12n
0287
(K12n
0287
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 10 11 4 1 8 5
Solving Sequence
2,6
3 7
4,10
8 1 11 5 9 12
c
2
c
6
c
3
c
7
c
1
c
10
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−14u
35
− 85u
34
+ ··· + b − 25, −27u
35
− 160u
34
+ ··· + 2a − 59, u
36
+ 6u
35
+ ··· + 11u + 2i
I
u
2
= h2u
15
+ 7u
13
− u
12
+ 12u
11
− 4u
10
+ 7u
9
− 5u
8
− 2u
7
− u
6
− 5u
5
+ 5u
4
+ 3u
2
+ b − u,
u
16
+ 5u
14
− u
13
+ 11u
12
− 5u
11
+ 12u
10
− 10u
9
+ 4u
8
− 8u
7
− 3u
6
+ 2u
5
− 3u
4
+ 8u
3
− u
2
+ a + 3u − 2,
u
17
− u
16
+ 5u
15
− 4u
14
+ 12u
13
− 9u
12
+ 16u
11
− 10u
10
+ 10u
9
− 5u
8
+ 3u
6
− 6u
5
+ 6u
4
− 4u
3
+ 4u
2
− 2u + 1i
I
u
3
= h−u
17
+ u
16
+ ··· + b + 1, u
17
a + 4u
17
+ ··· + a
2
− 5, u
18
− u
17
+ ··· − u + 1i
* 3 irreducible components of dim
C
= 0, with total 89 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−14u
35
− 85u
34
+ · · · + b − 25, −27u
35
− 160u
34
+ · · · + 2a −
59, u
36
+ 6u
35
+ · · · + 11u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
27
2
u
35
+ 80u
34
+ ··· +
287
2
u +
59
2
14u
35
+ 85u
34
+ ··· + 135u + 25
a
8
=
5
2
u
35
+ 15u
34
+ ··· +
55
2
u +
13
2
3u
35
+ 17u
34
+ ··· + 27u + 5
a
1
=
u
2
+ 1
−u
4
a
11
=
17
2
u
35
+ 51u
34
+ ··· +
205
2
u +
41
2
5u
35
+ 36u
34
+ ··· + 85u + 17
a
5
=
−
1
2
u
35
− 5u
34
+ ··· +
1
2
u +
3
2
−2u
35
− 14u
34
+ ··· − 19u − 3
a
9
=
7
2
u
35
+ 21u
34
+ ··· +
85
2
u +
17
2
u
35
+ 6u
34
+ ··· + 30u + 7
a
12
=
13
2
u
35
+ 38u
34
+ ··· +
121
2
u +
27
2
11u
35
+ 63u
34
+ ··· + 69u + 11
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −10u
35
−47u
34
−193u
33
−528u
32
−1308u
31
−2680u
30
−5100u
29
−8677u
28
−13841u
27
−
20439u
26
−28425u
25
−37282u
24
−46259u
23
−54570u
22
−61115u
21
−65180u
20
−66272u
19
−
64122u
18
−59268u
17
−52003u
16
−43524u
15
−34581u
14
−26106u
13
−18689u
12
−12638u
11
−
8103u
10
−4980u
9
−2882u
8
−1585u
7
−744u
6
−322u
5
−123u
4
−56u
3
−11u
2
+ 11u + 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 18u
35
+ ··· + 11u + 4
c
2
, c
6
u
36
− 6u
35
+ ··· − 11u + 2
c
3
u
36
+ 6u
35
+ ··· + 721u + 74
c
4
, c
12
u
36
− 28u
34
+ ··· + u + 1
c
5
, c
9
u
36
− 8u
34
+ ··· − 19u + 23
c
7
, c
10
u
36
− 3u
35
+ ··· − 4u + 1
c
8
, c
11
u
36
+ 17u
35
+ ··· − 1495u + 160
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 2y
35
+ ··· + 415y + 16
c
2
, c
6
y
36
+ 18y
35
+ ··· + 11y + 4
c
3
y
36
− 20y
35
+ ··· − 111805y + 5476
c
4
, c
12
y
36
− 56y
35
+ ··· − y + 1
c
5
, c
9
y
36
− 16y
35
+ ··· − 5421y + 529
c
7
, c
10
y
36
+ 9y
35
+ ··· + 16y + 1
c
8
, c
11
y
36
− 29y
35
+ ··· − 1047185y + 25600
