12a
0327
(K12a
0327
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 1 9 4 7 12 5 10
Solving Sequence
4,9
8
1,3
2 7 10 6 5 12 11
c
8
c
3
c
1
c
7
c
9
c
6
c
5
c
12
c
10
c
2
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
23
− u
22
+ ··· + 4b + 1, −u
6
+ u
4
− 2u
2
+ a + 1, u
24
− u
23
+ ··· − 3u
2
+ 1i
I
u
2
= h−1.28182 × 10
16
u
51
− 5.11407 × 10
16
u
50
+ ··· + 3.64498 × 10
17
b + 4.59559 × 10
17
,
2.08375 × 10
17
u
51
− 4.62594 × 10
17
u
50
+ ··· + 7.28997 × 10
17
a + 2.74422 × 10
18
, u
52
− 2u
51
+ ··· + 20u + 4i
I
u
3
= hu
3
+ u
2
+ b, −u
2
+ a + 1, u
4
− u
2
+ 1i
I
u
4
= hb − u, a, u
12
− u
11
− 2u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 3u
5
− 2u
4
+ 2u
2
− 2u + 1i
I
u
5
= ha
3
u
2
+ 8a
3
u + 5a
2
u
2
+ 10a
3
+ 17a
2
u − 57u
2
a + 27a
2
− 42au − 60u
2
+ 46b + 5a − 43u − 48,
a
4
− 2a
3
u − 2a
2
u
2
− a
2
u − 6u
2
a − a
2
+ 3u
2
+ 6a + 4u − 1, u
3
+ u
2
− 1i
I
u
6
= hb − u, a, u
3
+ u
2
− 1i
I
u
7
= h−u
2
+ b − u + 1, a − 1, u
4
− u
2
+ 1i
I
u
8
= hu
2
+ b − u, −u
2
+ a + 1, u
4
− u
2
+ 1i
I
u
9
= hu
3
− u
2
+ b + 1, a − 1, u
4
− u
2
+ 1i
* 9 irreducible components of dim
C
= 0, with total 119 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
= h−u
23
−u
22
+· · ·+4b+1, −u
6
+u
4
−2u
2
+a+1, u
24
−u
23
+· · ·−3u
2
+1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
u
6
− u
4
+ 2u
2
− 1
1
4
u
23
+
1
4
u
22
+ ··· + 2u
2
−
1
4
a
3
=
−u
−u
3
+ u
a
2
=
−
1
4
u
23
+ u
21
+ ··· +
1
4
u −
1
2
1
2
u
23
+
1
2
u
22
+ ··· + 2u
2
−
1
2
a
7
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
6
=
1
4
u
23
− u
21
+ ··· −
1
4
u +
1
2
1
4
u
22
−
1
2
u
21
+ ··· −
1
4
u −
3
4
a
5
=
u
−
1
4
u
23
+
1
4
u
22
+ ··· +
3
2
u +
1
4
a
12
=
u
2
− 1
1
4
u
23
+
1
4
u
22
+ ··· + 2u
2
−
1
4
a
11
=
1
−
1
4
u
23
+ u
21
+ ··· +
1
4
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= u
23
−
5
2
u
22
+ 6u
20
− u
19
− 21u
18
+ 19u
17
+ 29u
16
−
95
2
u
15
− 43u
14
+
193
2
u
13
+ 31u
12
−
295
2
u
11
− 3u
10
+ 161u
9
−
35
2
u
8
−
311
2
u
7
+
95
2
u
6
+ 95u
5
−
61
2
u
4
− 36u
3
+
7
2
u
2
+
23
2
u +
15
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 12u
23
+ ··· + 56u + 16
c
2
, c
5
u
24
+ 4u
23
+ ··· + 12u + 4
c
3
, c
4
, c
8
c
11
u
24
− u
23
+ ··· − 3u
2
+ 1
c
6
u
24
+ 12u
23
+ ··· + 876u + 188
c
7
, c
9
, c
10
c
12
u
24
− 7u
23
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 24y
22
+ ··· + 1760y + 256
c
2
, c
5
y
24
− 12y
23
+ ··· − 56y + 16
c
3
, c
4
, c
8
c
11
y
24
− 7y
23
+ ··· − 6y + 1
c
6
y
24
+ 12y
23
+ ··· − 37560y + 35344
c
7
, c
9
, c
10
c
12
y
24
+ 25y
23
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997654 + 0.063385I
a = 0.942467 − 0.373018I
b = 0.114843 + 0.496939I
5.25543 − 0.92360I 15.9667 + 0.9405I
u = −0.997654 − 0.063385I
a = 0.942467 + 0.373018I
b = 0.114843 − 0.496939I
5.25543 + 0.92360I 15.9667 − 0.9405I
u = 1.001330 + 0.130771I
a = 0.822888 + 0.752742I
b = 0.402636 − 1.030140I
3.57553 + 5.62812I 12.5450 − 6.6163I
u = 1.001330 − 0.130771I
a = 0.822888 − 0.752742I
b = 0.402636 + 1.030140I
3.57553 − 5.62812I 12.5450 + 6.6163I
u = −0.760211 + 0.865552I
a = 1.24479 − 0.91941I
b = −2.02625 − 0.25873I
