12a
0806
(K12a
0806
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 10 11 12 1 2 3 8 7
Solving Sequence
8,11
12 7 1 9
3,6
4 10 5 2
c
11
c
7
c
12
c
8
c
6
c
3
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h17065u
50
+ 58132u
49
+ ··· + 10949b + 696131,
− 681303u
50
− 3569366u
49
+ ··· + 120439a − 14235505, u
51
+ 6u
50
+ ··· + 17u + 11i
I
u
2
= h768u
38
a + 2716u
38
+ ··· − 4526a − 10377, −5u
38
a + 5u
38
+ ··· − 10a + 2, u
39
− 2u
38
+ ··· + 4u − 1i
I
u
3
= h−u
10
− 4u
8
− 5u
6
+ u
3
+ 4u
2
+ b + 2u + 1,
u
12
+ u
11
+ 5u
10
+ 4u
9
+ 9u
8
+ 5u
7
+ 4u
6
− u
5
− 7u
4
− 7u
3
− 7u
2
+ a − 3u + 1,
u
15
+ u
14
+ 7u
13
+ 6u
12
+ 19u
11
+ 14u
10
+ 22u
9
+ 13u
8
+ u
7
− 4u
6
− 22u
5
− 17u
4
− 16u
3
− 10u
2
− u − 1i
I
u
4
= hau − u
2
+ b + u − 1, −3u
2
a + a
2
− 3a − u + 1, u
3
− u
2
+ 2u − 1i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 151 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
= h17065u
50
+ 58132u
49
+ · · · + 10949b + 696131, −6.81 × 10
5
u
50
−
3.57 × 10
6
u
49
+ · · · + 1.20 × 10
5
a − 1.42 × 10
7
, u
51
+ 6u
50
+ · · · + 17u + 11i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
5.65683u
50
+ 29.6363u
49
+ ··· + 12.5028u + 118.197
−1.55859u
50
− 5.30934u
49
+ ··· + 30.0563u − 63.5794
a
6
=
−u
3
− 2u
u
3
+ u
a
4
=
8.37881u
50
+ 48.7374u
49
+ ··· + 50.8618u + 144.760
−1.53548u
50
− 10.7228u
49
+ ··· + 2.32012u − 92.1670
a
10
=
−6.19247u
50
− 28.1472u
49
+ ··· + 13.9193u − 64.2872
10.0141u
50
+ 55.3135u
49
+ ··· + 59.6389u + 98.3815
a
5
=
3.63966u
50
+ 23.9159u
49
+ ··· + 51.3463u + 6.74407
−0.613389u
50
− 7.84263u
49
+ ··· − 28.5497u − 51.1307
a
2
=
4.64825u
50
+ 26.2761u
49
+ ··· + 23.4246u + 101.470
−1.61339u
50
− 6.84263u
49
+ ··· + 21.4503u − 51.1307
(ii) Obstruction class = −1
(iii) Cusp Shapes =
138745
10949
u
50
+
762715
10949
u
49
+ ··· +
578532
10949
u +
1808552
10949
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
51
+ 8u
50
+ ··· − u + 1
c
2
u
51
+ 27u
50
+ ··· − 21u − 11
c
4
, c
10
u
51
− 8u
49
+ ··· − 7u + 3
c
5
, c
9
u
51
− 17u
49
+ ··· − 3u + 1
c
6
, c
8
u
51
+ 6u
50
+ ··· − 13127u − 1727
c
7
, c
11
, c
12
u
51
− 6u
50
+ ··· + 17u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
51
− 12y
50
+ ··· + 41y −1
c
2
y
51
− y
50
+ ··· + 265y −121
c
4
, c
10
y
51
− 16y
50
+ ··· + 109y −9
c
5
, c
9
y
51
− 34y
50
+ ··· + 63y −1
c
6
, c
8
y
51
− 46y
50
+ ··· + 6018391y −2982529
c
7
, c
11
, c
12
y
51
+ 42y
50
+ ··· + 751y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957849 + 0.091145I
a = −1.008770 − 0.320069I
b = 0.552197 + 0.030702I
5.37004 − 0.21205I 11.7933 + 19.3332I
u = −0.957849 − 0.091145I
a = −1.008770 + 0.320069I
b = 0.552197 − 0.030702I
5.37004 + 0.21205I 11.7933 − 19.3332I
u = −0.872610 + 0.107152I
a = 2.73299 − 0.35546I
b = −1.35191 + 0.89094I
6.3580 − 14.4453I 7.77501 + 8.25655I
u = −0.872610 − 0.107152I
a = 2.73299 + 0.35546I
b = −1.35191 − 0.89094I
6.3580 + 14.4453I 7.77501 − 8.25655I
u = 0.850284
a = −2.37050
b = 1.10715
7.35958 12.9810
u = −0.841318 + 0.059912I
a = −1.61858 + 0.39625I
b = 0.651279 − 0.942262I
