12a
1118
(K12a
1118
)
A knot diagram
1
Linearized knot diagam
4 7 12 11 10 9 3 1 6 5 2 8
Solving Sequence
6,10
5
2,11
12 4 1 9 7 3 8
c
5
c
10
c
11
c
4
c
1
c
9
c
6
c
2
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
25
+ 6u
24
+ ··· + 2b + 2, u
25
− 4u
24
+ ··· + 4a − 28, u
26
− 6u
25
+ ··· + 38u − 4i
I
u
2
= h23119780u
10
a
3
− 26302390u
10
a
2
+ ··· − 9354998a + 21323123, u
10
a
2
− 2u
10
a + ··· − 4a + 22,
u
11
+ u
10
+ 8u
9
+ 7u
8
+ 22u
7
+ 16u
6
+ 24u
5
+ 13u
4
+ 9u
3
+ 3u
2
− 1i
I
u
3
= hu
11
+ 2u
10
+ 9u
9
+ 14u
8
+ 29u
7
+ 34u
6
+ 40u
5
+ 33u
4
+ 21u
3
+ 10u
2
+ b + 2u,
u
9
+ 2u
8
+ 8u
7
+ 12u
6
+ 22u
5
+ 23u
4
+ 24u
3
+ 15u
2
+ a + 8u + 2,
u
13
+ u
12
+ 10u
11
+ 9u
10
+ 38u
9
+ 30u
8
+ 68u
7
+ 45u
6
+ 57u
5
+ 30u
4
+ 18u
3
+ 9u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 83 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
25
+6u
24
+· · ·+2b+2, u
25
−4u
24
+· · ·+4a−28, u
26
−6u
25
+· · ·+38u−4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
2
=
−
1
4
u
25
+ u
24
+ ··· −
141
4
u + 7
1
2
u
25
− 3u
24
+ ··· −
1
2
u − 1
a
11
=
u
u
3
+ u
a
12
=
−u
25
+
11
2
u
24
+ ··· + 73u −
21
2
1
2
u
25
− 3u
24
+ ··· −
27
2
u + 2
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
1
4
u
25
− 2u
24
+ ··· −
271
4
u + 10
1
2
u
25
− 2u
24
+ ··· +
7
2
u − 1
a
9
=
−u
u
a
7
=
u
2
+ 1
−u
2
a
3
=
1
4
u
25
− u
24
+ ··· −
71
4
u + 4
−
1
2
u
25
+ 2u
24
+ ··· +
3
2
u − 1
a
8
=
−u
25
+
11
2
u
24
+ ··· + 42u −
9
2
−
1
2
u
25
+ 3u
24
+ ··· +
71
2
u − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
10u
25
−57u
24
+332u
23
−1235u
22
+4198u
21
−11498u
20
+28340u
19
−60404u
18
+115879u
17
−
197385u
16
+ 302899u
15
−416264u
14
+ 513994u
13
−567135u
12
+ 556938u
11
−481994u
10
+
362452u
9
−230985u
8
+118944u
7
−43997u
6
+6370u
5
+5367u
4
−5117u
3
+2313u
2
−586u+70
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
26
− 8u
24
+ ··· + 12u − 1
c
2
, c
7
, c
8
c
12
u
26
+ u
25
+ ··· − 2u
2
+ 1
c
3
u
26
+ 22u
25
+ ··· − 18432u − 2048
c
4
, c
5
, c
6
c
9
, c
10
u
26
+ 6u
25
+ ··· − 38u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
26
− 16y
25
+ ··· − 70y + 1
c
2
, c
7
, c
8
c
12
y
26
− 17y
25
+ ··· − 4y + 1
c
3
y
26
+ 4y
25
+ ··· − 27262976y + 4194304
c
4
, c
5
, c
6
c
9
, c
10
y
26
+ 34y
25
+ ··· − 44y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451485 + 0.924968I
a = −0.130539 + 0.087112I
b = −0.420502 + 1.028160I
−1.83398 + 3.85554I 5.01598 − 5.40942I
u = 0.451485 − 0.924968I
a = −0.130539 − 0.087112I
b = −0.420502 − 1.028160I
−1.83398 − 3.85554I 5.01598 + 5.40942I
u = 0.145760 + 1.021400I
a = −0.753104 + 0.547406I
b = 0.342480 + 0.917771I
−5.29967 + 2.25279I −2.26265 − 1.02341I