−7.41712 − 0.40141I 2.13735 + 2.27627I
u = −0.760211 − 0.865552I
a = 1.24479 + 0.91941I
b = −2.02625 + 0.25873I
−7.41712 + 0.40141I 2.13735 − 2.27627I
u = 0.729818 + 0.904919I
a = 1.56496 + 1.41813I
b = −2.37154 + 0.16884I
−10.52250 − 4.79311I −0.73258 + 1.28832I
u = 0.729818 − 0.904919I
a = 1.56496 − 1.41813I
b = −2.37154 − 0.16884I
−10.52250 + 4.79311I −0.73258 − 1.28832I
u = 0.925994 + 0.739498I
a = −0.317422 − 0.284084I
b = −0.032960 − 1.025040I
−2.70773 + 8.50857I 3.70396 − 8.56767I
u = 0.925994 − 0.739498I
a = −0.317422 + 0.284084I
b = −0.032960 + 1.025040I
−2.70773 − 8.50857I 3.70396 + 8.56767I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820795 + 0.890761I
a = 1.65081 + 0.21101I
b = −1.82529 + 0.81637I
−12.04400 + 4.45797I −1.81976 − 4.80562I
u = 0.820795 − 0.890761I
a = 1.65081 − 0.21101I
b = −1.82529 − 0.81637I
−12.04400 − 4.45797I −1.81976 + 4.80562I
u = 1.024520 + 0.763888I
a = −1.15966 − 1.14324I
b = 2.19721 − 0.55212I
−5.73077 + 11.79410I 4.86199 − 7.29279I
u = 1.024520 − 0.763888I
a = −1.15966 + 1.14324I
b = 2.19721 + 0.55212I
−5.73077 − 11.79410I 4.86199 + 7.29279I
u = −1.004430 + 0.806604I
a = −0.56218 + 1.55066I
b = 1.64632 − 0.45435I
−10.85360 − 8.18091I −0.32980 + 5.06079I
u = −1.004430 − 0.806604I
a = −0.56218 − 1.55066I
b = 1.64632 + 0.45435I
−10.85360 + 8.18091I −0.32980 − 5.06079I
u = −0.602609 + 0.358517I
a = −0.517620 − 0.652115I
b = 0.102178 − 1.019880I
0.06490 − 4.25573I 5.05969 + 5.51828I
u = −0.602609 − 0.358517I
a = −0.517620 + 0.652115I
b = 0.102178 + 1.019880I
0.06490 + 4.25573I 5.05969 − 5.51828I
u = −1.051550 + 0.766917I
a = −1.53210 + 1.34344I
b = 2.87795 + 0.47141I
−8.4633 − 17.2201I 2.43977 + 10.58669I
u = −1.051550 − 0.766917I
a = −1.53210 − 1.34344I
b = 2.87795 − 0.47141I
−8.4633 + 17.2201I 2.43977 − 10.58669I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638863 + 0.153437I
a = −0.327734 + 0.320762I
b = 0.626252 + 0.329284I
1.105580 + 0.097930I 9.88722 − 0.56674I
u = 0.638863 − 0.153437I
a = −0.327734 − 0.320762I
b = 0.626252 − 0.329284I
1.105580 − 0.097930I 9.88722 + 0.56674I
u = −0.224865 + 0.471112I
a = −1.309200 − 0.505527I
b = −0.211349 − 0.055814I
−1.61046 + 1.10126I −1.71956 − 0.90297I
u = −0.224865 − 0.471112I
a = −1.309200 + 0.505527I
b = −0.211349 + 0.055814I
−1.61046 − 1.10126I −1.71956 + 0.90297I
7
II. I
u
2
= h−1.28 × 10
16
u
51
− 5.11 × 10
16
u
50
+ · · · + 3.64 × 10
17
b + 4.60 ×
10
17
, 2.08 × 10
17
u
51
− 4.63 × 10
17
u
50
+ · · · + 7.29 × 10
17
a + 2.74 ×
10
18
, u
52
− 2u
51
+ · · · + 20u + 4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−0.285839u
51
+ 0.634563u
50
+ ··· − 11.9888u − 3.76438
0.0351666u
51
+ 0.140304u
50
+ ··· − 7.18667u − 1.26080
a
3
=
−u
−u
3
+ u
a
2
=
−0.376087u
51
+ 0.637127u
50
+ ··· − 10.2579u − 3.06437
−0.0536490u
51
+ 0.328407u
50
+ ··· − 4.99796u − 1.24908
a
7
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
6
=
−0.0501715u
51
+ 0.417802u
50
+ ··· − 9.11537u − 4.14850
−0.102327u
51
− 0.0485043u
50
+ ··· − 8.90760u − 1.99867
a
5
=
0.0611096u
51
− 0.333673u
50
+ ··· + 7.08230u − 1.32447
−0.120328u
51
+ 0.230313u
50
+ ··· + 6.03865u + 0.284922
a
12
=
−0.336174u