3.92874 − 5.39698I 1.33611 + 5.91219I
u = −0.841318 − 0.059912I
a = −1.61858 − 0.39625I
b = 0.651279 + 0.942262I
3.92874 + 5.39698I 1.33611 − 5.91219I
u = −0.110159 + 1.171870I
a = −0.653100 − 0.676264I
b = 0.747128 − 0.387182I
−2.43106 − 2.02323I 0
u = −0.110159 − 1.171870I
a = −0.653100 + 0.676264I
b = 0.747128 + 0.387182I
−2.43106 + 2.02323I 0
u = 0.793654
a = 3.77720
b = −1.59505
2.43906 4.56150
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536539 + 0.581907I
a = 0.286173 − 1.079810I
b = −0.871692 + 0.727547I
−0.20392 − 5.98050I 4.39957 + 5.96035I
u = 0.536539 − 0.581907I
a = 0.286173 + 1.079810I
b = −0.871692 − 0.727547I
−0.20392 + 5.98050I 4.39957 − 5.96035I
u = −0.437498 + 1.162750I
a = −0.949926 − 0.859681I
b = 1.31754 + 0.83680I
3.12029 + 9.75993I 0
u = −0.437498 − 1.162750I
a = −0.949926 + 0.859681I
b = 1.31754 − 0.83680I
3.12029 − 9.75993I 0
u = −0.526323 + 1.137400I
a = 0.714167 − 0.057776I
b = −0.636089 + 0.260892I
2.16535 − 5.04396I 0
u = −0.526323 − 1.137400I
a = 0.714167 + 0.057776I
b = −0.636089 − 0.260892I
2.16535 + 5.04396I 0
u = 0.586583 + 0.460125I
a = −1.68040 + 0.19022I
b = 1.039040 + 0.827520I
0.14422 + 10.04010I 4.88180 − 10.18638I
u = 0.586583 − 0.460125I
a = −1.68040 − 0.19022I
b = 1.039040 − 0.827520I
0.14422 − 10.04010I 4.88180 + 10.18638I
u = −0.735576 + 0.015230I
a = 0.707092 − 0.935835I
b = −0.540635 + 0.818076I
1.75267 + 0.42707I 5.01249 − 1.26991I
u = −0.735576 − 0.015230I
a = 0.707092 + 0.935835I
b = −0.540635 − 0.818076I
1.75267 − 0.42707I 5.01249 + 1.26991I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386042 + 1.213460I
a = 0.305981 + 0.162011I
b = −0.683796 − 0.892751I
0.378949 + 0.984883I 0
u = −0.386042 − 1.213460I
a = 0.305981 − 0.162011I
b = −0.683796 + 0.892751I
0.378949 − 0.984883I 0
u = −0.010405 + 1.275500I
a = −0.11447 + 1.65867I
b = −1.197490 + 0.435739I
−5.65491 − 0.08091I 0
u = −0.010405 − 1.275500I
a = −0.11447 − 1.65867I
b = −1.197490 − 0.435739I
−5.65491 + 0.08091I 0
u = −0.315762 + 1.267550I
a = 0.587037 − 0.458569I
b = 0.734138 + 0.847727I
−2.14226 − 4.23397I 0
u = −0.315762 − 1.267550I
a = 0.587037 + 0.458569I
b = 0.734138 − 0.847727I
−2.14226 + 4.23397I 0
u = 0.346308 + 1.271350I
a = −2.07110 + 1.52413I
b = 1.60013 + 0.10545I
−1.50936 + 4.10568I 0
u = 0.346308 − 1.271350I
a = −2.07110 − 1.52413I
b = 1.60013 − 0.10545I
−1.50936 − 4.10568I 0
u = 0.140065 + 1.312000I
a = −1.17209 + 0.87013I
b = −0.102933 + 0.561947I
−6.73083 + 1.29013I 0
u = 0.140065 − 1.312000I
a = −1.17209 − 0.87013I
b = −0.102933 − 0.561947I
−6.73083 − 1.29013I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.390745 + 1.270750I
a = 1.35281 − 0.86884I
b = −1.104190 − 0.060462I
3.41454 + 4.45278I 0
u = 0.390745 − 1.270750I
a = 1.35281 + 0.86884I
b = −1.104190 + 0.060462I
3.41454 − 4.45278I 0
u = 0.123820 + 1.332570I
a = −0.25400 + 1.64570I
b = 0.377328 + 0.848131I
−6.88239 + 4.78231I 0
u = 0.123820 − 1.332570I
a = −0.25400 − 1.64570I
b = 0.377328 − 0.848131I
−6.88239 − 4.78231I 0
u = −0.305129 + 1.305590I
a = −0.741926 − 0.203882I
b = 0.310875 − 0.893081I
−2.38756 − 3.30581I 0