u = 0.145760 − 1.021400I
a = −0.753104 − 0.547406I
b = 0.342480 − 0.917771I
−5.29967 − 2.25279I −2.26265 + 1.02341I
u = −0.134335 + 1.100410I
a = 0.416493 − 0.318786I
b = −0.390034 − 0.369021I
−2.74898 − 2.01553I 1.43698 + 3.09740I
u = −0.134335 − 1.100410I
a = 0.416493 + 0.318786I
b = −0.390034 + 0.369021I
−2.74898 + 2.01553I 1.43698 − 3.09740I
u = 0.396788 + 1.050250I
a = 0.134501 − 0.556460I
b = 0.016917 − 1.255860I
1.46402 + 12.63110I 4.83525 − 8.43212I
u = 0.396788 − 1.050250I
a = 0.134501 + 0.556460I
b = 0.016917 + 1.255860I
1.46402 − 12.63110I 4.83525 + 8.43212I
u = 0.600772 + 0.564810I
a = −0.561165 − 0.113187I
b = 0.746852 − 0.565960I
4.56542 − 4.85080I 7.22981 + 3.61746I
u = 0.600772 − 0.564810I
a = −0.561165 + 0.113187I
b = 0.746852 + 0.565960I
4.56542 + 4.85080I 7.22981 − 3.61746I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.670718 + 0.249321I
a = −0.759309 + 1.103710I
b = −0.558746 − 0.364300I
5.48801 + 9.02308I 9.08097 − 7.68820I
u = 0.670718 − 0.249321I
a = −0.759309 − 1.103710I
b = −0.558746 + 0.364300I
5.48801 − 9.02308I 9.08097 + 7.68820I
u = 0.690457
a = 1.22468
b = 0.250949
0.998593 8.67860
u = 0.20001 + 1.43415I
a = 0.643331 − 0.201919I
b = −0.264059 + 0.214501I
−1.89647 − 1.89309I 0. + 6.08456I
u = 0.20001 − 1.43415I
a = 0.643331 + 0.201919I
b = −0.264059 − 0.214501I
−1.89647 + 1.89309I 0. − 6.08456I
u = −0.429222
a = 0.516067
b = 0.291290
0.763290 13.8640
u = 0.267171 + 0.243833I
a = 0.55910 − 1.66853I
b = −0.284304 + 0.462050I
−1.36903 + 0.83532I −2.70440 − 2.37254I
u = 0.267171 − 0.243833I
a = 0.55910 + 1.66853I
b = −0.284304 − 0.462050I
−1.36903 − 0.83532I −2.70440 + 2.37254I
u = 0.12117 + 1.70487I
a = −0.62468 + 1.80132I
b = 0.62452 − 2.89110I
−11.05900 + 6.11346I 0
u = 0.12117 − 1.70487I
a = −0.62468 − 1.80132I
b = 0.62452 + 2.89110I
−11.05900 − 6.11346I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03696 + 1.72884I
a = −0.22533 + 2.32808I
b = 0.64136 − 3.89431I
−15.1673 + 2.9962I 0
u = 0.03696 − 1.72884I
a = −0.22533 − 2.32808I
b = 0.64136 + 3.89431I
−15.1673 − 2.9962I 0
u = 0.10685 + 1.73374I
a = −0.06331 − 2.57899I
b = 0.50020 + 4.27014I
−8.3828 + 14.7085I 0
u = 0.10685 − 1.73374I
a = −0.06331 + 2.57899I
b = 0.50020 − 4.27014I
−8.3828 − 14.7085I 0
u = 0.00604 + 1.75193I
a = 0.243641 − 1.347570I
b = −0.72580 + 2.35283I
−13.16660 − 2.24388I 0
u = 0.00604 − 1.75193I
a = 0.243641 + 1.347570I
b = −0.72580 − 2.35283I
−13.16660 + 2.24388I 0
7
II. I
u
2
= h2.31 × 10
7
a
3
u
10
− 2.63 × 10
7
a
2
u
10
+ · · · − 9.35 × 10
6
a + 2.13 ×
10
7
, u
10
a
2
− 2u
10
a + · · · − 4a + 22, u
11
+ u
10
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
2
=
a
−0.412667a
3
u
10
+ 0.469473a
2
u
