12n
0397
(K12n
0397
)
A knot diagram
1
Linearized knot diagam
3 5 12 10 2 11 3 5 4 9 7 8
Solving Sequence
4,10 5,12
3 2 1 9 8 7 11 6
c
4
c
3
c
2
c
1
c
9
c
8
c
7
c
11
c
6
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ 8u
22
+ ··· + 2b + 26, −23u
23
− 133u
22
+ ··· + 8a − 112, u
24
+ 7u
23
+ ··· + 44u + 8i
I
u
2
= h2u
17
− 9u
15
+ 21u
13
− 28u
11
+ 2u
10
+ 23u
9
− 7u
8
− 7u
7
+ 10u
6
− 5u
5
− 6u
4
+ 7u
3
+ b − 3u + 1,
− 2u
17
+ u
16
+ ··· + a − 3,
u
18
− 5u
16
+ 13u
14
− 20u
12
+ u
11
+ 20u
10
− 4u
9
− 11u
8
+ 7u
7
+ u
6
− 6u
5
+ 4u
4
+ 2u
3
− 3u
2
+ 1i
I
u
3
= h109a
3
u
2
− 389a
2
u
2
+ ··· + 1134a − 188, a
4
+ a
3
u + a
2
u
2
− a
3
− 10a
2
u − 5u
2
a − 3au − 5a − 4u − 1,
u
3
− u
2
+ 1i
I
u
4
= hb + u, a
2
+ au + 4u
2
− 6u + 4, u
3
− u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 60 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
23
+ 8u
22
+ · · · + 2b + 26, −23u
23
− 133u
22
+ · · · + 8a − 112, u
24
+
7u
23
+ · · · + 44u + 8i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
23
8
u
23
+
133
8
u
22
+ ··· +
145
2
u + 14
−
1
2
u
23
− 4u
22
+ ··· −
105
2
u − 13
a
3
=
3.37500u
23
+ 20.8750u
22
+ ··· + 119.750u + 25.5000
−
3
4
u
23
−
25
4
u
22
+ ··· − 71u − 17
a
2
=
3.12500u
23
+ 18.1250u
22
+ ··· + 96.7500u + 20.5000
−
15
4
u
23
−
89
4
u
22
+ ··· − 117u − 25
a
1
=
−
57
8
u
23
−
339
8
u
22
+ ··· −
359
2
u − 34
−2u
23
−
13
2
u
22
+ ··· +
105
2
u + 15
a
9
=
−u
u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
21
8
u
23
+
133
8
u
22
+ ··· +
375
4
u + 19
−
1
4
u
23
−
13
4
u
22
+ ··· −
63
2
u − 7
a
11
=
u
3
−u
3
+ u
a
6
=
−
27
8
u
23
−
155
8
u
22
+ ··· −
281
4
u − 13
17
4
u
23
+
105
4
u
22
+ ··· +
273
2
u + 27
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5u
23
+ 31u
22
+ 68u
21
+ 5u
20
− 274u
19
− 532u
18
− 143u
17
+
1013u
16
+ 1701u
15
+ 430u
14
− 2124u
13
− 3067u
12
− 781u
11
+ 2554u
10
+ 3417u
9
+
1220u
8
− 1377u
7
− 2052u
6
− 1028u
5
+ 135u
4
+ 565u
3
+ 416u
2
+ 168u + 30
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 40u
23
+ ··· − 13u + 1
c
2
, c
5
, c
7
u
24
+ 20u
22
+ ··· − 3u + 1
c
3
u
24
− 12u
23
+ ··· − 80u + 8
c
4
, c
9
u
24
+ 7u
23
+ ··· + 44u + 8
c
6
, c
11
u
24
+ u
23
+ ··· − 2u + 1
c
8
u
24
+ 21u
23
+ ··· + 6588u + 1192
c
10
u
24
− 11u
23
+ ··· − 16u + 64
c
12
u
24
− u
23
+ ··· − 146u + 481
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 132y
23
+ ··· − 117y + 1
c
2
, c
5
, c
7
y
24
+ 40y
23
+ ··· − 13y + 1
c
3
y
24
+ 2y
23
+ ··· − 544y + 64
c
4
, c
9
y
24
− 11y
23
+ ··· − 16y + 64
c
6
, c
11
y
24
− 33y
23
+ ··· + 38y + 1
c
8
y
24
+ y
23
+ ··· + 2294768y + 1420864
c
10
y
24
+ 5y
23
+ ··· − 29952y + 4096
c
12
y
24
+ 57y
23
+ ··· − 2861140y + 231361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.915808 + 0.204074I
a = 0.308825 − 0.358584I
b = 0.420523 + 0.284056I