u = −0.305129 − 1.305590I
a = −0.741926 + 0.203882I
b = 0.310875 + 0.893081I
−2.38756 + 3.30581I 0
u = −0.378359 + 1.313350I
a = 1.53765 + 0.97583I
b = −0.620593 + 0.977590I
−0.36500 − 9.78081I 0
u = −0.378359 − 1.313350I
a = 1.53765 − 0.97583I
b = −0.620593 − 0.977590I
−0.36500 + 9.78081I 0
u = −0.432561 + 1.329610I
a = 0.774503 + 0.554838I
b = −0.519222 + 0.116435I
0.95775 − 5.14865I 0
u = −0.432561 − 1.329610I
a = 0.774503 − 0.554838I
b = −0.519222 − 0.116435I
0.95775 + 5.14865I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.389393 + 1.346220I
a = −1.91824 − 1.27982I
b = 1.36458 − 0.93696I
1.7948 − 18.9749I 0
u = −0.389393 − 1.346220I
a = −1.91824 + 1.27982I
b = 1.36458 + 0.93696I
1.7948 + 18.9749I 0
u = 0.160521 + 1.403010I
a = 0.507609 − 1.238780I
b = −1.07228 − 0.98924I
−5.80596 + 12.52430I 0
u = 0.160521 − 1.403010I
a = 0.507609 + 1.238780I
b = −1.07228 + 0.98924I
−5.80596 − 12.52430I 0
u = 0.08350 + 1.42941I
a = 0.467107 − 0.186161I
b = 0.633858 − 0.883697I
−6.78102 − 4.15065I 0
u = 0.08350 − 1.42941I
a = 0.467107 + 0.186161I
b = 0.633858 + 0.883697I
−6.78102 + 4.15065I 0
u = 0.408104 + 0.327214I
a = 0.979008 − 0.904889I
b = −0.474174 − 0.714874I
−1.77054 + 2.97070I −1.01011 − 9.07631I
u = 0.408104 − 0.327214I
a = 0.979008 + 0.904889I
b = −0.474174 + 0.714874I
−1.77054 − 2.97070I −1.01011 + 9.07631I
u = −0.433649
a = 1.37269
b = −0.608713
0.899501 11.2900
u = 0.317656 + 0.294660I
a = 1.068040 − 0.161364I
b = 0.395222 − 0.470941I
−1.93927 − 0.45602I −1.97537 − 1.16859I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317656 − 0.294660I
a = 1.068040 + 0.161364I
b = 0.395222 + 0.470941I
−1.93927 + 0.45602I −1.97537 + 1.16859I
10
II. I
u
2
= h768u
38
a + 2716u
38
+ · · · − 4526a − 10377, −5u
38
a + 5u
38
+ · · · −
10a + 2, u
39
− 2u
38
+ · · · + 4u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
a
−0.262924au
38
− 0.929819u
38
+ ··· + 1.54947a + 3.55255
a
6
=
−u
3
− 2u
u
3
+ u
a
4
=
−3.14755au
38
− 3.51660u
38
+ ··· − 0.508045a − 4.52585
1.17426au
38
− 0.482711u
38
+ ··· + 3.14755a + 6.51660
a
10
=
0.929819au
38
+ 2.43410u
38
+ ··· − 2.55255a + 5.13968
−1.41732au
38
− 2.57480u
38
+ ··· + 1.13386a − 2.74016
a
5
=
−2.21773au
38
− 3.08251u
38
+ ··· + 0.939404a − 3.38617
0.929819au
38
+ 0.434098u
38
+ ··· + 1.44745a + 5.13968
a
2
=
1.56179au
38
+ 3.78364u
38
+ ··· − 0.0842177a + 2.92092
−2.52996au
38
− 1.93667u
38
+ ··· − 0.845601a − 4.35502
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
38
− 16u
37
+ ··· − 15u + 31
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
78
− 7u
77
+ ··· − 3364u + 183
c
2
(u
39
− 19u
38
+ ··· + 28u − 8)
2
c
4
, c
10
u
78
− 8u
76
+ ··· + 16227u + 3957
c
5
, c
9
u
78
+ 6u
76
+ ··· − 13u + 3
c
6
, c
8
(u
39
− 2u
38
+ ··· + 2u
2
+ 5)
2
c
7
, c
11
, c
12
(u
39
+ 2u
38
+ ··· + 4u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
78
+ 33y
77
+ ··· + 910466y + 33489
c
2
(y
39
− 7y
38
+ ··· + 1296y −64)
2
c
4
, c
10
y
78
− 16y
77
+ ··· − 452246451y + 15657849
c
5
, c
9
y
78
+ 12y
77
+ ··· − 283y + 9
c
6
, c
8
(y
39
− 32y
38
+ ··· − 20y −25)
2
c
7
