.21994I
u = 1.120430 + 0.232272I
a = −0.796352 + 0.683257I
b = 1.25298 − 0.91224I
1.016470 + 0.519983I 6.28339 − 0.77505I
u = 1.120430 − 0.232272I
a = −0.796352 − 0.683257I
b = 1.25298 + 0.91224I
1.016470 − 0.519983I 6.28339 + 0.77505I
u = 0.331708 + 0.777509I
a = 0.88385 + 1.31325I
b = −0.233626 − 0.031651I
4.40946 + 4.65452I 11.20346 − 6.04247I
u = 0.331708 − 0.777509I
a = 0.88385 − 1.31325I
b = −0.233626 + 0.031651I
4.40946 − 4.65452I 11.20346 + 6.04247I
u = −0.196460 + 0.818278I
a = −1.03861 + 1.46561I
b = 0.189464 + 0.280707I
−1.54326 − 3.92983I 2.95600 + 3.21471I
u = −0.196460 − 0.818278I
a = −1.03861 − 1.46561I
b = 0.189464 − 0.280707I
−1.54326 + 3.92983I 2.95600 − 3.21471I
u = −0.399715 + 0.718129I
a = −0.74940 + 1.23357I
b = 0.366223 − 0.161582I
3.48717 9.73375 + 0.I
u = −0.399715 − 0.718129I
a = −0.74940 − 1.23357I
b = 0.366223 + 0.161582I
3.48717 9.73375 + 0.I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.237360 + 0.242641I
a = 0.263575 − 0.258220I
b = −1.58490 + 0.63271I
1.016470 − 0.519983I 6.00000 + 0.77505I
u = 1.237360 − 0.242641I
a = 0.263575 + 0.258220I
b = −1.58490 − 0.63271I
1.016470 + 0.519983I 6.00000 − 0.77505I
u = −1.333230 + 0.081709I
a = −0.057993 − 0.502701I
b = 1.01747 + 1.42606I
5.84675 14.3672 + 0.I
u = −1.333230 − 0.081709I
a = −0.057993 + 0.502701I
b = 1.01747 − 1.42606I
5.84675 14.3672 + 0.I
u = 1.341140 + 0.170431I
a = −0.334067 + 0.811377I
b = 0.56237 − 2.00124I
3.48717 6.00000 + 0.I
u = 1.341140 − 0.170431I
a = −0.334067 − 0.811377I
b = 0.56237 + 2.00124I
3.48717 6.00000 + 0.I
u = 1.316030 + 0.310134I
a = −0.523422 + 0.987925I
b = 1.46616 − 2.00702I
−1.54326 + 3.92983I 0
u = 1.316030 − 0.310134I
a = −0.523422 − 0.987925I
b = 1.46616 + 2.00702I
−1.54326 − 3.92983I 0
u = 1.337970 + 0.218560I
a = 0.279010 − 0.420680I
b = −1.73917 + 1.10941I
2.96491 + 6.68616I 0
u = 1.337970 − 0.218560I
a = 0.279010 + 0.420680I
b = −1.73917 − 1.10941I
2.96491 − 6.68616I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.356430 + 0.031317I
a = −0.007062 − 0.585271I
b = −0.76651 + 1.67915I
4.40946 − 4.65452I 11.20346 + 6.04247I
u = 1.356430 − 0.031317I
a = −0.007062 + 0.585271I
b = −0.76651 − 1.67915I
4.40946 + 4.65452I 11.20346 − 6.04247I
u = −1.348070 + 0.225139I
a = 0.389964 + 0.898034I
b = −0.90232 − 2.12727I
4.40946 − 4.65452I 0
u = −1.348070 − 0.225139I
a = 0.389964 − 0.898034I
b = −0.90232 + 2.12727I
4.40946 + 4.65452I 0
u = −1.356410 + 0.293193I
a = 0.450021 + 1.002480I
b = −1.33232 − 2.25052I
2.96491 − 6.68616I 0
u = −1.356410 − 0.293193I
a = 0.450021 − 1.002480I
b = −1.33232 + 2.25052I
2.96491 + 6.68616I 0
u = −0.062616 + 0.525185I
a = 1.28999 + 2.16247I
b = −0.857635 + 0.387749I
−1.54326 − 3.92983I 2.95600 + 3.21471I
u = −0.062616 − 0.525185I
a = 1.28999 − 2.16247I
b = −0.857635 − 0.387749I
−1.54326 + 3.92983I 2.95600 − 3.21471I
u = −0.059388 + 0.505857I
a = −0.89150 + 2.18224I
b = 0.764328 + 0.264884I
1.016470 − 0.519983I 6.28339 + 0.77505I
u = −0.059388 − 0.505857I
a = −0.89150 − 2.18224I
b = 0.764328 − 0.264884I
1.016470 + 0.519983I 6.28339 − 0.77505I
20
IV. I
u
4
= hb + a − 1, a
4
+ 2a
2
+ 2, u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
−1
a
6
=
1
−1
a
9
=
a
−a + 1
a
10
=
a + 1
−a
a
7
=
−a
a − 1
a
11
=
1
−1
a
4
=
0
1
a
1
=
0
−1
a
3
=
−a
2
a
2
− a + 1
a
8
=
a
1
a
2
=
−2a
2
− 2
a
3
+ a
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
7
u
4
− 2u
2
+ 2
c
3
, c