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149973 + 0.998728I
a = 0.826426 + 0.069933I
b = 0.978572 − 0.499137I
−2.48443 − 1.62652I −2.33035 + 4.22312I
u = −0.149973 − 0.998728I
a = 0.826426 − 0.069933I
b = 0.978572 + 0.499137I
−2.48443 + 1.62652I −2.33035 − 4.22312I
u = −0.991952 + 0.201272I
a = −0.095835 − 0.534611I
b = 0.1012230 − 0.0449035I
5.44078 − 0.44653I 17.6525 + 14.6221I
u = −0.991952 − 0.201272I
a = −0.095835 + 0.534611I
b = 0.1012230 + 0.0449035I
5.44078 + 0.44653I 17.6525 − 14.6221I
u = 0.722213 + 0.749533I
a = −0.458236 − 0.270213I
b = −0.182561 + 1.023860I
10.02280 + 8.45449I 8.41836 − 6.51159I
u = 0.722213 − 0.749533I
a = −0.458236 + 0.270213I
b = −0.182561 − 1.023860I
10.02280 − 8.45449I 8.41836 + 6.51159I
u = 0.704411 + 0.851124I
a = 0.304244 − 0.316418I
b = −0.793602 − 0.473087I
9.73048 − 3.08341I 8.49473 + 1.45967I
u = 0.704411 − 0.851124I
a = 0.304244 + 0.316418I
b = −0.793602 + 0.473087I
9.73048 + 3.08341I 8.49473 − 1.45967I
u = −0.839708 + 0.298444I
a = −2.16620 + 0.59359I
b = −0.604870 − 0.306470I
7.48792 + 11.15390I 7.02947 − 5.33510I
u = −0.839708 − 0.298444I
a = −2.16620 − 0.59359I
b = −0.604870 + 0.306470I
7.48792 − 11.15390I 7.02947 + 5.33510I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.459586 + 1.035300I
a = −0.189766 + 0.533405I
b = 0.983727 + 0.590961I
−0.955654 + 0.821545I 0. − 3.95614I
u = 0.459586 − 1.035300I
a = −0.189766 − 0.533405I
b = 0.983727 − 0.590961I
−0.955654 − 0.821545I 0. + 3.95614I
u = −0.349884 + 1.107310I
a = −0.40589 − 1.81289I
b = −1.19270 − 2.50026I
−4.05377 + 0.63572I 0.484295 − 0.443572I
u = −0.349884 − 1.107310I
a = −0.40589 + 1.81289I
b = −1.19270 + 2.50026I
−4.05377 − 0.63572I 0.484295 + 0.443572I
u = 0.489524 + 1.057530I
a = 0.323550 − 0.327963I
b = −0.560466 − 0.804802I
−0.66063 + 5.65062I 0.65729 − 7.68260I
u = 0.489524 − 1.057530I
a = 0.323550 + 0.327963I
b = −0.560466 + 0.804802I
−0.66063 − 5.65062I 0.65729 + 7.68260I
u = −0.477205 + 1.078410I
a = −0.219824 + 1.300630I
b = −0.24654 + 1.84787I
−0.93062 − 3.45682I 3.69827 + 2.78118I
u = −0.477205 − 1.078410I
a = −0.219824 − 1.300630I
b = −0.24654 − 1.84787I
−0.93062 + 3.45682I 3.69827 − 2.78118I
u = −0.516662 + 1.118490I
a = 0.37409 − 2.28317I
b = 0.64651 − 3.41250I
−2.89301 − 8.21064I 2.73606 + 6.67381I
u = −0.516662 − 1.118490I
a = 0.37409 + 2.28317I
b = 0.64651 + 3.41250I
−2.89301 + 8.21064I 2.73606 − 6.67381I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235187 + 1.215000I
a = 0.269343 + 1.318210I
b = 1.29431 + 2.00975I
2.56736 + 7.86975I 1.57367 − 3.75977I