51
+ 0.534328u
50
+ ··· − 6.12727u − 2.93706
0.185608u
51
+ 0.186049u
50
+ ··· − 7.63784u − 1.44011
a
11
=
−0.222742u
51
+ 0.513738u
50
+ ··· + 5.05004u + 4.21170
0.221796u
51
− 0.742510u
50
+ ··· − 0.144816u + 0.763127
(ii) Obstruction class = −1
(iii) Cusp Shapes =
175172589829383178
91124580510363867
u
51
−
434551767463876444
91124580510363867
u
50
+ ···+
784093020302745154
91124580510363867
u +
353320257970419306
30374860170121289
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
26
+ 15u
25
+ ··· + 4u + 1)
2
c
2
, c
5
(u
26
− u
25
+ ··· − 2u
2
+ 1)
2
c
3
, c
4
, c
8
c
11
u
52
− 2u
51
+ ··· + 20u + 4
c
6
(u
26
− 3u
25
+ ··· + 4u + 1)
2
c
7
, c
9
, c
10
c
12
u
52
− 16u
51
+ ··· − 152u + 16
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 3y
25
+ ··· − 16y + 1)
2
c
2
, c
5
(y
26
− 15y
25
+ ··· − 4y + 1)
2
c
3
, c
4
, c
8
c
11
y
52
− 16y
51
+ ··· − 152y + 16
c
6
(y
26
+ 21y
25
+ ··· − 68y + 1)
2
c
7
, c
9
, c
10
c
12
y
52
+ 40y
51
+ ··· + 78048y + 256
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752589 + 0.686692I
a = −1.19861 − 1.00203I
b = 1.75066 − 0.28301I
0.134724 − 0.617454I 7.60333 + 0.92062I
u = 0.752589 − 0.686692I
a = −1.19861 + 1.00203I
b = 1.75066 + 0.28301I
0.134724 + 0.617454I 7.60333 − 0.92062I
u = 1.021920 + 0.291673I
a = −0.675586 − 0.356154I
b = 0.0136506 − 0.1110620I
0.134724 + 0.617454I 7.60333 − 0.92062I
u = 1.021920 − 0.291673I
a = −0.675586 + 0.356154I
b = 0.0136506 + 0.1110620I
0.134724 − 0.617454I 7.60333 + 0.92062I
u = −0.842250 + 0.401014I
a = −0.301397 + 0.041356I
b = −0.014640 − 1.010940I
0.11473 − 4.15162I 6.01126 + 6.89813I
u = −0.842250 − 0.401014I
a = −0.301397 − 0.041356I
b = −0.014640 + 1.010940I
0.11473 + 4.15162I 6.01126 − 6.89813I
u = −0.752492 + 0.788189I
a = −1.69455 + 1.94272I
b = 2.70085 − 0.03238I
−2.50569 + 4.90020I 3.66047 − 4.25570I
u = −0.752492 − 0.788189I
a = −1.69455 − 1.94272I
b = 2.70085 + 0.03238I
−2.50569 − 4.90020I 3.66047 + 4.25570I
u = 0.951867 + 0.554822I
a = −1.110860 + 0.329191I
b = 0.36805 − 1.46263I
−0.330999 4.51777 + 0.I
u = 0.951867 − 0.554822I
a = −1.110860 − 0.329191I
b = 0.36805 + 1.46263I
−0.330999 4.51777 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.084340 + 0.227015I
a = 0.703611 − 0.413455I
b = 0.194210 − 0.006182I
0.74787 − 5.97219I 9.15925 + 6.03254I
u = −1.084340 − 0.227015I
a = 0.703611 + 0.413455I
b = 0.194210 + 0.006182I
0.74787 + 5.97219I 9.15925 − 6.03254I
u = −0.885563 + 0.095980I
a = 1.47605 + 0.13629I
b = −0.239465 − 1.096400I
2.16312 − 4.62114I 11.65491 + 5.89029I
u = −0.885563 − 0.095980I
a = 1.47605 − 0.13629I
b = −0.239465 + 1.096400I
2.16312 + 4.62114I 11.65491 − 5.89029I
u = −0.988091 + 0.542376I
a = 0.473259 + 0.644867I
b = 0.136840 − 1.204680I
−1.24430 − 4.51893I 1.06028 + 5.49831I
u = −0.988091 − 0.542376I
a = 0.473259 − 0.644867I
b = 0.136840 + 1.204680I
−1.24430 + 4.51893I 1.06028 − 5.49831I
u = 0.652457 + 0.571498I
a = 0.98577 − 1.47704I
b = 0.58799 + 1.32773I
−1.24430 + 4.51893I 1.06028 − 5.49831I
u = 0.652457 − 0.571498I
a = 0.98577 + 1.47704I
b = 0.58799 − 1.32773I
−1.24430 − 4.51893I 1.06028 + 5.49831I
u = 0.722344 + 0.873653I