1.43685 + 0.26824I 8.25591 − 0.95433I
u = 0.915808 − 0.204074I
a = 0.308825 + 0.358584I
b = 0.420523 − 0.284056I
1.43685 − 0.26824I 8.25591 + 0.95433I
u = −0.768219 + 0.429349I
a = −0.123850 + 0.819559I
b = −0.846044 − 0.245760I
−1.24603 − 1.86074I −2.80514 + 4.17649I
u = −0.768219 − 0.429349I
a = −0.123850 − 0.819559I
b = −0.846044 + 0.245760I
−1.24603 + 1.86074I −2.80514 − 4.17649I
u = −0.485800 + 1.043550I
a = 0.700910 − 0.279759I
b = 1.10350 + 1.17587I
−16.7128 − 1.0407I −2.67460 + 1.48969I
u = −0.485800 − 1.043550I
a = 0.700910 + 0.279759I
b = 1.10350 − 1.17587I
−16.7128 + 1.0407I −2.67460 − 1.48969I
u = −0.533713 + 1.023160I
a = 0.687357 + 0.197125I
b = 1.16784 − 1.06324I
−17.0702 + 7.3018I −2.46091 − 2.45661I
u = −0.533713 − 1.023160I
a = 0.687357 − 0.197125I
b = 1.16784 + 1.06324I
−17.0702 − 7.3018I −2.46091 + 2.45661I
u = −0.454642 + 0.697047I
a = 1.245930 + 0.051953I
b = 0.672512 − 0.074959I
−2.81566 + 1.10173I −1.51034 + 1.46986I
u = −0.454642 − 0.697047I
a = 1.245930 − 0.051953I
b = 0.672512 + 0.074959I
−2.81566 − 1.10173I −1.51034 − 1.46986I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115630 + 0.467131I
a = 1.09132 + 1.37936I
b = 0.103648 − 1.034020I
3.47697 + 2.26614I 7.38300 + 0.31343I
u = 1.115630 − 0.467131I
a = 1.09132 − 1.37936I
b = 0.103648 + 1.034020I
3.47697 − 2.26614I 7.38300 − 0.31343I
u = −1.065690 + 0.574907I
a = 0.844325 − 1.000110I
b = 0.707678 + 0.133194I
−1.01811 − 6.00438I 3.14307 + 1.73510I
u = −1.065690 − 0.574907I
a = 0.844325 + 1.000110I
b = 0.707678 − 0.133194I
−1.01811 + 6.00438I 3.14307 − 1.73510I
u = −1.162360 + 0.452653I
a = −0.55210 + 1.89083I
b = −0.452316 − 1.190600I
3.55309 − 5.72713I 8.49615 + 7.00160I
u = −1.162360 − 0.452653I
a = −0.55210 − 1.89083I
b = −0.452316 + 1.190600I
3.55309 + 5.72713I 8.49615 − 7.00160I
u = −0.068716 + 0.634302I
a = 0.139760 − 0.437493I
b = −0.335421 + 0.843529I
0.48313 + 1.57128I 3.43704 − 4.17540I
u = −0.068716 − 0.634302I
a = 0.139760 + 0.437493I
b = −0.335421 − 0.843529I
0.48313 − 1.57128I 3.43704 + 4.17540I
u = 1.373310 + 0.032921I
a = −0.55767 + 1.51729I
b = 1.20249 − 1.15069I
−9.59467 + 4.37178I 1.10728 − 2.37526I
u = 1.373310 − 0.032921I
a = −0.55767 − 1.51729I
b = 1.20249 + 1.15069I
−9.59467 − 4.37178I 1.10728 + 2.37526I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165950 + 0.738930I
a = 1.12460 − 1.76379I
b = 1.18433 + 1.02927I
−15.0954 − 13.6960I −0.56874 + 6.51708I
u = −1.165950 − 0.738930I
a = 1.12460 + 1.76379I
b = 1.18433 − 1.02927I
−15.0954 + 13.6960I −0.56874 − 6.51708I
u = −1.199670 + 0.725513I
a = −0.909394 − 0.070498I
b = 1.07127 − 1.22148I
−14.4845 − 5.3708I −0.80273 + 2.57897I
u = −1.199670 − 0.725513I
a = −0.909394 + 0.070498I
b = 1.07127 + 1.22148I
−14.4845 + 5.3708I −0.80273 − 2.57897I
7
II.