10
+ ··· + 0.166978a − 0.380598
a
11
=
u
u
3
+ u
a
12
=
−0.0858867a
3
u
10
− 0.0605538a
2
u
10
+ ··· + 0.000325567a − 0.0737747
−1.13526a
3
u
10
+ 0.251129a
2
u
10
+ ··· − 0.150324a − 0.602754
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
0.0633228a
3
u
10
− 0.468909a
2
u
10
+ ··· + 0.271627a + 0.426519
0.0410336a
3
u
10
+ 0.393880a
2
u
10
+ ··· − 0.430740a − 0.364930
a
9
=
−u
u
a
7
=
u
2
+ 1
−u
2
a
3
=
0.0633228a
3
u
10
− 0.468909a
2
u
10
+ ··· + 0.271627a + 0.426519
−0.796648a
3
u
10
+ 0.684500a
2
u
10
+ ··· + 0.614664a − 0.672255
a
8
=
−0.0967847a
3
u
10
+ 0.188328a
2
u
10
+ ··· + 0.565347a − 0.481624
0.148469a
3
u
10
− 0.590797a
2
u
10
+ ··· + 0.472771a + 0.763252
(ii) Obstruction class = −1
(iii) Cusp Shapes =
6227312
4309639
u
10
a
3
+
5964000
4309639
u
10
a
2
+ ··· −
1111192
4309639
a +
41519866
4309639
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
44
− 11u
43
+ ··· + 38u + 13
c
2
, c
7
, c
8
c
12
u
44
− u
43
+ ··· + 2u + 523
c
3
(u
2
− u + 1)
22
c
4
, c
5
, c
6
c
9
, c
10
(u
11
− u
10
+ 8u
9
− 7u
8
+ 22u
7
− 16u
6
+ 24u
5
− 13u
4
+ 9u
3
− 3u
2
+ 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
44
+ 3y
43
+ ··· − 352y + 169
c
2
, c
7
, c
8
c
12
y
44
− 33y
43
+ ··· − 4215384y + 273529
c
3
(y
2
+ y + 1)
22
c
4
, c
5
, c
6
c
9
, c
10
(y
11
+ 15y
10
+ ··· + 6y − 1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.275765 + 1.061690I
a = −0.728865 − 0.809753I
b = 0.080233 − 0.451905I
−2.83219 − 6.29362I 3.04971 + 7.48739I
u = −0.275765 + 1.061690I
a = 0.557010 − 0.084213I
b = −0.240918 − 0.000795I
−2.83219 − 2.23386I 3.04971 + 0.55918I
u = −0.275765 + 1.061690I
a = −0.010262 + 0.496761I
b = −0.352183 + 1.366660I
−2.83219 − 6.29362I 3.04971 + 7.48739I
u = −0.275765 + 1.061690I
a = 0.083613 − 0.399393I
b = −0.415306 − 0.692098I
−2.83219 − 2.23386I 3.04971 + 0.55918I
u = −0.275765 − 1.061690I
a = −0.728865 + 0.809753I
b = 0.080233 + 0.451905I
−2.83219 + 6.29362I 3.04971 − 7.48739I
u = −0.275765 − 1.061690I
a = 0.557010 + 0.084213I
b = −0.240918 + 0.000795I
−2.83219 + 2.23386I 3.04971 − 0.55918I
u = −0.275765 − 1.061690I
a = −0.010262 − 0.496761I
b = −0.352183 − 1.366660I
−2.83219 + 6.29362I 3.04971 − 7.48739I
u = −0.275765 − 1.061690I
a = 0.083613 + 0.399393I
b = −0.415306 + 0.692098I
−2.83219 + 2.23386I 3.04971 − 0.55918I
u = 0.147502 + 0.884325I
a = −0.460680 − 0.739819I
b = −0.14293 − 2.00358I
2.91253 − 0.37141I 6.54419 − 1.26506I
u = 0.147502 + 0.884325I
a = −0.830945 − 0.100702I
b = 1.92441 − 0.89790I
2.91253 + 3.68836I 6.54419 − 8.19326I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.147502 + 0.884325I
a = 1.75919 − 0.06636I
b = −0.902380 + 0.298066I
2.91253 − 0.37141I 6.54419 − 1.26506I