a = −1.27009 − 0.90834I
b = 2.02407 − 0.21519I
−6.66680 − 5.70836I 3.28436 + 2.61089I
u = 0.722344 − 0.873653I
a = −1.27009 + 0.90834I
b = 2.02407 + 0.21519I
−6.66680 + 5.70836I 3.28436 − 2.61089I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971674 + 0.598016I
a = −0.392194 − 0.140230I
b = 0.003048 − 0.949049I
2.16312 + 4.62114I 11.65491 − 5.89029I
u = 0.971674 − 0.598016I
a = −0.392194 + 0.140230I
b = 0.003048 + 0.949049I
2.16312 − 4.62114I 11.65491 + 5.89029I
u = −0.695608 + 0.907900I
a = −1.66112 + 1.35074I
b = 2.39253 + 0.23778I
−9.5709 + 11.0305I 0.68896 − 6.00028I
u = −0.695608 − 0.907900I
a = −1.66112 − 1.35074I
b = 2.39253 − 0.23778I
−9.5709 − 11.0305I 0.68896 + 6.00028I
u = −0.128928 + 0.836166I
a = 0.704339 − 0.655474I
b = −0.253889 − 0.601697I
−6.22742 − 7.20928I −0.73612 + 6.27610I
u = −0.128928 − 0.836166I
a = 0.704339 + 0.655474I
b = −0.253889 + 0.601697I
−6.22742 + 7.20928I −0.73612 − 6.27610I
u = 0.834456 + 0.812598I
a = 1.21182 + 1.89134I
b = −2.39545 − 0.28919I
−6.53686 − 1.23377I −1.59190 + 0.83965I
u = 0.834456 − 0.812598I
a = 1.21182 − 1.89134I
b = −2.39545 + 0.28919I
−6.53686 + 1.23377I −1.59190 − 0.83965I
u = 0.054522 + 0.827933I
a = −0.782373 − 0.644964I
b = 0.272506 − 0.513614I
−6.53686 + 1.23377I −1.59190 − 0.83965I
u = 0.054522 − 0.827933I
a = −0.782373 + 0.644964I
b = 0.272506 + 0.513614I
−6.53686 − 1.23377I −1.59190 + 0.83965I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.139850 + 0.271378I
a = −0.431580 + 0.818565I
b = −0.237751 − 0.669102I
−2.50569 − 4.90020I 3.66047 + 4.25570I
u = −1.139850 − 0.271378I
a = −0.431580 − 0.818565I
b = −0.237751 + 0.669102I
−2.50569 + 4.90020I 3.66047 − 4.25570I
u = 0.955556 + 0.693925I
a = −1.33481 − 1.07208I
b = 2.06526 − 0.70643I
0.74787 + 5.97219I 9.15925 − 6.03254I
u = 0.955556 − 0.693925I
a = −1.33481 + 1.07208I
b = 2.06526 + 0.70643I
0.74787 − 5.97219I 9.15925 + 6.03254I
u = 1.160440 + 0.222987I
a = 0.476162 + 0.877504I
b = 0.345484 − 0.648450I
−1.81559 + 10.65820I 6.00000 − 9.11948I
u = 1.160440 − 0.222987I
a = 0.476162 − 0.877504I
b = 0.345484 + 0.648450I
−1.81559 − 10.65820I 6.00000 + 9.11948I
u = −0.782234 + 0.897806I
a = −1.60548 + 0.09310I
b = 1.66931 + 0.79077I
−11.54940 + 1.88087I 0
u = −0.782234 − 0.897806I
a = −1.60548 − 0.09310I
b = 1.66931 − 0.79077I
−11.54940 − 1.88087I 0
u = −0.535320 + 0.606452I
a = −1.054240 − 0.782163I
b = −0.070591 + 0.734237I
−2.58244 −2.20453 + 0.I
u = −0.535320 − 0.606452I
a = −1.054240 + 0.782163I
b = −0.070591 − 0.734237I
−2.58244 −2.20453 + 0.I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.934473 + 0.782146I
a = 2.03442 + 0.84782I
b = −2.58958 + 1.04646I
−6.22742 + 7.20928I 0. − 6.27610I
u = 0.934473 − 0.782146I
a = 2.03442 − 0.84782I
b = −2.58958 − 1.04646I
−6.22742 − 7.20928I 0. + 6.27610I
u = −0.978705 + 0.735947I
a = −2.06142 + 1.31787I
b = 3.02109 + 0.91961I
−1.81559 − 10.65820I 6.00000 + 9.11948I
u = −0.978705 − 0.735947I
a = −2.06142 − 1.31787I
b = 3.02109 − 0.91961I
−1.81559 + 10.65820I 6.00000 − 9.11948I
u = −1.001680 + 0.777271I
a = 1.16815 − 1.10223I
b = −2.16629 − 0.53914I
−6.66680 − 5.70836I 0