I
u
2
= h2u
17
−9u
15
+· · ·+b+1, −2u
17
+u
16
+· · ·+a−3, u
18
−5u
16
+· · ·−3u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
2u
17
− u
16
+ ··· − 3u + 3
−2u
17
+ 9u
15
+ ··· + 3u − 1
a
3
=
2u
17
− 3u
16
+ ··· − 3u + 4
−2u
17
+ 2u
16
+ ··· + 3u − 3
a
2
=
3u
17
− 3u
16
+ ··· − 4u + 4
−3u
17
+ 2u
16
+ ··· + 4u − 3
a
1
=
3u
17
− 12u
15
+ ··· − 4u + 2
−3u
17
+ 13u
15
+ ··· + 4u − 1
a
9
=
−u
u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
−2u
17
− u
16
+ ··· − 2u
2
+ 5u
−u
15
+ 4u
13
− 8u
11
+ 8u
9
− u
8
− 4u
7
+ 3u
6
− u
5
− 3u
4
+ 2u
3
− u + 1
a
11
=
u
3
−u
3
+ u
a
6
=
−2u
17
+ 10u
15
+ ··· + 5u − 1
−u
15
+ u
14
+ ··· − 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
17
−9u
16
−36u
15
+ 40u
14
+ 85u
13
−93u
12
−115u
11
+ 128u
10
+
88u
9
− 123u
8
− u
7
+ 66u
6
− 62u
5
− 10u
4
+ 52u
3
− 25u
2
− 10u + 9
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 18u
17
+ ··· − 11u + 1
c
2
, c
7
u
18
+ 9u
16
+ ··· − u + 1
c
3
u
18
+ 7u
17
+ ··· − 8u
2
+ 1
c
4
u
18
− 5u
16
+ ··· − 3u
2
+ 1
c
5
u
18
+ 9u
16
+ ··· + u + 1
c
6
u
18
+ u
17
+ ··· + 2u + 1
c
8
u
18
+ 3u
16
+ ··· − 3u
2
+ 1
c
9
u
18
− 5u
16
+ ··· − 3u
2
+ 1
c
10
u
18
− 10u
17
+ ··· − 6u + 1
c
11
u
18
− u
17
+ ··· − 2u + 1
c
12
u
18
+ u
17
+ ··· − 4u
2
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 34y
17
+ ··· + 15y + 1
c
2
, c
5
, c
7
y
18
+ 18y
17
+ ··· + 11y + 1
c
3
y
18
+ 3y
17
+ ··· − 16y + 1
c
4
, c
9
y
18
− 10y
17
+ ··· − 6y + 1
c
6
, c
11
y
18
− 7y
17
+ ··· − 10y + 1
c
8
y
18
+ 6y
17
+ ··· − 6y + 1
c
10
y
18
+ 2y
17
+ ··· − 2y + 1
c
12
y
18
+ 19y
17
+ ··· − 8y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904746 + 0.245141I
a = 0.82192 + 2.64809I
b = 0.886797 − 0.175898I
−4.91866 + 1.07876I −1.73448 − 6.58149I
u = 0.904746 − 0.245141I
a = 0.82192 − 2.64809I
b = 0.886797 + 0.175898I
−4.91866 − 1.07876I −1.73448 + 6.58149I
u = −1.016240 + 0.389137I
a = 0.572143 − 0.544697I
b = −1.041090 + 0.572987I
−0.238865 + 0.538366I 0.033663 + 0.201088I
u = −1.016240 − 0.389137I
a = 0.572143 + 0.544697I
b = −1.041090 − 0.572987I
−0.238865 − 0.538366I 0.033663 − 0.201088I
u = −0.881768 + 0.726056I
a = −1.46172 − 0.04608I
b = 0.357663 − 0.073463I
−8.08514 − 2.77083I 1.63500 + 2.47333I
