12n
0669
(K12n
0669
)
A knot diagram
1
Linearized knot diagam
4 5 6 8 9 12 11 2 3 8 7 6
Solving Sequence
7,12
6
1,4
2 3 11 8 5 10 9
c
6
c
12
c
1
c
3
c
11
c
7
c
4
c
10
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−99u
27
− 595u
26
+ ··· + 181b − 1270, −7972u
27
− 42371u
26
+ ··· + 11403a − 75384,
u
28
+ 5u
27
+ ··· + 18u + 9i
I
u
2
= h−u
15
a − 13u
15
+ ··· + a − 9, u
14
a + u
15
+ ··· + a + 2, u
16
− 3u
15
+ ··· + 4u
2
+ 1i
I
u
3
= h−u
11
+ 3u
10
− 11u
9
+ 22u
8
− 41u
7
+ 55u
6
− 63u
5
+ 54u
4
− 37u
3
+ 18u
2
+ b − 6u + 1,
− u
11
+ 2u
10
− 9u
9
+ 13u
8
− 27u
7
+ 26u
6
− 29u
5
+ 13u
4
− 4u
3
− 7u
2
+ a + 4u − 4,
u
12
− 2u
11
+ 10u
10
− 16u
9
+ 37u
8
− 46u
7
+ 62u
6
− 56u
5
+ 46u
4
− 25u
3
+ 13u
2
− 2u + 1i
I
v
1
= ha, b − 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 73 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−99u
27
− 595u
26
+ · · · + 181b − 1270, −7972u
27
− 42371u
26
+ · · · +
11403a − 75384, u
28
+ 5u
27
+ · · · + 18u + 9i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
0.699114u
27
+ 3.71578u
26
+ ··· + 13.4910u + 6.61089
0.546961u
27
+ 3.28729u
26
+ ··· + 8.67956u + 7.01657
a
2
=
1.45523u
27
+ 7.64395u
26
+ ··· + 37.2140u + 25.2139
−1.21547u
27
− 3.08287u
26
+ ··· + 5.82320u + 13.6298
a
3
=
0.559414u
27
+ 2.93677u
26
+ ··· + 11.9148u + 11.6456
−0.220205u
27
− 0.414365u
26
+ ··· + 5.97316u + 6.29203
a
11
=
u
u
a
8
=
u
2
+ 1
u
2
a
5
=
0.419714u
27
+ 2.15777u
26
+ ··· + 8.33868u + 6.68035
0.122336u
27
+ 0.563536u
26
+ ··· − 0.540647u + 3.05998
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
−1.11225u
27
− 4.07980u
26
+ ··· − 12.1491u − 1.59984
−0.775848u
27
− 2.30939u
26
+ ··· − 0.764799u + 3.32281
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1388
1267
u
27
−
1029
181
u
26
+ ··· −
71766
1267
u +
12063
1267
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
28
+ 2u
27
+ ··· − 4u + 1
c
2
u
28
+ 18u
27
+ ··· + 72u + 9
c
4
, c
9
u
28
− 2u
27
+ ··· − u + 8
c
5
, c
8
u
28
− u
27
+ ··· + u + 1
c
6
, c
7
, c
10
c
11
, c
12
u
28
− 5u
27
+ ··· − 18u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
28
− 34y
27
+ ··· − 12y + 1
c
2
y
28
+ 46y
26
+ ··· + 1260y + 81
c
4
, c
9
y
28
+ 10y
27
+ ··· + 879y + 64
c
5
, c
8
y
28
− 11y
27
+ ··· − 27y + 1
c
6
, c
7
, c
10
c
11
, c
12
y
28
+ 33y
27
+ ··· − 90y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279310 + 1.005780I
a = 0.111453 − 0.538123I
b = −0.460280 − 0.329159I
2.15334 − 3.08002I −5.41932 + 2.17495I
u = 0.279310 − 1.005780I
a = 0.111453 + 0.538123I
b = −0.460280 + 0.329159I
2.15334 + 3.08002I −5.41932 − 2.17495I
u = −0.720208 + 0.617732I
a = −0.067974 − 1.221620I
b = −0.518022 + 0.676690I
−5.18301 + 11.95320I −6.36826 − 8.35721I
u = −0.720208 − 0.617732I