u = −1.001680 − 0.777271I
a = 1.16815 + 1.10223I
b = −2.16629 + 0.53914I
−6.66680 + 5.70836I 0
u = 0.978293 + 0.824595I
a = 0.66515 + 1.58276I
b = −1.76953 − 0.40279I
−11.54940 + 1.88087I 0
u = 0.978293 − 0.824595I
a = 0.66515 − 1.58276I
b = −1.76953 + 0.40279I
−11.54940 − 1.88087I 0
u = 1.034790 + 0.782497I
a = 1.58803 + 1.23418I
b = −2.80611 + 0.54589I
−9.5709 + 11.0305I 0
u = 1.034790 − 0.782497I
a = 1.58803 − 1.23418I
b = −2.80611 − 0.54589I
−9.5709 − 11.0305I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210315 + 0.193461I
a = −0.16245 − 3.16407I
b = 0.497755 − 0.746437I
0.11473 − 4.15162I 6.01126 + 6.89813I
u = −0.210315 − 0.193461I
a = −0.16245 + 3.16407I
b = 0.497755 + 0.746437I
0.11473 + 4.15162I 6.01126 − 6.89813I
16
III. I
u
3
= hu
3
+ u
2
+ b, −u
2
+ a + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
u
2
− 1
−u
3
− u
2
a
3
=
−u
−u
3
+ u
a
2
=
u
3
+ u
2
− u − 1
−2u
3
− u
2
a
7
=
−u
2
+ 1
u
2
a
10
=
0
−u
2
+ 1
a
6
=
−u
3
− u
2
+ u + 1
u
3
+ 2u
2
− 1
a
5
=
u
u
3
− u − 1
a
12
=
u
2
− 1
−u
3
− u
2
+ 1
a
11
=
−1
−u
3
− u
2
+ u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
2
+ 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
(y
2
− y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.500000 + 0.866025I
b = −0.50000 − 1.86603I
6.08965I 6.00000 − 10.39230I
u = 0.866025 − 0.500000I
a = −0.500000 − 0.866025I
b = −0.50000 + 1.86603I
− 6.08965I 6.00000 + 10.39230I
u = −0.866025 + 0.500000I
a = −0.500000 − 0.866025I
b = −0.500000 − 0.133975I
− 6.08965I 6.00000 + 10.39230I
u = −0.866025 − 0.500000I
a = −0.500000 + 0.866025I
b = −0.500000 + 0.133975I
6.08965I 6.00000 − 10.39230I
20
IV. I
u
4
= hb − u, a, u
12
− u
11
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
0
u
a
3
=
−u
−u
3
+ u
a
2
=
−u
3
−u
5
+ u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
u
4
− u
2
+ 1
u
6
− 2u
4
+ u
2
a
12
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
u
9
− u
7
+ u
5
+ u
a
11
=
−u
11
+ u
10
+ 3u
9
− 3u
8
− 4u
7
+ 5u
6
+ 2u
5
− 4u
4
+ u
2
− u + 1
−u
7
+ u
5
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
10
− 8u
8
+ 12u
6
− 4u
5
− 8u
4
+ 4u
3
+ 4u
2
− 4u + 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 5u
11
+ 14u
10
+ 25u
9
+ 32u
8
+ 27u
7
+ 13u
6
− 3u
5
− 8u
4
− 6u
3
+ 1
c
2
, c
3
, c
5
c
8
u
12
− u
11
− 2u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 3u
5
− 2u
4
+ 2u
2
− 2u + 1
c
4
, c
11
(u
3
+ u
2
− 1)
4
c
6
u
12
− 3u
11
+ ··· − 12u + 5
c
7
, c
9
u
12
− 5u
11
+ 14u
10
− 25u
9
+ 32u
8
− 27u
7
+ 13u
6
+ 3u
5
− 8u
4
+ 6u
3
+ 1
c
10
, c
12
(u
3
− u
2
+ 2u − 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
12
+ 3y
11
+ ··· − 16y
2
+ 1
c
2
, c
3
, c
5
c
8
y
12
− 5y
11
+ 14y
10
− 25y
9
+ 32y
8
− 27y
7
+ 13y
6
+ 3y
5
− 8y
4
+ 6y
3
+ 1
c
4
, c
11
(y
3
− y
2
+ 2y − 1)
4
c
6
y
12
− y
11
+ ··· + 36y + 25
c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823263 + 0.757838I
a = 0
b = 0.823263 + 0.757838I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = 0.823263 − 0.757838I
a = 0
b = 0.823263 − 0.757838I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.968261 + 0.566202I
a = 0
b = −0.968261 + 0.566202I