u = 0.147502 + 0.884325I
a = 0.87986 + 1.62833I
b = 0.075265 + 0.845390I
2.91253 + 3.68836I 6.54419 − 8.19326I
u = 0.147502 − 0.884325I
a = −0.460680 + 0.739819I
b = −0.14293 + 2.00358I
2.91253 + 0.37141I 6.54419 + 1.26506I
u = 0.147502 − 0.884325I
a = −0.830945 + 0.100702I
b = 1.92441 + 0.89790I
2.91253 − 3.68836I 6.54419 + 8.19326I
u = 0.147502 − 0.884325I
a = 1.75919 + 0.06636I
b = −0.902380 − 0.298066I
2.91253 + 0.37141I 6.54419 + 1.26506I
u = 0.147502 − 0.884325I
a = 0.87986 − 1.62833I
b = 0.075265 − 0.845390I
2.91253 − 3.68836I 6.54419 + 8.19326I
u = −0.499488 + 0.319159I
a = 1.208330 + 0.110857I
b = 0.046892 − 0.246928I
1.46463 + 0.40435I 7.42199 + 0.45025I
u = −0.499488 + 0.319159I
a = 0.259039 + 0.666603I
b = 0.021941 − 0.860156I
1.46463 − 3.65542I 7.42199 + 7.37845I
u = −0.499488 + 0.319159I
a = −0.351543 + 0.419479I
b = 0.761598 + 0.127213I
1.46463 + 0.40435I 7.42199 + 0.45025I
u = −0.499488 + 0.319159I
a = −0.22815 − 1.67377I
b = −0.529863 + 0.219840I
1.46463 − 3.65542I 7.42199 + 7.37845I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.499488 − 0.319159I
a = 1.208330 − 0.110857I
b = 0.046892 + 0.246928I
1.46463 − 0.40435I 7.42199 − 0.45025I
u = −0.499488 − 0.319159I
a = 0.259039 − 0.666603I
b = 0.021941 + 0.860156I
1.46463 + 3.65542I 7.42199 − 7.37845I
u = −0.499488 − 0.319159I
a = −0.351543 − 0.419479I
b = 0.761598 − 0.127213I
1.46463 − 0.40435I 7.42199 − 0.45025I
u = −0.499488 − 0.319159I
a = −0.22815 + 1.67377I
b = −0.529863 − 0.219840I
1.46463 + 3.65542I 7.42199 − 7.37845I
u = 0.337740
a = 1.01271 + 1.56832I
b = 1.173410 − 0.619485I
5.57164 − 2.02988I 17.6982 + 3.4641I
u = 0.337740
a = 1.01271 − 1.56832I
b = 1.173410 + 0.619485I
5.57164 + 2.02988I 17.6982 − 3.4641I
u = 0.337740
a = −3.49129 + 2.72471I
b = −0.742021 − 0.127702I
5.57164 − 2.02988I 17.6982 + 3.4641I
u = 0.337740
a = −3.49129 − 2.72471I
b = −0.742021 + 0.127702I
5.57164 + 2.02988I 17.6982 − 3.4641I
u = 0.03037 + 1.69780I
a = 0.314985 + 0.028310I
b = −1.41879 + 0.04931I
−6.31060 + 0.27231I 5.67978 + 0.60080I
u = 0.03037 + 1.69780I
a = 2.00060 − 1.04238I
b = −2.34894 + 1.64792I
−6.31060 + 4.33207I 5.67978 − 6.32740I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03037 + 1.69780I
a = 1.01690 + 2.65293I
b = −2.14979 − 4.64665I
−6.31060 + 4.33207I 5.67978 − 6.32740I
u = 0.03037 + 1.69780I
a = −0.42896 − 3.44681I
b = 1.07118 + 5.34607I
−6.31060 + 0.27231I 5.67978 + 0.60080I
u = 0.03037 − 1.69780I
a = 0.314985 − 0.028310I
b = −1.41879 − 0.04931I
−6.31060 − 0.27231I 5.67978 − 0.60080I
u = 0.03037 − 1.69780I
a = 2.00060 + 1.04238I
b = −2.34894 − 1.64792I
−6.31060 − 4.33207I 5.67978 + 6.32740I
u = 0.03037 − 1.69780I