a = −0.067974 + 1.221620I
b = −0.518022 − 0.676690I
−5.18301 − 11.95320I −6.36826 + 8.35721I
u = −0.778368 + 0.420776I
a = 0.148251 − 0.811625I
b = −1.044860 + 0.185626I
−5.77287 − 6.98018I −7.82028 + 3.54637I
u = −0.778368 − 0.420776I
a = 0.148251 + 0.811625I
b = −1.044860 − 0.185626I
−5.77287 + 6.98018I −7.82028 − 3.54637I
u = −0.588348 + 0.532762I
a = −0.326563 + 1.326180I
b = 0.777651 − 0.025379I
−4.60494 + 0.48065I −11.27827 + 0.66157I
u = −0.588348 − 0.532762I
a = −0.326563 − 1.326180I
b = 0.777651 + 0.025379I
−4.60494 − 0.48065I −11.27827 − 0.66157I
u = −0.609349 + 0.472094I
a = 0.554010 + 1.282630I
b = 0.814858 − 0.516381I
−4.78529 + 3.61019I −12.2949 − 8.1596I
u = −0.609349 − 0.472094I
a = 0.554010 − 1.282630I
b = 0.814858 + 0.516381I
−4.78529 − 3.61019I −12.2949 + 8.1596I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230601 + 0.555602I
a = −0.857392 − 0.551333I
b = −0.249740 + 0.519303I
0.39899 − 1.65572I −2.33445 + 5.92900I
u = 0.230601 − 0.555602I
a = −0.857392 + 0.551333I
b = −0.249740 − 0.519303I
0.39899 + 1.65572I −2.33445 − 5.92900I
u = 0.02508 + 1.41638I
a = −0.74984 + 1.49379I
b = −0.20717 + 2.40362I
3.21161 − 0.20656I −6.00000 − 0.51080I
u = 0.02508 − 1.41638I
a = −0.74984 − 1.49379I
b = −0.20717 − 2.40362I
3.21161 + 0.20656I −6.00000 + 0.51080I
u = −0.29358 + 1.42827I
a = 1.004870 − 0.924707I
b = 1.49328 − 0.86181I
0.13364 − 3.10062I −6.00000 + 3.00953I
u = −0.29358 − 1.42827I
a = 1.004870 + 0.924707I
b = 1.49328 + 0.86181I
0.13364 + 3.10062I −6.00000 − 3.00953I
u = −0.18111 + 1.50663I
a = −0.84422 + 2.04492I
b = −1.34773 + 3.07117I
1.71233 + 6.43075I −9.24234 − 8.11110I
u = −0.18111 − 1.50663I
a = −0.84422 − 2.04492I
b = −1.34773 − 3.07117I
1.71233 − 6.43075I −9.24234 + 8.11110I
u = 0.05585 + 1.53567I
a = −0.229321 − 1.036530I
b = −1.01658 − 1.57906I
7.40879 − 2.63530I 0. + 1.41712I
u = 0.05585 − 1.53567I
a = −0.229321 + 1.036530I
b = −1.01658 + 1.57906I
7.40879 + 2.63530I 0. − 1.41712I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.449761 + 0.053633I
a = −0.698805 − 0.615735I
b = 0.311401 + 0.365904I
−1.113100 − 0.415234I −10.08873 + 1.99111I
u = 0.449761 − 0.053633I
a = −0.698805 + 0.615735I
b = 0.311401 − 0.365904I
−1.113100 + 0.415234I −10.08873 − 1.99111I
u = −0.17350 + 1.54958I
a = −1.34694 + 1.07933I
b = −2.24580 + 1.72156I
2.33140 + 3.21187I −6.00000 + 0.I
u = −0.17350 − 1.54958I
a = −1.34694 − 1.07933I
b = −2.24580 − 1.72156I
2.33140 − 3.21187I −6.00000 + 0.I
u = −0.24174 + 1.57099I
a = 0.93340 − 1.79161I
b = 1.98417 − 2.74478I
2.0404 + 15.5256I −6.00000 − 8.00298I
u = −0.24174 − 1.57099I
a = 0.93340 + 1.79161I
b = 1.98417 + 2.74478I
2.0404 − 15.5256I −6.00000 + 8.00298I
u = 0.04560 + 1.71954I