, c
11
, c
12
(y
39
+ 32y
38
+ ··· + 16y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862765 + 0.111414I
a = 1.52394 − 0.50769I
b = −0.909524 − 0.267244I
7.83503 + 6.29239I 11.47825 − 6.12903I
u = 0.862765 + 0.111414I
a = −2.71691 − 0.48168I
b = 1.41000 + 0.84330I
7.83503 + 6.29239I 11.47825 − 6.12903I
u = 0.862765 − 0.111414I
a = 1.52394 + 0.50769I
b = −0.909524 + 0.267244I
7.83503 − 6.29239I 11.47825 + 6.12903I
u = 0.862765 − 0.111414I
a = −2.71691 + 0.48168I
b = 1.41000 − 0.84330I
7.83503 − 6.29239I 11.47825 + 6.12903I
u = 0.845481
a = −2.29657 + 0.11006I
b = 1.064370 + 0.116416I
7.33955 12.5360
u = 0.845481
a = −2.29657 − 0.11006I
b = 1.064370 − 0.116416I
7.33955 12.5360
u = 0.022826 + 1.155060I
a = −0.299063 − 0.119240I
b = 1.177390 − 0.545665I
−1.55883 − 2.57852I 5.28000 + 1.21669I
u = 0.022826 + 1.155060I
a = −1.04903 − 2.13457I
b = 0.097150 + 0.275988I
−1.55883 − 2.57852I 5.28000 + 1.21669I
u = 0.022826 − 1.155060I
a = −0.299063 + 0.119240I
b = 1.177390 + 0.545665I
−1.55883 + 2.57852I 5.28000 − 1.21669I
u = 0.022826 − 1.155060I
a = −1.04903 + 2.13457I
b = 0.097150 − 0.275988I
−1.55883 + 2.57852I 5.28000 − 1.21669I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824869 + 0.019258I
a = 1.92077 − 1.02736I
b = −0.655761 − 0.138542I
6.72772 − 4.49457I 11.91335 + 5.12079I
u = −0.824869 + 0.019258I
a = −2.85897 + 1.05925I
b = 1.45369 − 1.14548I
6.72772 − 4.49457I 11.91335 + 5.12079I
u = −0.824869 − 0.019258I
a = 1.92077 + 1.02736I
b = −0.655761 + 0.138542I
6.72772 + 4.49457I 11.91335 − 5.12079I
u = −0.824869 − 0.019258I
a = −2.85897 − 1.05925I
b = 1.45369 + 1.14548I
6.72772 + 4.49457I 11.91335 − 5.12079I
u = 0.796735 + 0.070027I
a = 2.33321 − 0.32438I
b = −1.024300 − 0.668662I
3.10138 + 5.89865I 3.86727 − 7.38217I
u = 0.796735 + 0.070027I
a = 0.08693 − 2.63933I
b = −0.18679 + 1.79967I
3.10138 + 5.89865I 3.86727 − 7.38217I
u = 0.796735 − 0.070027I
a = 2.33321 + 0.32438I
b = −1.024300 + 0.668662I
3.10138 − 5.89865I 3.86727 + 7.38217I
u = 0.796735 − 0.070027I
a = 0.08693 + 2.63933I
b = −0.18679 − 1.79967I
3.10138 − 5.89865I 3.86727 + 7.38217I
u = 0.425356 + 1.152970I
a = −0.664842 + 0.046535I
b = 0.940951 − 0.165473I
4.64181 − 1.67568I 8.99923 + 1.98848I
u = 0.425356 + 1.152970I
a = 0.891746 − 1.049000I
b = −1.34348 + 0.74421I
4.64181 − 1.67568I 8.99923 + 1.98848I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425356 − 1.152970I
a = −0.664842 − 0.046535I
b = 0.940951 + 0.165473I
4.64181 + 1.67568I 8.99923 − 1.98848I
u = 0.425356 − 1.152970I
a = 0.891746 + 1.049000I
b = −1.34348 − 0.74421I
4.64181 + 1.67568I 8.99923 − 1.98848I
u = 0.331729 + 1.210260I
a = −0.974613 + 0.001886I
b = 1.044950 − 0.605163I
−0.38131 − 1.81925I 0. + 3.85200I
u = 0.331729 + 1.210260I
a = −1.66523 − 0.77408I
b = −0.00527 + 1.71179I
−0.38131 − 1.81925I 0. + 3.85200I
u = 0.331729 − 1.210260I
a = −0.974613 − 0.001886I
b = 1.044950 + 0.605163I
−0.38131 + 1.81925I 0. − 3.85200I
u = 0.331729 − 1.210260I
a = −1.66523 + 0.77408I
b = −0.00527 − 1.71179I
−0.38131 + 1.81925I 0. − 3.85200I
u = 0.067881 + 1.254700I