a = 1.01690 − 2.65293I
b = −2.14979 + 4.64665I
−6.31060 − 4.33207I 5.67978 + 6.32740I
u = 0.03037 − 1.69780I
a = −0.42896 + 3.44681I
b = 1.07118 − 5.34607I
−6.31060 − 0.27231I 5.67978 − 0.60080I
u = −0.07149 + 1.73688I
a = 0.162493 + 0.742689I
b = −0.547608 − 1.209520I
−12.82460 − 3.66856I 2.45524 − 0.62833I
u = −0.07149 + 1.73688I
a = −0.21407 − 1.93867I
b = 0.03324 + 3.34038I
−12.82460 − 3.66856I 2.45524 − 0.62833I
u = −0.07149 + 1.73688I
a = −0.45177 − 2.10999I
b = 0.90946 + 3.80724I
−12.8246 − 7.7283I 2.45524 + 6.29988I
u = −0.07149 + 1.73688I
a = −0.55819 + 2.75265I
b = 1.19310 − 4.42722I
−12.8246 − 7.7283I 2.45524 + 6.29988I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07149 − 1.73688I
a = 0.162493 − 0.742689I
b = −0.547608 + 1.209520I
−12.82460 + 3.66856I 2.45524 + 0.62833I
u = −0.07149 − 1.73688I
a = −0.21407 + 1.93867I
b = 0.03324 − 3.34038I
−12.82460 + 3.66856I 2.45524 + 0.62833I
u = −0.07149 − 1.73688I
a = −0.45177 + 2.10999I
b = 0.90946 − 3.80724I
−12.8246 + 7.7283I 2.45524 − 6.29988I
u = −0.07149 − 1.73688I
a = −0.55819 − 2.75265I
b = 1.19310 + 4.42722I
−12.8246 + 7.7283I 2.45524 − 6.29988I
15
III.
I
u
3
= hu
11
+2u
10
+· · · +b + 2u, u
9
+2u
8
+· · · +a + 2, u
13
+u
12
+· · · +9u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
2
=
−u
9
− 2u
8
− 8u
7
− 12u
6
− 22u
5
− 23u
4
− 24u
3
− 15u
2
− 8u − 2
−u
11
− 2u
10
+ ··· − 10u
2
− 2u
a
11
=
u
u
3
+ u
a
12
=
−u
12
− u
11
+ ··· + u + 3
u
12
+ 2u
11
+ ··· + 5u + 1
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
10
− 2u
9
+ ··· − 10u − 2
−u
12
− 2u
11
+ ··· − 10u
2
− 2u
a
9
=
−u
u
a
7
=
u
2
+ 1
−u
2
a
3
=
−u
10
− 2u
9
+ ··· − 9u − 1
−u
12
− 2u
11
+ ··· − 11u
2
− 3u
a
8
=
u
12
+ u
11
+ ··· + 12u + 3
−u
9
− 5u
7
+ u
6
− 6u
5
+ 4u
4
+ u
3
+ 4u
2
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
11
− u
10
+ 9u
9
− 5u
8
+ 29u
7
− 4u
6
+ 40u
5
+ 9u
4
+ 22u
3
+ 9u
2
+ 3u + 7
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
13
− 4u
10
+ 4u
9
+ 6u
7
− 9u
6
+ 3u
5
− 4u
4
+ 6u
3
− 2u
2
+ u − 1
c
2
, c
8
u
13
+ u
12
+ ··· + u + 1
c
3
u
13
+ u
12
+ 2u
11
+ 6u
10
+ 4u
9
+ 3u
8
+ 9u
7
+ 6u
6
+ 4u
4
+ 4u
3
+ 1
c
4
, c
5
, c
6
u
13
+ u
12
+ ··· + 9u
2
+ 1
c
7
, c
12
u
13
− u
12
+ ··· + u − 1
c
9
, c
10
u
13
− u
12
+ ··· − 9u
2
− 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
13
+ 8y
11
+ ··· − 3y − 1
c
2
, c
7
, c
8
c
12
y
13
− 13y
12
+ ··· + 11y − 1
c
3
y
13
+ 3y
12
+ ··· − 8y
2
− 1
c
4
, c
5
, c
6
c
9
, c
10
y
13
+ 19y
12
+ ··· − 18y − 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363309 + 0.993875I
a = −0.234037 − 0.199816I
b = −0.153313 − 0.741103I
−3.28638 − 3.32543I −0.20293 + 6.40733I
u = −0.363309 − 0.993875I