a = 0.369072 − 0.185559I
b = 0.708836 − 0.625204I
11.93830 − 4.23690I 0
u = 0.04560 − 1.71954I
a = 0.369072 + 0.185559I
b = 0.708836 + 0.625204I
11.93830 + 4.23690I 0
7
II. I
u
2
=
h−u
15
a−13u
15
+· · ·+a − 9, u
14
a+u
15
+· · ·+a + 2, u
16
−3u
15
+· · ·+4u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
a
0.0454545au
15
+ 0.590909u
15
+ ··· − 0.0454545a + 0.409091
a
2
=
0.590909au
15
− 0.318182u
15
+ ··· + 0.409091a − 0.681818
0.409091au
15
− 0.681818u
15
+ ··· − 0.409091a − 0.318182
a
3
=
0.0454545au
15
+ 0.590909u
15
+ ··· + 0.954545a + 0.409091
u
15
− 4u
14
+ ··· + au + u
a
11
=
u
u
a
8
=
u
2
+ 1
u
2
a
5
=
0.181818au
15
+ 0.363636u
15
+ ··· + 0.818182a + 0.636364
0.136364au
15
+ 0.772727u
15
+ ··· − 0.136364a + 0.227273
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
−0.0454545au
15
+ 0.409091u
15
+ ··· + 1.04545a − 0.409091
−0.181818au
15
+ 0.636364u
15
+ ··· + 0.181818a + 0.363636
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
− 4u
14
+ 28u
13
− 16u
12
+ 52u
11
+ 16u
10
− 40u
9
+ 164u
8
−
224u
7
+ 284u
6
− 232u
5
+ 188u
4
− 88u
3
+ 40u
2
− 16u + 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
32
+ u
31
+ ··· − 27u + 976
c
2
(u
16
− 7u
15
+ ··· + 4u
2
+ 1)
2
c
4
, c
9
u
32
+ u
31
+ ··· + 298u + 43
c
5
, c
8
u
32
+ u
31
+ ··· + 13u + 8
c
6
, c
7
, c
10
c
11
, c
12
(u
16
+ 3u
15
+ ··· + 4u
2
+ 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
32
− 9y
31
+ ··· + 352583y + 952576
c
2
(y
16
+ y
15
+ ··· + 8y + 1)
2
c
4
, c
9
y
32
+ 11y
31
+ ··· − 23702y + 1849
c
5
, c
8
y
32
+ 7y
31
+ ··· − 377y + 64
c
6
, c
7
, c
10
c
11
, c
12
(y
16
+ 17y
15
+ ··· + 8y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.736907 + 0.630715I
a = −0.347357 − 1.185090I
b = 0.346570 + 0.897786I
−3.73069 − 3.30359I −11.5550 + 13.2403I
u = 0.736907 + 0.630715I
a = −0.097352 + 0.707530I
b = −0.595615 − 0.098261I
−3.73069 − 3.30359I −11.5550 + 13.2403I
u = 0.736907 − 0.630715I
a = −0.347357 + 1.185090I
b = 0.346570 − 0.897786I
−3.73069 + 3.30359I −11.5550 − 13.2403I
u = 0.736907 − 0.630715I
a = −0.097352 − 0.707530I
b = −0.595615 + 0.098261I
−3.73069 + 3.30359I −11.5550 − 13.2403I
u = 0.770485 + 0.383157I
a = −0.501042 + 0.870322I
b = −0.419626 − 0.267018I
−4.45888 − 1.70911I −18.3582 + 0.4103I
u = 0.770485 + 0.383157I
a = −0.250273 − 0.516782I
b = 1.35131 + 0.47758I
−4.45888 − 1.70911I −18.3582 + 0.4103I
u = 0.770485 − 0.383157I
a = −0.501042 − 0.870322I
b = −0.419626 + 0.267018I
−4.45888 + 1.70911I −18.3582 − 0.4103I
u = 0.770485 − 0.383157I
a = −0.250273 + 0.516782I
b = 1.35131 − 0.47758I
−4.45888 + 1.70911I −18.3582 − 0.4103I
u = 0.23207 + 1.42418I
a = 0.22218 + 1.51395I
b = 0.52047 + 2.40459I
1.25225 − 5.27528I −9.67373 + 5.08255I
u = 0.23207 + 1.42418I