u = −0.235187 − 1.215000I
a = 0.269343 − 1.318210I
b = 1.29431 − 2.00975I
2.56736 − 7.86975I 1.57367 + 3.75977I
u = 0.437735 + 0.549718I
a = 0.890033 + 0.585768I
b = 0.312734 − 1.109250I
0.56302 + 2.97658I 7.22028 + 1.12421I
u = 0.437735 − 0.549718I
a = 0.890033 − 0.585768I
b = 0.312734 + 1.109250I
0.56302 − 2.97658I 7.22028 − 1.12421I
u = −0.579068 + 1.162280I
a = −0.18131 + 2.07088I
b = −0.66974 + 3.26898I
4.9093 − 16.4009I 4.03368 + 8.81881I
u = −0.579068 − 1.162280I
a = −0.18131 − 2.07088I
b = −0.66974 − 3.26898I
4.9093 + 16.4009I 4.03368 − 8.81881I
u = −0.645401 + 0.250421I
a = 2.56211 − 0.68246I
b = 0.796733 − 0.012403I
−0.44102 + 3.68764I 6.93148 − 2.97663I
u = −0.645401 − 0.250421I
a = 2.56211 + 0.68246I
b = 0.796733 + 0.012403I
−0.44102 − 3.68764I 6.93148 + 2.97663I
u = −0.379298 + 1.270510I
a = −0.367307 + 0.599503I
b = −0.495507 + 1.221510I
0.75632 − 4.99885I 0. + 9.16274I
u = −0.379298 − 1.270510I
a = −0.367307 − 0.599503I
b = −0.495507 − 1.221510I
0.75632 + 4.99885I 0. − 9.16274I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507489 + 0.424879I
a = −0.697425 − 0.253280I
b = 0.190814 + 0.745125I
1.18510 − 1.52172I 5.49872 + 4.62592I
u = 0.507489 − 0.424879I
a = −0.697425 + 0.253280I
b = 0.190814 − 0.745125I
1.18510 + 1.52172I 5.49872 − 4.62592I
u = −0.505579 + 0.388688I
a = −1.192940 + 0.572586I
b = −0.480909 + 0.224460I
1.086520 − 0.606535I 7.97928 + 3.45064I
u = −0.505579 − 0.388688I
a = −1.192940 − 0.572586I
b = −0.480909 − 0.224460I
1.086520 + 0.606535I 7.97928 − 3.45064I
u = −0.651042 + 1.222950I
a = 0.174939 − 0.327220I
b = 0.422269 − 0.499103I
2.39061 − 5.47394I 20.9532 + 20.3381I
u = −0.651042 − 1.222950I
a = 0.174939 + 0.327220I
b = 0.422269 + 0.499103I
2.39061 + 5.47394I 20.9532 − 20.3381I
8
II.
I
u
2
= h2u
15
+7u
13
+· · ·+b −u, u
16
+5u
14
+· · ·+a −2, u
17
−u
16
+· · ·−2u +1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
−u
16
− 5u
14
+ ··· − 3u + 2
−2u
15
− 7u
13
+ ··· − 3u
2
+ u
a
8
=
2u
16
− u
15
+ ··· + 4u − 3
u
16
+ 5u
14
+ ··· + 2u − 1
a
1
=
u
2
+ 1
−u
4
a
11
=
−2u
16
+ u
15
+ ··· − 4u + 2
−u
16
− 4u
14
+ ··· − u + 1
a
5
=
3u
16
− 5u
15
+ ··· + 11u − 7
u
16
− 4u
15
+ ··· + 6u − 5
a
9
=
−2u
16
+ u
15
+ ··· − 5u + 2
−u
16
+ u
15
+ ··· − 2u + 2
a
12
=
−5u
16
+ 2u
15
+ ··· − 12u + 8
−2u
16
− 2u
15
+ ··· − 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
15
− 4u
14
+ 24u
13
− 12u
12
+ 48u
11
− 20u
10
+ 44u
9
− 6u
8
+
6u
7
+ 12u
6
− 21u
5
+ 22u
4
− 14u
3
+ 10u
2
− u + 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 9u
16
+ ··· − 4u + 1
c
2
u
17
− u
16