a = −0.234037 + 0.199816I
b = −0.153313 + 0.741103I
−3.28638 + 3.32543I −0.20293 − 6.40733I
u = 0.068223 + 0.860959I
a = 1.16656 + 0.93044I
b = −1.01746 + 1.16245I
2.84340 + 2.46222I 5.75228 − 1.11123I
u = 0.068223 − 0.860959I
a = 1.16656 − 0.93044I
b = −1.01746 − 1.16245I
2.84340 − 2.46222I 5.75228 + 1.11123I
u = −0.607046
a = 1.00467
b = 0.0554938
−0.159667 0.213830
u = 0.05505 + 1.46562I
a = 0.604850 − 0.524644I
b = −0.213415 + 0.805814I
−1.30630 − 1.19378I 7.88487 − 0.81336I
u = 0.05505 − 1.46562I
a = 0.604850 + 0.524644I
b = −0.213415 − 0.805814I
−1.30630 + 1.19378I 7.88487 + 0.81336I
u = 0.111741 + 0.305914I
a = −1.08614 − 2.80587I
b = 0.998300 − 0.585449I
4.72620 − 1.85764I 6.09818 + 1.03366I
u = 0.111741 − 0.305914I
a = −1.08614 + 2.80587I
b = 0.998300 + 0.585449I
4.72620 + 1.85764I 6.09818 − 1.03366I
u = 0.01867 + 1.69606I
a = −0.29196 + 2.24184I
b = −0.27954 − 3.66705I
−6.32539 + 2.80660I 5.56241 − 1.03151I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01867 − 1.69606I
a = −0.29196 − 2.24184I
b = −0.27954 + 3.66705I
−6.32539 − 2.80660I 5.56241 + 1.03151I
u = −0.08685 + 1.73120I
a = −0.16161 − 1.73134I
b = 0.13768 + 2.89130I
−13.02100 − 5.11261I 1.29827 + 4.74921I
u = −0.08685 − 1.73120I
a = −0.16161 + 1.73134I
b = 0.13768 − 2.89130I
−13.02100 + 5.11261I 1.29827 − 4.74921I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
13
− 4u
10
+ 4u
9
+ 6u
7
− 9u
6
+ 3u
5
− 4u
4
+ 6u
3
− 2u
2
+ u − 1)
· (u
26
− 8u
24
+ ··· + 12u − 1)(u
44
− 11u
43
+ ··· + 38u + 13)
c
2
, c
8
(u
13
+ u
12
+ ··· + u + 1)(u
26
+ u
25
+ ··· − 2u
2
+ 1)
· (u
44
− u
43
+ ··· + 2u + 523)
c
3
(u
2
− u + 1)
22
· (u
13
+ u
12
+ 2u
11
+ 6u
10
+ 4u
9
+ 3u
8
+ 9u
7
+ 6u
6
+ 4u
4
+ 4u
3
+ 1)
· (u
26
+ 22u
25
+ ··· − 18432u − 2048)
c
4
, c
5
, c
6
(u
11
− u
10
+ 8u
9
− 7u
8
+ 22u
7
− 16u
6
+ 24u
5
− 13u
4
+ 9u
3
− 3u
2
+ 1)
4
· (u
13
+ u
12
+ ··· + 9u
2
+ 1)(u
26
+ 6u
25
+ ··· − 38u − 4)
c
7
, c
12
(u
13
− u
12
+ ··· + u − 1)(u
26
+ u
25
+ ··· − 2u
2
+ 1)
· (u
44
− u
43
+ ··· + 2u + 523)
c
9
, c
10
(u
11
− u
10
+ 8u
9
− 7u
8
+ 22u
7
− 16u
6
+ 24u
5
− 13u
4
+ 9u
3
− 3u
2
+ 1)
4
· (u
13
− u
12
+ ··· − 9u
2
− 1)(u
26
+ 6u
25
+ ··· − 38u − 4)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
13
+ 8y
11
+ ··· − 3y − 1)(y
26
− 16y
25
+ ··· − 70y + 1)
· (y
44
+ 3y
43
+ ··· − 352y + 169)
c
2
, c
7
, c
8
c
12
(y
13
− 13y
12
+ ··· + 11y − 1)(y
26
− 17y
25
+ ··· − 4y + 1)
· (y
44
− 33y
43
+ ··· − 4215384y + 273529)
c
3
((y
2
+ y + 1)
22
)(y
13
+ 3y
12
+ ··· − 8y
2
− 1)
· (y
26
+ 4y
25
+ ··· − 27262976y + 4194304)
c
4
, c
5
, c
6
c
9
, c
10
((y
11
+ 15y
10
+ ··· + 6y − 1)
4
)(y
13
+ 19y
12
+ ··· − 18y − 1)
· (y
26
+ 34y
25
+ ··· − 44y + 16)
22