1.11345 9.01951 + 0.I
u = −0.968261 − 0.566202I
a = 0
b = −0.968261 − 0.566202I
1.11345 9.01951 + 0.I
u = 1.120810 + 0.355729I
a = 0
b = 1.120810 + 0.355729I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 1.120810 − 0.355729I
a = 0
b = 1.120810 − 0.355729I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −1.120460 + 0.417373I
a = 0
b = −1.120460 + 0.417373I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −1.120460 − 0.417373I
a = 0
b = −1.120460 − 0.417373I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = 0.590822 + 0.500935I
a = 0
b = 0.590822 + 0.500935I
1.11345 9.01951 + 0.I
u = 0.590822 − 0.500935I
a = 0
b = 0.590822 − 0.500935I
1.11345 9.01951 + 0.I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053832 + 0.729598I
a = 0
b = 0.053832 + 0.729598I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.053832 − 0.729598I
a = 0
b = 0.053832 − 0.729598I
−3.02413 − 2.82812I 2.49024 + 2.97945I
25
V.
I
u
5
= ha
3
u
2
+ 5a
2
u
2
+ · · · + 5a − 48, −2a
2
u
2
− 6u
2
a + · · · + 6a − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
a
−0.0217391a
3
u
2
− 0.108696a
2
u
2
+ ··· − 0.108696a + 1.04348
a
3
=
−u
u
2
+ u − 1
a
2
=
0.0652174a
3
u
2
+ 0.326087a
2
u
2
+ ··· + 0.326087a + 0.369565
0.108696a
3
u
2
+ 0.0434783a
2
u
2
+ ··· + 0.543478a + 0.782609
a
7
=
−u
2
+ 1
u
2
a
10
=
u
−u
2
− u + 1
a
6
=
−0.173913a
3
u
2
+ 0.130435a
2
u
2
+ ··· + 0.630435a + 1.34783
0.521739a
3
u
2
+ 0.108696a
2
u
2
+ ··· − 0.891304a − 1.04348
a
5
=
−0.0217391a
3
u
2
− 0.108696a
2
u
2
+ ··· + 0.891304a + 1.04348
−0.108696a
3
u
2
− 0.543478a
2
u
2
+ ··· − 0.543478a − 1.78261
a
12
=
0.0652174a
3
u
2
+ 0.326087a
2
u
2
+ ··· + 0.326087a + 0.369565
0.108696a
3
u
2
+ 0.0434783a
2
u
2
+ ··· + 0.543478a + 0.782609
a
11
=
0.369565a
3
u
2
− 0.152174a
2
u
2
+ ··· − 0.652174a − 0.239130
−0.0869565a
3
u
2
− 0.434783a
2
u
2
+ ··· − 0.434783a − 1.82609
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 5u
11
+ 14u
10
+ 25u
9
+ 32u
8
+ 27u
7
+ 13u
6
− 3u
5
− 8u
4
− 6u
3
+ 1
c
2
, c
4
, c
5
c
11
u
12
− u
11
− 2u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 3u
5
− 2u
4
+ 2u
2
− 2u + 1
c
3
, c
8
(u
3
+ u
2
− 1)
4
c
6
u
12
− 3u
11
+ ··· − 12u + 5
c
7
, c
9
(u
3
− u
2
+ 2u − 1)
4
c
10
, c
12
u
12
− 5u
11
+ 14u
10
− 25u
9
+ 32u
8
− 27u
7
+ 13u
6
+ 3u
5
− 8u
4
+ 6u
3
+ 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
12
+ 3y
11
+ ··· − 16y
2
+ 1
c
2
, c
4
, c
5
c
11
y
12
− 5y
11
+ 14y
10
− 25y
9
+ 32y
8
− 27y
7
+ 13y
6
+ 3y
5
− 8y
4
+ 6y
3
+ 1
c
3
, c
8
(y
3
− y
2
+ 2y − 1)
4
c
6
y
12
− y
11
+ ··· + 36y + 25
c
7
, c
9
(y
3
+ 3y
2
+ 2y − 1)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.290605 − 0.301472I
b = 0.010927 − 1.027890I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 + 0.744862I
a = 1.24058 − 0.98320I
b = −1.95244 − 0.50017I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 + 0.744862I
a = −0.83409 + 2.24143I
b = 2.38794 − 0.77609I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 + 0.744862I
a = −2.45197 + 0.53297I
b = 2.43100 + 1.55928I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 − 0.744862I
a = 0.290605 + 0.301472I