+ ··· − 2u + 1
c
3
u
17
+ u
16
+ ··· + 2u + 5
c
4
, c
12
u
17
− 2u
16
+ ··· − 3u + 1
c
5
, c
9
u
17
− 8u
15
+ ··· − u + 1
c
6
u
17
+ u
16
+ ··· − 2u − 1
c
7
, c
10
u
17
− 3u
16
+ ··· + 2u + 1
c
8
u
17
+ 14u
16
+ ··· + 23u + 5
c
11
u
17
− 14u
16
+ ··· + 23u − 5
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ y
16
+ ··· − 8y −1
c
2
, c
6
y
17
+ 9y
16
+ ··· − 4y −1
c
3
y
17
− 13y
16
+ ··· − 86y −25
c
4
, c
12
y
17
− 16y
16
+ ··· − 3y −1
c
5
, c
9
y
17
− 16y
16
+ ··· + 9y −1
c
7
, c
10
y
17
− 7y
16
+ ··· + 4y −1
c
8
, c
11
y
17
− 18y
16
+ ··· − 371y −25
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.431008 + 0.942233I
a = 0.209460 + 0.502451I
b = −0.824758 + 0.503665I
−0.436145 − 0.105477I 5.17968 − 2.38886I
u = −0.431008 − 0.942233I
a = 0.209460 − 0.502451I
b = −0.824758 − 0.503665I
−0.436145 + 0.105477I 5.17968 + 2.38886I
u = −0.874680
a = −0.192244
b = 0.315231
5.41472 11.0230
u = −0.468457 + 0.715892I
a = −0.678237 + 0.210938I
b = −0.173523 − 0.977457I
0.24900 − 3.62004I 1.98563 + 8.95063I
u = −0.468457 − 0.715892I
a = −0.678237 − 0.210938I
b = −0.173523 + 0.977457I
0.24900 + 3.62004I 1.98563 − 8.95063I
u = 0.464004 + 1.050320I
a = −0.31217 + 3.03749I
b = −0.65170 + 4.08273I
5.02616 + 3.30361I 0.39237 − 4.97703I
u = 0.464004 − 1.050320I
a = −0.31217 − 3.03749I
b = −0.65170 − 4.08273I
5.02616 − 3.30361I 0.39237 + 4.97703I
u = 0.773218 + 0.228170I
a = −1.92418 − 0.33198I
b = −0.478975 + 0.164410I
−2.06386 − 4.46334I 0.46360 + 4.84315I
u = 0.773218 − 0.228170I
a = −1.92418 + 0.33198I
b = −0.478975 − 0.164410I
−2.06386 + 4.46334I 0.46360 − 4.84315I
u = 0.305634 + 1.188350I
a = 0.051305 − 1.236500I
b = 0.65454 − 1.98487I
−6.36852 − 1.01335I −5.48366 + 1.62767I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.305634 − 1.188350I
a = 0.051305 + 1.236500I
b = 0.65454 + 1.98487I
−6.36852 + 1.01335I −5.48366 − 1.62767I
u = 0.539603 + 1.156090I
a = −0.00613 − 1.80864I
b = −0.17533 − 2.86609I
−4.76857 + 9.35771I −2.38330 − 7.93311I
u = 0.539603 − 1.156090I
a = −0.00613 + 1.80864I
b = −0.17533 + 2.86609I
−4.76857 − 9.35771I −2.38330 + 7.93311I
u = −0.596101 + 1.176370I
a = −0.0194796 − 0.1364700I
b = 0.343510 − 0.109245I
2.18794 − 5.27328I −0.326316 − 0.621275I
u = −0.596101 − 1.176370I
a = −0.0194796 + 0.1364700I
b = 0.343510 + 0.109245I
2.18794 + 5.27328I −0.326316 + 0.621275I
u = 0.350446 + 0.524920I
a = 2.77555 − 1.60523I
b = 1.64862 − 0.37193I
6.75650 + 0.40196I 5.16061 + 1.96558I
u = 0.350446 − 0.524920I
a = 2.77555 + 1.60523I
b = 1.64862 + 0.37193I
6.75650 − 0.40196I 5.16061 − 1.96558I
13
III.