a = 1.95646 − 0.02933I
b = −0.887796 − 0.295962I
−2.63455 + 5.05675I 1.50570 − 9.56205I
u = 0.067881 + 1.254700I
a = 0.34613 + 2.03183I
b = 0.86825 + 1.32919I
−2.63455 + 5.05675I 1.50570 − 9.56205I
u = 0.067881 − 1.254700I
a = 1.95646 + 0.02933I
b = −0.887796 + 0.295962I
−2.63455 − 5.05675I 1.50570 + 9.56205I
u = 0.067881 − 1.254700I
a = 0.34613 − 2.03183I
b = 0.86825 − 1.32919I
−2.63455 − 5.05675I 1.50570 + 9.56205I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539737 + 0.491474I
a = −0.319753 − 0.984087I
b = 0.686004 + 0.238628I
2.08119 − 1.94210I 12.17714 + 4.61373I
u = −0.539737 + 0.491474I
a = 1.117600 − 0.066387I
b = −0.817065 + 0.624057I
2.08119 − 1.94210I 12.17714 + 4.61373I
u = −0.539737 − 0.491474I
a = −0.319753 + 0.984087I
b = 0.686004 − 0.238628I
2.08119 + 1.94210I 12.17714 − 4.61373I
u = −0.539737 − 0.491474I
a = 1.117600 + 0.066387I
b = −0.817065 − 0.624057I
2.08119 + 1.94210I 12.17714 − 4.61373I
u = −0.370668 + 1.252870I
a = 0.592944 + 1.205510I
b = −1.48011 − 1.05361I
2.90973 + 0.19610I 8.26615 + 0.I
u = −0.370668 + 1.252870I
a = −1.20274 − 1.76224I
b = 0.565165 − 0.161917I
2.90973 + 0.19610I 8.26615 + 0.I
u = −0.370668 − 1.252870I
a = 0.592944 − 1.205510I
b = −1.48011 + 1.05361I
2.90973 − 0.19610I 8.26615 + 0.I
u = −0.370668 − 1.252870I
a = −1.20274 + 1.76224I
b = 0.565165 + 0.161917I
2.90973 − 0.19610I 8.26615 + 0.I
u = 0.386988 + 1.267600I
a = 1.166230 − 0.681178I
b = −1.132120 + 0.079081I
3.40613 + 4.42352I 0
u = 0.386988 + 1.267600I
a = 1.41876 − 1.06506I
b = −0.987505 − 0.144274I
3.40613 + 4.42352I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.386988 − 1.267600I
a = 1.166230 + 0.681178I
b = −1.132120 − 0.079081I
3.40613 − 4.42352I 0
u = 0.386988 − 1.267600I
a = 1.41876 + 1.06506I
b = −0.987505 + 0.144274I
3.40613 − 4.42352I 0
u = −0.369439 + 1.283770I
a = −1.313240 + 0.478217I
b = 0.735564 + 0.114822I
2.67215 − 8.78848I 0
u = −0.369439 + 1.283770I
a = 2.21858 + 1.22748I
b = −1.42500 + 1.23072I
2.67215 − 8.78848I 0
u = −0.369439 − 1.283770I
a = −1.313240 − 0.478217I
b = 0.735564 − 0.114822I
2.67215 + 8.78848I 0
u = −0.369439 − 1.283770I
a = 2.21858 − 1.22748I
b = −1.42500 − 1.23072I
2.67215 + 8.78848I 0
u = −0.067670 + 1.359240I
a = −0.474081 − 0.636837I
b = −0.83150 − 1.50691I
−6.62180 − 4.34090I 0
u = −0.067670 + 1.359240I
a = −0.41872 + 1.45730I
b = −0.783478 + 0.633009I
−6.62180 − 4.34090I 0
u = −0.067670 − 1.359240I
a = −0.474081 + 0.636837I
b = −0.83150 + 1.50691I
−6.62180 + 4.34090I 0
u = −0.067670 − 1.359240I
a = −0.41872 − 1.45730I
b = −0.783478 − 0.633009I
−6.62180 + 4.34090I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351229 + 1.316650I
a = 1.37076 + 0.85246I
b = 0.30604 − 1.87383I
−1.24250 + 10.04150I 0
u = 0.351229 + 1.316650I
a = −1.51696 + 1.64909I
b = 1.006870 + 0.715982I
−1.24250 + 10.04150I 0
u = 0.351229 − 1.316650I
a = 1.37076 − 0.85246I
b = 0.30604 + 1.87383I
−1.24250 − 10.04150I 0
u = 0.351229 − 1.316650I
a = −1.51696 − 1.64909I
b = 1.006870 − 0.715982I
−1.24250 − 10.04150I 0
u = −0.235139 + 1.342860I
a = 0.735554 − 0.250002I
b = 0.629522 + 0.309614I