b = 0.010927 + 1.027890I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = 1.24058 + 0.98320I
b = −1.95244 + 0.50017I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = −0.83409 − 2.24143I
b = 2.38794 + 0.77609I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = −2.45197 − 0.53297I
b = 2.43100 − 1.55928I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.754878
a = −1.024590 + 0.311643I
b = 0.570737 + 0.650080I
1.11345 9.01950
u = 0.754878
a = −1.024590 − 0.311643I
b = 0.570737 − 0.650080I
1.11345 9.01950
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754878
a = 1.77946 + 0.29139I
b = 0.05182 − 1.57785I
1.11345 9.01950
u = 0.754878
a = 1.77946 − 0.29139I
b = 0.05182 + 1.57785I
1.11345 9.01950
30
VI. I
u
6
= hb − u, a, u
3
+ u
2
− 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
0
u
a
3
=
−u
u
2
+ u − 1
a
2
=
u
2
− 1
−u
2
+ 2u
a
7
=
−u
2
+ 1
u
2
a
10
=
u
−u
2
− u + 1
a
6
=
−u
2
+ 1
u
2
− u + 1
a
5
=
u
−2u
2
− u + 2
a
12
=
u
2
− 1
−u
2
+ 2u
a
11
=
1
2u
2
− 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
+ 2u + 1
c
2
, c
3
, c
4
c
5
, c
8
, c
11
u
3
+ u
2
− 1
c
6
u
3
+ 3u
2
+ 2u − 1
c
7
, c
9
, c
10
c
12
u
3
− u
2
+ 2u − 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
3
, c
4
c
5
, c
8
, c
11
y
3
− y
2
+ 2y − 1
c
6
y
3
− 5y
2
+ 10y − 1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0
b = −0.877439 + 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 − 0.744862I
a = 0
b = −0.877439 − 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.754878
a = 0
b = 0.754878
1.11345 9.01950
34
VII. I
u
7
= h−u
2
+ b − u + 1, a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
1
u
2
+ u − 1
a
3
=
−u
−u
3
+ u
a
2
=
−u
3
+ 1
u
2
+ 2u − 1
a
7
=
−u
2
+ 1
u
2
a
10
=
0
−u
2
+ 1
a
6
=
−u
3
− u
2
+ u + 1
u
3
+ u
2
+ 1
a
5
=
−u
3
−u
2
+ u + 1
a
12
=
1
u − 1
a
11
=
−u
2
+ 1
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
+ u + 1)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
(y
2
− y + 1)
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.00000
b = 0.36603 + 1.36603I
− 2.02988I 6.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 1.00000
b = 0.36603 − 1.36603I
2.02988I 6.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 1.00000
b = −1.36603 − 0.36603I
2.02988I 6.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 1.00000
b = −1.36603 + 0.36603I
− 2.02988I 6.00000 + 3.46410I
38
VIII. I
u
8
= hu
2
+ b − u, −u
2
+ a + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
u
2
− 1
−u
2
+ u
a
3
=
−u
−u
3
+ u
a
2
=
−u
3
+ u
2
− 1
−u
2
+ 2u
a
7
=
−u
2
+ 1
u
2
a
10
=
0
−u
2
+ 1
a
6
=
u
3
− u
2
+ 1
u
2
− u + 1
a
5
=
u
u
3
− u
2
− u + 1
a
12
=
u
2
− 1
−u
2
+ u + 1
a
11
=
−1
u
3
− u
2
+ 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
+ u + 1)
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
(y
2
− y + 1)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.500000 + 0.866025I
b = 0.366025 − 0.366025I
2.02988I 6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.500000 − 0.866025I
b = 0.366025 + 0.366025I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = −0.500000 − 0.866025I
b = −1.36603 + 1.36603I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = −0.500000 + 0.866025I