I
u
3
= h−u
17
+u
16
+· · ·+b+1, u
17
a+4u
17
+· · ·+a
2
−5, u
18
−u
17
+· · ·−u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
a
u
17
− u
16
+ ··· + u − 1
a
8
=
−u
17
+ u
16
+ ··· − a − 1
−2u
17
+ 2u
16
+ ··· − 2u + 1
a
1
=
u
2
+ 1
−u
4
a
11
=
u
17
− u
16
+ ··· + a + 1
2u
17
− 2u
16
+ ··· + 2u − 1
a
5
=
3u
17
− 3u
16
+ ··· − a − 4
4u
17
− 4u
16
+ ··· + 4u − 3
a
9
=
u
17
− u
16
+ ··· + a + 1
2u
17
− 2u
16
+ ··· + u − 1
a
12
=
−3u
17
+ 2u
16
+ ··· − 3a − 2
−6u
17
+ 5u
16
+ ··· − 6u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 4u
16
−16u
15
+ 12u
14
−32u
13
+ 24u
12
−36u
11
+ 28u
10
−
24u
9
+ 28u
8
− 12u
7
+ 16u
6
− 8u
5
+ 8u
4
− 8u
3
− 4u + 14
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
+ 9u
17
+ ··· + u + 1)
2
c
2
, c
6
(u
18
+ u
17
+ ··· + u + 1)
2
c
3
(u
18
− u
17
+ ··· − u + 5)
2
c
4
, c
12
u
36
+ u
35
+ ··· − 4000u + 889
c
5
, c
9
u
36
+ u
35
+ ··· − 84188u + 25097
c
7
, c
10
u
36
− 15u
35
+ ··· − 340u + 25
c
8
, c
11
(u
18
− 15u
17
+ ··· + 29u + 3)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ y
17
+ ··· + 9y + 1)
2
c
2
, c
6
(y
18
+ 9y
17
+ ··· + y + 1)
2
c
3
(y
18
− 7y
17
+ ··· − 91y + 25)
2
c
4
, c
12
y
36
− 45y
35
+ ··· − 11217180y + 790321
c
5
, c
9
y
36
− 25y
35
+ ··· − 7934994452y + 629859409
c
7
, c
10
y
36
− 9y
35
+ ··· + 14100y + 625
c
8
, c
11
(y
18
− 35y
17
+ ··· − 211y + 9)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.606951 + 0.762732I
a = −0.672810 + 0.417119I
b = −0.184656 − 0.365220I
1.63218 − 2.36433I 8.96106 + 3.34702I
u = −0.606951 + 0.762732I
a = 0.085009 + 0.384811I
b = −0.428365 + 0.927160I
1.63218 − 2.36433I 8.96106 + 3.34702I
u = −0.606951 − 0.762732I
a = −0.672810 − 0.417119I
b = −0.184656 + 0.365220I
1.63218 + 2.36433I 8.96106 − 3.34702I
u = −0.606951 − 0.762732I
a = 0.085009 − 0.384811I
b = −0.428365 − 0.927160I
1.63218 + 2.36433I 8.96106 − 3.34702I
u = −0.320154 + 1.065080I
a = −1.344920 + 0.399822I
b = −0.333397 + 0.527308I
2.99038 − 0.58479I 3.81506 − 0.42463I
u = −0.320154 + 1.065080I
a = −0.54509 + 1.40985I
b = −1.52871 + 2.64353I
2.99038 − 0.58479I 3.81506 − 0.42463I
u = −0.320154 − 1.065080I
a = −1.344920 − 0.399822I
b = −0.333397 − 0.527308I
2.99038 + 0.58479I 3.81506 + 0.42463I
u = −0.320154 − 1.065080I
a = −0.54509 − 1.40985I
b = −1.52871 − 2.64353I
2.99038 + 0.58479I 3.81506 + 0.42463I
u = 0.483861 + 1.030980I
a = −0.41599 + 2.66215I
b = −0.88355 + 4.52483I
5.97153 + 3.09151I 11.11493 − 2.77317I
u = 0.483861 + 1.030980I
a = −0.32117 − 3.24954I
b = −0.56235 − 3.23198I