a = −1.29258 − 1.32241I
b = −1.73185 − 1.01396I
1.25225 − 5.27528I −9.67373 + 5.08255I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23207 − 1.42418I
a = 0.22218 − 1.51395I
b = 0.52047 − 2.40459I
1.25225 + 5.27528I −9.67373 − 5.08255I
u = 0.23207 − 1.42418I
a = −1.29258 + 1.32241I
b = −1.73185 + 1.01396I
1.25225 + 5.27528I −9.67373 − 5.08255I
u = −0.113421 + 0.521878I
a = −1.094860 + 0.565660I
b = −1.051420 + 0.591620I
1.35067 − 2.72058I −0.320802 − 0.633673I
u = −0.113421 + 0.521878I
a = −1.72097 − 2.11921I
b = 0.195684 + 0.312539I
1.35067 − 2.72058I −0.320802 − 0.633673I
u = −0.113421 − 0.521878I
a = −1.094860 − 0.565660I
b = −1.051420 − 0.591620I
1.35067 + 2.72058I −0.320802 + 0.633673I
u = −0.113421 − 0.521878I
a = −1.72097 + 2.11921I
b = 0.195684 − 0.312539I
1.35067 + 2.72058I −0.320802 + 0.633673I
u = −0.07564 + 1.47034I
a = 0.804239 + 0.140801I
b = 2.39710 + 0.12858I
6.50466 + 5.66478I −1.14168 − 7.61626I
u = −0.07564 + 1.47034I
a = 0.46427 + 2.67817I
b = 0.20535 + 3.65834I
6.50466 + 5.66478I −1.14168 − 7.61626I
u = −0.07564 − 1.47034I
a = 0.804239 − 0.140801I
b = 2.39710 − 0.12858I
6.50466 − 5.66478I −1.14168 + 7.61626I
u = −0.07564 − 1.47034I
a = 0.46427 − 2.67817I
b = 0.20535 − 3.65834I
6.50466 − 5.66478I −1.14168 + 7.61626I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00370 + 1.51777I
a = 0.594067 − 0.444832I
b = −0.016890 − 0.443911I
8.17367 − 2.54285I 2.47471 + 1.82426I
u = 0.00370 + 1.51777I
a = −0.60427 − 2.10333I
b = −1.19623 − 3.64553I
8.17367 − 2.54285I 2.47471 + 1.82426I
u = 0.00370 − 1.51777I
a = 0.594067 + 0.444832I
b = −0.016890 + 0.443911I
8.17367 + 2.54285I 2.47471 − 1.82426I
u = 0.00370 − 1.51777I
a = −0.60427 + 2.10333I
b = −1.19623 + 3.64553I
8.17367 + 2.54285I 2.47471 − 1.82426I
u = −0.307694 + 0.311549I
a = 0.85542 + 1.13412I
b = −0.08749 − 1.42606I
0.57349 + 4.39205I −7.1332 − 12.4476I
u = −0.307694 + 0.311549I
a = 2.63362 − 1.90072I
b = 0.530367 + 0.052913I
0.57349 + 4.39205I −7.1332 − 12.4476I
u = −0.307694 − 0.311549I
a = 0.85542 − 1.13412I
b = −0.08749 + 1.42606I
0.57349 − 4.39205I −7.1332 + 12.4476I
u = −0.307694 − 0.311549I
a = 2.63362 + 1.90072I
b = 0.530367 − 0.052913I
0.57349 − 4.39205I −7.1332 + 12.4476I
u = 0.25359 + 1.56853I
a = 0.667535 + 1.052820I
b = 1.12652 + 1.60326I
3.49430 − 7.00115I −2.29217 + 10.66775I
u = 0.25359 + 1.56853I
a = −0.83262 − 1.61500I
b = −2.07424 − 2.36731I
3.49430 − 7.00115I −2.29217 + 10.66775I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25359 − 1.56853I
a = 0.667535 − 1.052820I
b = 1.12652 − 1.60326I
3.49430 + 7.00115I −2.29217 − 10.66775I
u = 0.25359 − 1.56853I
a = −0.83262 + 1.61500I
b = −2.07424 + 2.36731I
3.49430 + 7.00115I −2.29217 − 10.66775I
14
III.