−4.60958 − 2.40159I 0
u = −0.235139 + 1.342860I
a = −1.48293 − 1.23073I
b = 1.51706 − 0.90511I
−4.60958 − 2.40159I 0
u = −0.235139 − 1.342860I
a = 0.735554 + 0.250002I
b = 0.629522 − 0.309614I
−4.60958 + 2.40159I 0
u = −0.235139 − 1.342860I
a = −1.48293 + 1.23073I
b = 1.51706 + 0.90511I
−4.60958 + 2.40159I 0
u = −0.568822 + 0.204692I
a = 0.376393 + 0.784643I
b = −0.820136 − 0.300724I
0.207956 + 0.558026I 7.50495 − 2.82454I
u = −0.568822 + 0.204692I
a = 2.96451 − 0.36761I
b = −1.082510 + 0.643552I
0.207956 + 0.558026I 7.50495 − 2.82454I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568822 − 0.204692I
a = 0.376393 − 0.784643I
b = −0.820136 + 0.300724I
0.207956 − 0.558026I 7.50495 + 2.82454I
u = −0.568822 − 0.204692I
a = 2.96451 + 0.36761I
b = −1.082510 − 0.643552I
0.207956 − 0.558026I 7.50495 + 2.82454I
u = 0.383276 + 1.347030I
a = −0.79750 + 1.19096I
b = 0.869798 + 0.333740I
3.25410 + 10.76850I 0
u = 0.383276 + 1.347030I
a = 1.84320 − 1.14214I
b = −1.44239 − 0.92442I
3.25410 + 10.76850I 0
u = 0.383276 − 1.347030I
a = −0.79750 − 1.19096I
b = 0.869798 − 0.333740I
3.25410 − 10.76850I 0
u = 0.383276 − 1.347030I
a = 1.84320 + 1.14214I
b = −1.44239 + 0.92442I
3.25410 − 10.76850I 0
u = −0.13988 + 1.40875I
a = −0.441546 − 0.731949I
b = 0.802503 − 1.091540I
−3.98406 − 4.16220I 0
u = −0.13988 + 1.40875I
a = −0.159209 + 0.584021I
b = −0.445257 + 0.037599I
−3.98406 − 4.16220I 0
u = −0.13988 − 1.40875I
a = −0.441546 + 0.731949I
b = 0.802503 + 1.091540I
−3.98406 + 4.16220I 0
u = −0.13988 − 1.40875I
a = −0.159209 − 0.584021I
b = −0.445257 − 0.037599I
−3.98406 + 4.16220I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235593 + 0.479135I
a = −0.551597 − 1.087440I
b = 0.582390 + 1.096000I
−1.03901 − 3.34829I −1.06567 + 7.94658I
u = −0.235593 + 0.479135I
a = −0.327750 − 1.274330I
b = 0.889698 − 0.519938I
−1.03901 − 3.34829I −1.06567 + 7.94658I
u = −0.235593 − 0.479135I
a = −0.551597 + 1.087440I
b = 0.582390 − 1.096000I
−1.03901 + 3.34829I −1.06567 − 7.94658I
u = −0.235593 − 0.479135I
a = −0.327750 + 1.274330I
b = 0.889698 + 0.519938I
−1.03901 + 3.34829I −1.06567 − 7.94658I
u = 0.300292 + 0.075872I
a = 2.06333 − 1.10343I
b = −0.963277 − 0.917710I
1.30386 + 3.83847I 14.1552 − 8.5698I
u = 0.300292 + 0.075872I
a = −3.39580 − 3.91397I
b = 0.575904 + 0.390307I
1.30386 + 3.83847I 14.1552 − 8.5698I
u = 0.300292 − 0.075872I
a = 2.06333 + 1.10343I
b = −0.963277 + 0.917710I
1.30386 − 3.83847I 14.1552 + 8.5698I
u = 0.300292 − 0.075872I
a = −3.39580 + 3.91397I
b = 0.575904 − 0.390307I
1.30386 − 3.83847I 14.1552 + 8.5698I
21
III. I
u
3
= h−u
10
− 4u
8
− 5u
6
+ u
3
+ 4u
2
+ b + 2u + 1, u
12
+ u
11
+ · · · + a +
1, u
15
+ u
14
+ · · · − u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
−u
12
− u
11
+ ··· + 3u − 1
u
10
+ 4u
8
+ 5u
6
− u
3
− 4u
2
− 2u − 1
a
6
=
−u
3
− 2u
u
3
+ u
a
4
=
−2u
14
− 2u
13
+ ··· + 23u
2
+ 4u
u
13
+ u
12
+ ··· − 2u − 2
a
10
=
u
14
+ u
13
+ ··· + u + 3
−2u
13
− u
12
+ ··· + 4u + 1
a
5
=
−u
14
− u
13
+ ··· + 4u − 1
u
10
+ 4u
8
+ 5u
6
− 4u
2
− u − 1
a
2
=
−u
14
− 2u
13
+ ··· + 8u + 3
−u