u = −0.881768 − 0.726056I
a = −1.46172 + 0.04608I
b = 0.357663 + 0.073463I
−8.08514 + 2.77083I 1.63500 − 2.47333I
u = 1.037690 + 0.534998I
a = −1.34462 − 1.39462I
b = −0.838028 + 0.445978I
−1.29375 + 6.79726I 0.08657 − 10.35459I
u = 1.037690 − 0.534998I
a = −1.34462 + 1.39462I
b = −0.838028 − 0.445978I
−1.29375 − 6.79726I 0.08657 + 10.35459I
u = 0.551142 + 0.552499I
a = −1.46793 − 0.56794I
b = −0.719476 − 0.551592I
−2.79898 − 2.36719I −1.07277 + 3.81163I
u = 0.551142 − 0.552499I
a = −1.46793 + 0.56794I
b = −0.719476 + 0.551592I
−2.79898 + 2.36719I −1.07277 − 3.81163I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098568 + 0.770121I
a = −0.1181270 + 0.0762608I
b = −0.399233 + 1.101750I
−0.95237 + 1.65920I −2.51109 − 2.64437I
u = 0.098568 − 0.770121I
a = −0.1181270 − 0.0762608I
b = −0.399233 − 1.101750I
−0.95237 − 1.65920I −2.51109 + 2.64437I
u = −0.703037 + 0.218633I
a = 0.48139 + 1.75543I
b = −1.019720 − 0.825776I
−1.54644 − 3.40184I −4.66379 + 8.73031I
u = −0.703037 − 0.218633I
a = 0.48139 − 1.75543I
b = −1.019720 + 0.825776I
−1.54644 + 3.40184I −4.66379 − 8.73031I
u = −1.194980 + 0.426737I
a = −0.46757 + 1.90862I
b = −0.59911 − 1.38196I
2.73425 − 5.77721I −1.49014 + 6.51918I
u = −1.194980 − 0.426737I
a = −0.46757 − 1.90862I
b = −0.59911 + 1.38196I
2.73425 + 5.77721I −1.49014 − 6.51918I
u = 1.203880 + 0.487334I
a = 0.98453 + 1.10774I
b = −0.127799 − 1.272500I
2.29556 + 3.01264I 0.71705 − 2.77521I
u = 1.203880 − 0.487334I
a = 0.98453 − 1.10774I
b = −0.127799 + 1.272500I
2.29556 − 3.01264I 0.71705 + 2.77521I
12
III. I
u
3
=
h109a
3
u
2
−389a
2
u
2
+· · ·+1134a −188, a
2
u
2
−5u
2
a+· · ·−5a −1, u
3
−u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
a
−0.0527590a
3
u
2
+ 0.188287a
2
u
2
+ ··· − 0.548887a + 0.0909971
a
3
=
0.0387222a
3
u
2
+ 0.260891a
2
u
2
+ ··· + 0.861568a + 0.836883
−0.227009a
3
u
2
+ 0.264279a
2
u
2
+ ··· − 2.42594a − 0.424976
a
2
=
0.170378a
3
u
2
+ 0.0479187a
2
u
2
+ ··· + 1.79090a + 0.582285
−0.251210a
3
u
2
+ 0.0387222a
2
u
2
+ ··· − 2.71442a − 1.13553
a
1
=
−0.300581a
3
u
2
+ 0.118587a
2
u
2
+ ··· − 1.06292a − 1.16505
−0.174250a
3
u
2
+ 0.0759923a
2
u
2
+ ··· − 0.877057a − 0.515973
a
9
=
−u
u
a
8
=
−u
2
+ 1
−u
2