I
u
3
= h−u
11
+3u
10
+· · ·+b+1, −u
11
+2u
10
+· · ·+a−4, u
12
−2u
11
+· · ·−2u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
11
− 2u
10
+ ··· − 4u + 4
u
11
− 3u
10
+ ··· + 6u − 1
a
2
=
−u
11
+ 2u
10
+ ··· − 16u + 1
u
11
− 2u
10
+ 8u
9
− 12u
8
+ 22u
7
− 23u
6
+ 24u
5
− 15u
4
+ 9u
3
− u
2
+ 1
a
3
=
u
11
− 2u
10
+ ··· + u + 3
−u
10
+ 3u
9
+ ··· + 6u − 1
a
11
=
u
u
a
8
=
u
2
+ 1
u
2
a
5
=
u
11
− 2u
10
+ ··· − u + 4
−u
10
+ 3u
9
+ ··· + 5u − 1
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
−u
11
+ 2u
10
+ ··· − 8u − 1
u
6
− 2u
5
+ 5u
4
− 6u
3
+ 6u
2
− 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
9
+ 12u
8
− 31u
7
+ 71u
6
− 97u
5
+ 129u
4
− 106u
3
+ 70u
2
− 28u + 6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
12
− 5u
11
+ ··· − 4u + 1
c
2
u
12
+ 7u
11
+ ··· − 2u
2
+ 1
c
4
, c
9
u
12
− u
11
+ 3u
10
− 2u
9
+ 4u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
− u
3
+ 2u
2
+ 1
c
5
, c
8
u
12
+ 2u
10
+ u
9
+ 5u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 4u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
, c
7
u
12
− 2u
11
+ ··· − 2u + 1
c
10
, c
11
, c
12
u
12
+ 2u
11
+ ··· + 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
12
+ y
11
+ ··· + 12y + 1
c
2
y
12
− y
11
+ ··· − 4y + 1
c
4
, c
9
y
12
+ 5y
11
+ ··· + 4y + 1
c
5
, c
8
y
12
+ 4y
11
+ ··· + 5y + 1
c
6
, c
7
, c
10
c
11
, c
12
y
12
+ 16y
11
+ ··· + 22y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062845 + 0.891437I
a = −0.628237 + 0.822197I
b = −0.566446 + 0.024137I
3.05705 − 3.82507I 1.89342 + 5.86722I
u = 0.062845 − 0.891437I
a = −0.628237 − 0.822197I
b = −0.566446 − 0.024137I
3.05705 + 3.82507I 1.89342 − 5.86722I
u = 0.707140 + 0.501490I
a = −0.069670 + 0.915815I
b = −0.685751 − 0.402378I
−3.69632 − 2.35930I −7.76501 + 3.34696I
u = 0.707140 − 0.501490I
a = −0.069670 − 0.915815I
b = −0.685751 + 0.402378I
−3.69632 + 2.35930I −7.76501 − 3.34696I
u = 0.22473 + 1.49020I
a = 0.66766 + 1.50515I
b = 1.17799 + 2.08028I
2.75451 − 5.74454I −3.13416 + 4.41804I
u = 0.22473 − 1.49020I
a = 0.66766 − 1.50515I
b = 1.17799 − 2.08028I
2.75451 + 5.74454I −3.13416 − 4.41804I
u = −0.01439 + 1.51623I
a = 0.49936 − 1.54519I
b = 1.57217 − 2.22848I
7.50866 + 3.81798I −0.96857 − 7.15164I
u = −0.01439 − 1.51623I
a = 0.49936 + 1.54519I
b = 1.57217 + 2.22848I
7.50866 − 3.81798I −0.96857 + 7.15164I
u = −0.013723 + 0.332523I