b = −1.36603 − 1.36603I
2.02988I 6.00000 − 3.46410I
42
IX. I
u
9
= hu
3
− u
2
+ b + 1, a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
1
−u
3
+ u
2
− 1
a
3
=
−u
−u
3
+ u
a
2
=
u
3
− u + 1
−2u
3
+ u
2
− 1
a
7
=
−u
2
+ 1
u
2
a
10
=
0
−u
2
+ 1
a
6
=
−u
2
− u + 1
−u
3
+ 2u
2
+ u − 1
a
5
=
−u
3
u − 1
a
12
=
1
−u
3
− 1
a
11
=
−u
2
+ 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
u
4
− u
2
+ 1
c
7
, c
10
(u
2
+ u + 1)
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
c
10
, c
12
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
11
(y
2
− y + 1)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.00000
b = −0.500000 − 0.133975I
2.02988I 6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = 1.00000
b = −0.500000 + 0.133975I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 1.00000
b = −0.50000 − 1.86603I
− 2.02988I 6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 1.00000
b = −0.50000 + 1.86603I
2.02988I 6.00000 − 3.46410I
46
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
8
(u
3
+ u
2
+ 2u + 1)
· (u
12
+ 5u
11
+ 14u
10
+ 25u
9
+ 32u
8
+ 27u
7
+ 13u
6
− 3u
5
− 8u
4
− 6u
3
+ 1)
2
· (u
24
+ 12u
23
+ ··· + 56u + 16)(u
26
+ 15u
25
+ ··· + 4u + 1)
2
c
2
, c
5
(u
3
+ u
2
− 1)(u
4
− u
2
+ 1)
4
· (u
12
− u
11
− 2u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 3u
5
− 2u
4
+ 2u
2
− 2u + 1)
2
· (u
24
+ 4u
23
+ ··· + 12u + 4)(u
26
− u
25
+ ··· − 2u
2
+ 1)
2
c
3
, c
4
, c
8
c
11
(u
3
+ u
2
− 1)
5
(u
4
− u
2
+ 1)
4
· (u
12
− u
11
− 2u
10
+ 3u
9
+ 2u
8
− 5u
7
+ u
6
+ 3u
5
− 2u
4
+ 2u
2
− 2u + 1)
· (u
24
− u
23
+ ··· − 3u
2
+ 1)(u
52
− 2u
51
+ ··· + 20u + 4)
c
6
(u
3
+ 3u
2
+ 2u − 1)(u
4
− u
2
+ 1)
4
(u
12
− 3u
11
+ ··· − 12u + 5)
2
· (u
24
+ 12u
23
+ ··· + 876u + 188)(u
26
− 3u
25
+ ··· + 4u + 1)
2
c
7
, c
10
(u
2
+ u + 1)
8
(u
3
− u
2
+ 2u − 1)
5
· (u
12
− 5u
11
+ 14u
10
− 25u
9
+ 32u
8
− 27u
7
+ 13u
6
+ 3u
5
− 8u
4
+ 6u
3
+ 1)
· (u
24
− 7u
23
+ ··· − 6u + 1)(u
52
− 16u
51
+ ··· − 152u + 16)
c
9
, c
12
(u
2
− u + 1)
8
(u
3
− u
2
+ 2u − 1)
5
· (u
12
− 5u
11
+ 14u
10
− 25u
9
+ 32u
8
− 27u
7
+ 13u
6
+ 3u
5
− 8u
4
+ 6u
3
+ 1)
· (u
24
− 7u
23
+ ··· − 6u + 1)(u
52
− 16u
51
+ ··· − 152u + 16)
47
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
8
)(y
3
+ 3y
2
+ 2y − 1)(y
12
+ 3y
11
+ ··· − 16y
2
+ 1)
2
· (y
24
+ 24y
22
+ ··· + 1760y + 256)(y
26
− 3y
25
+ ··· − 16y + 1)
2
c
2
, c
5
(y
2
− y + 1)
8
(y
3
− y
2
+ 2y − 1)
· (y
12
− 5y
11
+ 14y
10
− 25y
9
+ 32y
8
− 27y
7
+ 13y
6
+ 3y
5
− 8y
4
+ 6y
3
+ 1)
2
· (y
24
− 12y
23
+ ··· − 56y + 16)(y
26
− 15y
25
+ ··· − 4y + 1)
2
c
3
, c
4
, c
8
c
11
(y
2
− y + 1)
8
(y
3
− y
2
+ 2y − 1)
5
· (y
12
− 5y
11
+ 14y
10
− 25y
9
+ 32y
8
− 27y
7
+ 13y
6
+ 3y
5
− 8y
4
+ 6y
3
+ 1)
· (y
24
− 7y
23
+ ··· − 6y + 1)(y
52
− 16y
51
+ ··· − 152y + 16)
c
6
((y
2
− y + 1)
8
)(y
3
− 5y
2
+ 10y − 1)(y
12
− y
11
+ ··· + 36y + 25)
2
· (y
24
+ 12y
23
+ ··· − 37560y + 35344)(y
26
+ 21y
25
+ ··· − 68y + 1)
2
c
7
, c
9
, c
10
c
12
((y
2
+ y + 1)
8
)(y
3
+ 3y
2
+ 2y − 1)
5
(y
12
+ 3y
11
+ ··· − 16y
2
+ 1)
· (y
24
+ 25y
23
+ ··· + 6y + 1)(y
52
+ 40y
51
+ ··· + 78048y + 256)
48