a
7
=
0.316070a
3
u
2
− 0.114230a
2
u
2
+ ··· + 2.40755a + 2.39981
−0.0963214a
3
u
2
+ 0.0822846a
2
u
2
+ ··· − 1.26815a − 0.787996
a
11
=
u
2
− 1
−u
2
+ u + 1
a
6
=
0.188771a
3
u
2
− 0.0406583a
2
u
2
+ ··· + 1.45015a + 1.64230
−0.241530a
3
u
2
+ 0.228945a
2
u
2
+ ··· − 1.99903a − 0.551307
(ii) Obstruction class = −1
(iii) Cusp Shapes =
218
1033
a
3
u
2
−
938
1033
a
3
u −
778
1033
a
2
u
2
+
198
1033
a
3
+
1092
1033
a
2
u +
7756
1033
u
2
a −
138
1033
a
2
−
2856
1033
au +
2132
1033
u
2
+
2268
1033
a −
3582
1033
u −
2442
1033
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 20u
11
+ ··· − 972u + 729
c
2
, c
5
, c
7
u
12
+ 4u
11
+ ··· + 108u + 27
c
3
(u
3
+ u
2
− 1)
4
c
4
, c
9
(u
3
− u
2
+ 1)
4
c
6
, c
11
u
12
+ 3u
11
+ ··· + 8u + 8
c
8
(u
3
− 3u
2
+ 2u + 1)
4
c
10
(u
3
− u
2
+ 2u − 1)
4
c
12
u
12
+ 5u
11
+ ··· − 52u + 8
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 60y
11
+ ··· + 157464y + 531441
c
2
, c
5
, c
7
y
12
+ 20y
11
+ ··· − 972y + 729
c
3
, c
4
, c
9
(y
3
− y
2
+ 2y −1)
4
c
6
, c
11
y
12
+ y
11
+ ··· + 288y + 64
c
8
(y
3
− 5y
2
+ 10y −1)
4
c
10
(y
3
+ 3y
2
+ 2y −1)
4
c
12
y
12
+ 37y
11
+ ··· − 1360y + 64
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.803930 − 0.531274I
b = −0.877439 + 0.744862I
−4.93480 + 5.65624I −2.00000 − 5.95889I
u = 0.877439 + 0.744862I
a = −0.423353 + 0.379086I
b = 0.754878
−9.07239 + 2.82812I −8.52927 − 2.97945I
u = 0.877439 + 0.744862I
a = −2.29278 − 1.33815I
b = −0.877439 + 0.744862I
−4.93480 + 5.65624I −2.00000 − 5.95889I
u = 0.877439 + 0.744862I
a = 3.64263 + 0.74547I
b = 0.754878
−9.07239 + 2.82812I −8.52927 − 2.97945I
u = 0.877439 − 0.744862I
a = −0.803930 + 0.531274I
b = −0.877439 − 0.744862I
−4.93480 − 5.65624I −2.00000 + 5.95889I
u = 0.877439 − 0.744862I
a = −0.423353 − 0.379086I
b = 0.754878
−9.07239 − 2.82812I −8.52927 + 2.97945I
u = 0.877439 − 0.744862I
a = −2.29278 + 1.33815I
b = −0.877439 − 0.744862I
−4.93480 − 5.65624I −2.00000 + 5.95889I
u = 0.877439 − 0.744862I
a = 3.64263 − 0.74547I
b = 0.754878
−9.07239 − 2.82812I −8.52927 + 2.97945I
u = −0.754878
a = 0.374103 + 0.381158I
b = −0.877439 − 0.744862I
−0.79722 − 2.82812I 4.52927 + 2.97945I
u = −0.754878
a = 0.374103 − 0.381158I