8
u
4
+ 2u
2
+ 2
c
4
, c
5
, c
9
c
10
(u + 1)
4
c
6
, c
11
(u − 1)
4
c
12
u
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
7
(y
2
− 2y + 2)
2
c
3
, c
8
(y
2
+ 2y + 2)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
4
c
12
y
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.455090 + 1.098680I
b = 0.544910 − 1.098680I
0.82247 + 3.66386I 8.00000 − 4.00000I
u = −1.00000
a = 0.455090 − 1.098680I
b = 0.544910 + 1.098680I
0.82247 − 3.66386I 8.00000 + 4.00000I
u = −1.00000
a = −0.455090 + 1.098680I
b = 1.45509 − 1.09868I
0.82247 − 3.66386I 8.00000 + 4.00000I
u = −1.00000
a = −0.455090 − 1.098680I
b = 1.45509 + 1.09868I
0.82247 + 3.66386I 8.00000 − 4.00000I
24
V. I
u
5
= hb + a + 1, a
3
, u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
1
a
6
=
1
−1
a
9
=
a
−a − 1
a
10
=
a − 1
−a
a
7
=
a
−a − 1
a
11
=
−1
1
a
4
=
0
1
a
1
=
0
1
a
3
=
−a
2
a
2
+ a + 1
a
8
=
a
−1
a
2
=
0
a
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
+ 12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
12
u
3
c
4
, c
5
, c
9
c
10
(u − 1)
3
c
6
, c
11
(u + 1)
3
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
12
y
3
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
3
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
3.28987 12.0000
u = 1.00000
a = 0
b = −1.00000
3.28987 12.0000
u = 1.00000
a = 0
b = −1.00000
3.28987 12.0000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
2
− 2u + 2)
2
(u
7
+ 4u
6
+ 8u
5
+ 8u
4
+ 4u
3
+ u
2
+ 2u + 1)
2
· ((u
20
+ 9u
19
+ ··· + 2u
2
+ 1)
2
)(u
35
+ 17u
34
+ ··· + 4u + 4)
c
2
, c
7
u
3
(u
4
− 2u
2
+ 2)(u
7
− 2u
5
+ ··· + u
2
− 1)
2
(u
20
− u
19
+ ··· − 2u + 1)
2
· (u
35
+ 3u
34
+ ··· + 6u + 2)
c
3
u
3
(u
4
+ 2u
2
+ 2)(u
7
+ 5u
6
+ 12u
5
+ 17u
4
+ 15u
3
+ 5u
2
− 4u − 4)
2
· (u
10
− 2u
9
+ u
8
+ 4u
6
− 6u
5
+ u
4
+ 6u
3
− 5u
2
+ 1)
4
· (u
35
− 3u
34
+ ··· + 72u + 296)
c
4
, c
5
, c
9
c
10
(u − 1)
3
(u + 1)
4
· (u
14
− 5u
12
+ 9u
10
+ u
9
− 5u
8
− 4u
7
− 3u
6
+ 6u
5
+ 4u
4
− 2u
3
− 2u − 1)
· (u
35
− u
34
+ ··· + 5u
2
− 1)(u
40
− u
39
+ ··· + 6u + 5)
c
6
, c
11
(u − 1)
4
(u + 1)
3
· (u
14
− 5u
12
+ 9u
10
+ u
9
− 5u
8
− 4u
7
− 3u
6
+ 6u
5
+ 4u
4
− 2u
3
− 2u − 1)
· (u
35
− u
34
+ ··· + 5u
2
− 1)(u
40
− u
39
+ ··· + 6u + 5)
c
8
u
3
(u
4
+ 2u
2
+ 2)(u
7
+ 2u
5
+ 2u
4
+ 4u
3
+ u
2
+ 2u − 1)
2
· ((u
20
− 3u
19
+ ··· − 16u + 5)
2
)(u
35
+ 9u
34
+ ··· − 70u − 46)
c
12
u
7
(u
7
+ 2u
5
+ ··· + 2u + 1)
2
(u
20
+ 3u
19
+ ··· + 16u + 5)
2
· (u
35
+ 3u
34
+ ··· + 256u + 256)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
2
+ 4)
2
(y
7
+ 8y
5
− 4y
4
+ 24y
3
− y
2
+ 2y −1)
2
· ((y
20
+ 3y
19
+ ··· + 4y + 1)
2
)(y
35
+ 3y
34
+ ··· − 240y −16)
c
2
, c
7
y
3
(y
2
− 2y + 2)
2
(y
7
− 4y
6
+ 8y
5
− 8y
4
+ 4y
3
− y
2
+ 2y −1)
2
· ((y
20
− 9y
19
+ ··· + 2y
2
+ 1)
2
)(y
35
− 17y
34
+ ··· + 4y −4)
c
3
y
3
(y
2
+ 2y + 2)
2
(y
7
− y
6
+ 4y
5
+ 13y
4
− y
3
− 9y
2
+ 56y −16)
2
· ((y
10
− 2y
9
+ ··· − 10y + 1)
4
)(y
35
− y
34
+ ··· + 704928y −87616)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((y −1)
7
)(y
14
− 10y
13
+ ··· − 4y + 1)(y
35
− 37y
34
+ ··· + 10y −1)
· (y
40
− 31y
39
+ ··· + 204y + 25)
c
8
y
3
(y
2
+ 2y + 2)
2
(y
7
+ 4y
6
+ 12y
5
+ 16y
4
+ 20y
3
+ 19y
2
+ 6y −1)
2
· ((y
20
+ 3y
19
+ ··· + 204y + 25)
2
)(y
35
+ 11y
34
+ ··· + 28820y −2116)
c
12
y
7
(y
7
+ 4y
6
+ 12y
5
+ 16y
4
+ 20y
3
+ 19y
2
+ 6y −1)
2
· (y
20
+ 3y
19
+ ··· + 204y + 25)
2
· (y
35
+ 7y
34
+ ··· + 1441792y −65536)
30