14
− 5u
12
− 8u
10
− u
9
− 3u
7
+ 12u
6
− 2u
5
+ 7u
4
− 4u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
13
+ 6u
12
+ 58u
11
+ 30u
10
+ 122u
9
+ 54u
8
+ 87u
7
+ 22u
6
−
56u
5
− 54u
4
− 106u
3
− 58u
2
− 26u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
15
− 3u
14
+ ··· + 3u + 1
c
2
u
15
+ 12u
14
+ ··· + 597u + 89
c
4
, c
10
u
15
+ u
14
+ ··· − u − 1
c
5
, c
9
u
15
− u
14
+ ··· − u + 1
c
6
, c
8
u
15
+ u
14
+ ··· + u + 1
c
7
u
15
− u
14
+ ··· − u + 1
c
11
, c
12
u
15
+ u
14
+ ··· − u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
15
+ 15y
14
+ ··· + 3y −1
c
2
y
15
+ 6y
14
+ ··· − 16145y −7921
c
4
, c
10
y
15
+ 3y
14
+ ··· + 3y −1
c
5
, c
9
y
15
− 3y
14
+ ··· − 3y −1
c
6
, c
8
y
15
− 15y
14
+ ··· − 27y −1
c
7
, c
11
, c
12
y
15
+ 13y
14
+ ··· − 19y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973615
a = −1.08086
b = 0.592073
5.50540 28.3560
u = −0.818918 + 0.057821I
a = −1.41235 + 0.50667I
b = 0.708958 − 1.012480I
4.93823 − 5.62153I 9.98189 + 7.30165I
u = −0.818918 − 0.057821I
a = −1.41235 − 0.50667I
b = 0.708958 + 1.012480I
4.93823 + 5.62153I 9.98189 − 7.30165I
u = −0.009806 + 1.193550I
a = −1.29640 − 1.28501I
b = 0.828639 − 0.705317I
−2.09295 − 3.71723I 2.32036 + 6.39169I
u = −0.009806 − 1.193550I
a = −1.29640 + 1.28501I
b = 0.828639 + 0.705317I
−2.09295 + 3.71723I 2.32036 − 6.39169I
u = −0.362178 + 1.221320I
a = −0.062398 + 0.147907I
b = −0.758360 − 0.971335I
1.36157 + 1.36777I 6.49192 − 4.04196I
u = −0.362178 − 1.221320I
a = −0.062398 − 0.147907I
b = −0.758360 + 0.971335I
1.36157 − 1.36777I 6.49192 + 4.04196I
u = 0.460271 + 1.215170I
a = 0.959125 − 0.101839I
b = −0.659569 − 0.253329I
1.79820 + 5.10776I 1.36573 − 10.27038I
u = 0.460271 − 1.215170I
a = 0.959125 + 0.101839I
b = −0.659569 + 0.253329I
1.79820 − 5.10776I 1.36573 + 10.27038I
u = −0.364476 + 1.312270I
a = 1.30531 + 0.94532I
b = −0.668358 + 1.047800I
0.65103 − 9.88256I 5.41523 + 9.50189I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.364476 − 1.312270I
a = 1.30531 − 0.94532I
b = −0.668358 − 1.047800I
0.65103 + 9.88256I 5.41523 − 9.50189I
u = 0.073276 + 1.378290I
a = 0.193473 + 0.729192I
b = 0.384212 + 0.853344I
−5.02585 + 4.30225I −1.06431 − 7.73809I
u = 0.073276 − 1.378290I
a = 0.193473 − 0.729192I
b = 0.384212 − 0.853344I
−5.02585 − 4.30225I −1.06431 + 7.73809I
u = 0.035024 + 0.330532I
a = −1.64633 + 0.87718I
b = −0.631559 − 0.715221I
0.55188 + 3.68810I 1.81099 − 6.17747I
u = 0.035024 − 0.330532I
a = −1.64633 − 0.87718I
b = −0.631559 + 0.715221I
0.55188 − 3.68810I 1.81099 + 6.17747I
26
IV. I
u
4
= hau − u
2
+ b + u − 1, −3u
2
a + a
2
− 3a − u + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
9
=
1
0
a
3
=
a
−au + u
2
− u + 1
a
6
=
−u
2
− 1
u
2
− u + 1
a
4
=
−u
2
+ a − 1
−au + 2u
2
− 2u + 2
a
10
=
−2u
2
a + 2au − u
2
− 2a + u + 1
−au + a − u + 1
a
5
=
−au + u
2
+ a − 2u + 1
−au + 2u
2
− 2u + 2
a
2
=
a
−au + u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
− 8u + 4
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
6
c
2
u
6
c
4
, c
5
, c
9
c
10
u
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