b = −0.877439 + 0.744862I
−0.79722 + 2.82812I 4.52927 − 2.97945I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 0.50334 + 2.61282I
b = −0.877439 − 0.744862I
−0.79722 − 2.82812I 4.52927 + 2.97945I
u = −0.754878
a = 0.50334 − 2.61282I
b = −0.877439 + 0.744862I
−0.79722 + 2.82812I 4.52927 − 2.97945I
17
IV. I
u
4
= hb + u, a
2
+ au + 4u
2
− 6u + 4, u
3
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
12
=
a
−u
a
3
=
au + 1
−u
2
a
2
=
−u
2
a + au + a + 1
−au − u
2
− a
a
1
=
au + 2u
2
+ 2a − 1
−u
2
a + au + u
2
+ a
a
9
=
−u
u
a
8
=
−u
2
+ 1
−u
2
a
7
=
u
2
a − a + u − 2
au + a + u
a
11
=
u
2
− 1
−u
2
+ u + 1
a
6
=
−u
2
a + au + a + 2u − 1
u
2
a − au − u
2
− a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 7u
5
+ 30u
4
+ 79u
3
+ 120u
2
+ 112u + 64
c
2
, c
5
, c
7
u
6
− 3u
5
+ 8u
4
− 11u
3
+ 16u
2
− 12u + 8
c
3
(u
3
+ u
2
− 1)
2
c
4
, c
9
(u
3
− u
2
+ 1)
2
c
6
, c
11
u
6
− 5u
4
− 4u
3
+ 6u
2
+ 12u + 7
c
8
(u
3
− 3u
2
+ 2u + 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
c
12
u
6
− 4u
5
+ 9u
4
− 18u
3
+ 34u
2
− 34u + 19
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 11y
5
+ 34y
4
− 481y
3
+ 544y
2
+ 2816y + 4096
c
2
, c
5
, c
7
y
6
+ 7y
5
+ 30y
4
+ 79y
3
+ 120y
2
+ 112y + 64
c
3
, c
4
, c
9
(y
3
− y
2
+ 2y −1)
2
c
6
, c
11
y
6
− 10y
5
+ 37y
4
− 62y
3
+ 62y
2
− 60y + 49
c
8
(y
3
− 5y
2
+ 10y −1)
2
c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
12
y
6
+ 2y
5
+ 5y
4
+ 54y
3
+ 274y
2
+ 136y + 361
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −1.176340 − 0.079183I
b = −0.877439 − 0.744862I
−4.93480 −2.00000
u = 0.877439 + 0.744862I
a = 0.298897 − 0.665679I
b = −0.877439 − 0.744862I
−4.93480 −2.00000
u = 0.877439 − 0.744862I
a = −1.176340 + 0.079183I
b = −0.877439 + 0.744862I
−4.93480 −2.00000
u = 0.877439 − 0.744862I
a = 0.298897 + 0.665679I
b = −0.877439 + 0.744862I
−4.93480 −2.00000
u = −0.754878
a = 0.37744 + 3.26591I
b = 0.754878
−4.93480 −2.00000
u = −0.754878
a = 0.37744 − 3.26591I
b = 0.754878
−4.93480 −2.00000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 7u
5
+ 30u
4
+ 79u
3
+ 120u
2
+ 112u + 64)
· (u
12
+ 20u
11
+ ··· − 972u + 729)(u
18
− 18u
17
+ ··· − 11u + 1)
· (u
24
+ 40u
23
+ ··· − 13u + 1)
c
2
, c
7
(u
6