a = 3.15459 − 1.45385I
b = 0.441210 + 0.948917I
1.08380 + 3.67567I −0.27845 − 6.20952I
u = −0.013723 − 0.332523I
a = 3.15459 + 1.45385I
b = 0.441210 − 0.948917I
1.08380 − 3.67567I −0.27845 + 6.20952I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03339 + 1.69695I
a = −0.123705 + 0.529063I
b = −0.439173 + 1.086920I
12.32140 − 4.31104I 8.75276 + 5.09710I
u = 0.03339 − 1.69695I
a = −0.123705 − 0.529063I
b = −0.439173 − 1.086920I
12.32140 + 4.31104I 8.75276 − 5.09710I
19
IV. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
1
0
a
6
=
1
0
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
1
1
a
11
=
1
0
a
8
=
1
0
a
5
=
1
1
a
10
=
1
0
a
9
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
u + 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
u
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
y − 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
y
22
(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
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u + 1)(u
12
− 5u
11
+ ··· − 4u + 1)(u
28
+ 2u
27
+ ··· − 4u + 1)
· (u
32
+ u
31
+ ··· − 27u + 976)
c
2
u(u
12
+ 7u
11
+ ··· − 2u
2
+ 1)(u
16
− 7u
15
+ ··· + 4u
2
+ 1)
2
· (u
28
+ 18u
27
+ ··· + 72u + 9)
c
4
, c
9
(u + 1)
· (u
12
− u
11
+ 3u
10
− 2u
9
+ 4u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
− u
3
+ 2u
2
+ 1)
· (u
28
− 2u
27
+ ··· − u + 8)(u
32
+ u
31
+ ··· + 298u + 43)
c
5
, c
8
(u + 1)(u
12
+ 2u
10
+ ··· + u + 1)
· (u
28
− u
27
+ ··· + u + 1)(u
32
+ u
31
+ ··· + 13u + 8)
c
6
, c
7
u(u
12
− 2u
11
+ ··· − 2u + 1)(u
16
+ 3u
15
+ ··· + 4u
2
+ 1)
2
· (u
28
− 5u
27
+ ··· − 18u + 9)
c
10
, c
11
, c
12
u(u
12
+ 2u
11
+ ··· + 2u + 1)(u
16
+ 3u
15
+ ··· + 4u
2
+ 1)
2
· (u
28
− 5u
27
+ ··· − 18u + 9)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y − 1)(y
12
+ y
11
+ ··· + 12y + 1)(y
28
− 34y
27
+ ··· − 12y + 1)
· (y
32
− 9y
31
+ ··· + 352583y + 952576)
c
2
y(y
12
− y
11
+ ··· − 4y + 1)(y
16
+ y
15
+ ··· + 8y + 1)
2
· (y
28
+ 46y
26
+ ··· + 1260y + 81)
c
4
, c
9
(y − 1)(y
12
+ 5y
11
+ ··· + 4y + 1)(y
28
+ 10y
27
+ ··· + 879y + 64)
· (y
32
+ 11y
31
+ ··· − 23702y + 1849)
c
5
, c
8
(y − 1)(y
12
+ 4y
11
+ ··· + 5y + 1)(y
28
− 11y
27
+ ··· − 27y + 1)
· (y
32
+ 7y
31
+ ··· − 377y + 64)
c
6
, c
7
, c
10
c
11
, c
12
y(y
12
+ 16y
11
+ ··· + 22y + 1)(y
16
+ 17y
15
+ ··· + 8y + 1)
2
· (y
28
+ 33y
27
+ ··· − 90y + 81)
25