− u − 1
c
6
, c
8
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
6
c
2
y
6
c
4
, c
5
, c
9
c
10
y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1
c
6
, c
8
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.749065 + 0.089148I
b = −0.599800 + 0.215099I
−4.66906 + 2.82812I −2.70772 − 8.77029I
u = 0.215080 + 1.307140I
a = −1.23801 + 1.59769I
b = 1.47724 + 0.52976I
−4.66906 + 2.82812I −2.70772 − 8.77029I
u = 0.215080 − 1.307140I
a = −0.749065 − 0.089148I
b = −0.599800 − 0.215099I
−4.66906 − 2.82812I −2.70772 + 8.77029I
u = 0.215080 − 1.307140I
a = −1.23801 − 1.59769I
b = 1.47724 − 0.52976I
−4.66906 − 2.82812I −2.70772 + 8.77029I
u = 0.569840
a = 0.111360
b = 0.691420
−0.531480 0.415430
u = 0.569840
a = 3.86279
b = −1.44630
−0.531480 0.415430
30
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
8
=
−1
0
a
11
=
1
0
a
12
=
1
0
a
7
=
−1
0
a
1
=
1
0
a
9
=
−1
0
a
3
=
0
1
a
6
=
−1
0
a
4
=
−1
1
a
10
=
1
1
a
5
=
0
1
a
2
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
u + 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
u
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
y − 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
34
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
6
)(u + 1)(u
15
− 3u
14
+ ··· + 3u + 1)(u
51
+ 8u
50
+ ··· − u + 1)
· (u
78
− 7u
77
+ ··· − 3364u + 183)
c
2
u
7
(u
15
+ 12u
14
+ ··· + 597u + 89)(u
39
− 19u
38
+ ··· + 28u − 8)
2
· (u
51
+ 27u
50
+ ··· − 21u − 11)
c
4
, c
10
(u + 1)(u
6
− u
5
+ ··· − u − 1)(u
15
+ u
14
+ ··· − u − 1)
· (u
51
− 8u
49
+ ··· − 7u + 3)(u
78
− 8u
76
+ ··· + 16227u + 3957)
c
5
, c
9
(u + 1)(u
6
− u
5
+ ··· − u − 1)(u
15
− u
14
+ ··· − u + 1)
· (u
51
− 17u
49
+ ··· − 3u + 1)(u
78
+ 6u
76
+ ··· − 13u + 3)
c
6
, c
8
u(u
3
− u
2
+ 1)
2
(u
15
+ u
14
+ ··· + u + 1)(u
39
− 2u
38
+ ··· + 2u
2
+ 5)
2
· (u
51
+ 6u
50
+ ··· − 13127u − 1727)
c
7
u(u
3
+ u
2
+ 2u + 1)
2
(u
15
− u
14
+ ··· − u + 1)
· ((u
39
+ 2u
38
+ ··· + 4u + 1)
2
)(u
51
− 6u
50
+ ··· + 17u − 11)
c
11
, c
12
u(u
3
− u
2
+ 2u − 1)
2
(u
15
+ u
14
+ ··· − u − 1)
· ((u
39
+ 2u
38
+ ··· + 4u + 1)
2
)(u
51
− 6u
50
+ ··· + 17u − 11)
35
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y − 1)
7
)(y
15
+ 15y
14
+ ··· + 3y − 1)(y
51
− 12y
50
+ ··· + 41y − 1)
· (y
78
+ 33y
77
+ ··· + 910466y + 33489)
c
2
y
7
(y
15
+ 6y
14
+ ··· − 16145y − 7921)
· ((y
39
− 7y
38
+ ··· + 1296y − 64)
2
)(y
51
− y
50
+ ··· + 265y − 121)
c
4
, c
10
(y − 1)(y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1)
· (y
15
+ 3y
14
+ ··· + 3y − 1)(y
51
− 16y
50
+ ··· + 109y − 9)
· (y
78
− 16y
77
+ ··· − 452246451y + 15657849)
c
5
, c
9
(y − 1)(y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1)
· (y
15
− 3y
14
+ ··· − 3y − 1)(y
51
− 34y
50
+ ··· + 63y − 1)
· (y
78
+ 12y
77
+ ··· − 283y + 9)
c
6
, c
8
y(y
3
− y
2
+ 2y − 1)
2
(y
15
− 15y
14
+ ··· − 27y − 1)
· (y
39
− 32y
38
+ ··· − 20y − 25)
2
· (y
51
− 46y
50
+ ··· + 6018391y − 2982529)
c
7
, c
11
, c
12
y(y
3
+ 3y
2
+ 2y − 1)
2
(y
15
+ 13y
14
+ ··· − 19y − 1)
· ((y
39
+ 32y
38
+ ··· + 16y − 1)
2
)(y
51
+ 42y
50
+ ··· + 751y − 121)
36