− 3u
5
+ ··· − 12u + 8)(u
12
+ 4u
11
+ ··· + 108u + 27)
· (u
18
+ 9u
16
+ ··· − u + 1)(u
24
+ 20u
22
+ ··· − 3u + 1)
c
3
((u
3
+ u
2
− 1)
6
)(u
18
+ 7u
17
+ ··· − 8u
2
+ 1)(u
24
− 12u
23
+ ··· − 80u + 8)
c
4
((u
3
− u
2
+ 1)
6
)(u
18
− 5u
16
+ ··· − 3u
2
+ 1)(u
24
+ 7u
23
+ ··· + 44u + 8)
c
5
(u
6
− 3u
5
+ ··· − 12u + 8)(u
12
+ 4u
11
+ ··· + 108u + 27)
· (u
18
+ 9u
16
+ ··· + u + 1)(u
24
+ 20u
22
+ ··· − 3u + 1)
c
6
(u
6
− 5u
4
− 4u
3
+ 6u
2
+ 12u + 7)(u
12
+ 3u
11
+ ··· + 8u + 8)
· (u
18
+ u
17
+ ··· + 2u + 1)(u
24
+ u
23
+ ··· − 2u + 1)
c
8
((u
3
− 3u
2
+ 2u + 1)
6
)(u
18
+ 3u
16
+ ··· − 3u
2
+ 1)
· (u
24
+ 21u
23
+ ··· + 6588u + 1192)
c
9
((u
3
− u
2
+ 1)
6
)(u
18
− 5u
16
+ ··· − 3u
2
+ 1)(u
24
+ 7u
23
+ ··· + 44u + 8)
c
10
((u
3
− u
2
+ 2u − 1)
6
)(u
18
− 10u
17
+ ··· − 6u + 1)
· (u
24
− 11u
23
+ ··· − 16u + 64)
c
11
(u
6
− 5u
4
− 4u
3
+ 6u
2
+ 12u + 7)(u
12
+ 3u
11
+ ··· + 8u + 8)
· (u
18
− u
17
+ ··· − 2u + 1)(u
24
+ u
23
+ ··· − 2u + 1)
c
12
(u
6
− 4u
5
+ ··· − 34u + 19)(u
12
+ 5u
11
+ ··· − 52u + 8)
· (u
18
+ u
17
+ ··· − 4u
2
+ 1)(u
24
− u
23
+ ··· − 146u + 481)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ 11y
5
+ 34y
4
− 481y
3
+ 544y
2
+ 2816y + 4096)
· (y
12
− 60y
11
+ ··· + 157464y + 531441)(y
18
− 34y
17
+ ··· + 15y + 1)
· (y
24
− 132y
23
+ ··· − 117y + 1)
c
2
, c
5
, c
7
(y
6
+ 7y
5
+ 30y
4
+ 79y
3
+ 120y
2
+ 112y + 64)
· (y
12
+ 20y
11
+ ··· − 972y + 729)(y
18
+ 18y
17
+ ··· + 11y + 1)
· (y
24
+ 40y
23
+ ··· − 13y + 1)
c
3
((y
3
− y
2
+ 2y −1)
6
)(y
18
+ 3y
17
+ ··· − 16y + 1)
· (y
24
+ 2y
23
+ ··· − 544y + 64)
c
4
, c
9
((y
3
− y
2
+ 2y −1)
6
)(y
18
− 10y
17
+ ··· − 6y + 1)
· (y
24
− 11y
23
+ ··· − 16y + 64)
c
6
, c
11
(y
6
− 10y
5
+ 37y
4
− 62y
3
+ 62y
2
− 60y + 49)
· (y
12
+ y
11
+ ··· + 288y + 64)(y
18
− 7y
17
+ ··· − 10y + 1)
· (y
24
− 33y
23
+ ··· + 38y + 1)
c
8
((y
3
− 5y
2
+ 10y −1)
6
)(y
18
+ 6y
17
+ ··· − 6y + 1)
· (y
24
+ y
23
+ ··· + 2294768y + 1420864)
c
10
((y
3
+ 3y
2
+ 2y −1)
6
)(y
18
+ 2y
17
+ ··· − 2y + 1)
· (y
24
+ 5y
23
+ ··· − 29952y + 4096)
c
12
(y
6
+ 2y
5
+ 5y
4
+ 54y
3
+ 274y
2
+ 136y + 361)
· (y
12
+ 37y
11
+ ··· − 1360y + 64)(y
18
+ 19y
17
+ ··· − 8y + 1)
· (y
24
+ 57y
23
+ ··· − 2861140y + 231361)
23