5.97153 + 3.09151I 11.11493 − 2.77317I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.483861 − 1.030980I
a = −0.41599 − 2.66215I
b = −0.88355 − 4.52483I
5.97153 − 3.09151I 11.11493 + 2.77317I
u = 0.483861 − 1.030980I
a = −0.32117 + 3.24954I
b = −0.56235 + 3.23198I
5.97153 − 3.09151I 11.11493 + 2.77317I
u = 0.781793 + 0.257942I
a = 1.50733 + 0.37688I
b = 0.649577 − 0.040046I
−0.79783 − 3.98828I 8.01934 + 2.30410I
u = 0.781793 + 0.257942I
a = −1.81527 − 0.39003I
b = −0.249789 + 0.261114I
−0.79783 − 3.98828I 8.01934 + 2.30410I
u = 0.781793 − 0.257942I
a = 1.50733 − 0.37688I
b = 0.649577 + 0.040046I
−0.79783 + 3.98828I 8.01934 − 2.30410I
u = 0.781793 − 0.257942I
a = −1.81527 + 0.39003I
b = −0.249789 − 0.261114I
−0.79783 + 3.98828I 8.01934 − 2.30410I
u = 0.286599 + 1.176040I
a = 0.129696 − 1.018410I
b = 0.84736 − 1.88349I
−5.21072 − 0.69909I 2.61745 − 0.31146I
u = 0.286599 + 1.176040I
a = 0.111176 + 1.187900I
b = −0.28946 + 1.60976I
−5.21072 − 0.69909I 2.61745 − 0.31146I
u = 0.286599 − 1.176040I
a = 0.129696 + 1.018410I
b = 0.84736 + 1.88349I
−5.21072 + 0.69909I 2.61745 + 0.31146I
u = 0.286599 − 1.176040I
a = 0.111176 − 1.187900I
b = −0.28946 − 1.60976I
−5.21072 + 0.69909I 2.61745 + 0.31146I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527745 + 1.103190I
a = 1.191070 + 0.466746I
b = 2.91002 + 0.99091I
4.40791 − 6.64525I 7.35959 + 7.71274I
u = −0.527745 + 1.103190I
a = 1.43943 + 1.42860I
b = 0.83094 + 1.94919I
4.40791 − 6.64525I 7.35959 + 7.71274I
u = −0.527745 − 1.103190I
a = 1.191070 − 0.466746I
b = 2.91002 − 0.99091I
4.40791 + 6.64525I 7.35959 − 7.71274I
u = −0.527745 − 1.103190I
a = 1.43943 − 1.42860I
b = 0.83094 − 1.94919I
4.40791 + 6.64525I 7.35959 − 7.71274I
u = 0.500651 + 0.525564I
a = −2.56302 − 0.46993I
b = −2.37571 + 0.29310I
7.49746 + 0.97328I 14.1139 − 4.5518I
u = 0.500651 + 0.525564I
a = 3.00132 − 1.06603I
b = 0.551934 − 0.024389I
7.49746 + 0.97328I 14.1139 − 4.5518I
u = 0.500651 − 0.525564I
a = −2.56302 + 0.46993I
b = −2.37571 − 0.29310I
7.49746 − 0.97328I 14.1139 + 4.5518I
u = 0.500651 − 0.525564I
a = 3.00132 + 1.06603I
b = 0.551934 + 0.024389I
7.49746 − 0.97328I 14.1139 + 4.5518I
u = 0.548853 + 1.153160I
a = 0.00604 − 1.65136I
b = −0.30591 − 2.86421I
−3.42686 + 8.95499I 4.97585 − 5.84784I
u = 0.548853 + 1.153160I
a = 0.22040 + 1.64693I
b = 0.40384 + 2.31431I
−3.42686 + 8.95499I 4.97585 − 5.84784I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548853 − 1.153160I
a = 0.00604 + 1.65136I
b = −0.30591 + 2.86421I
−3.42686 − 8.95499I 4.97585 + 5.84784I
u = 0.548853 − 1.153160I
a = 0.22040 − 1.64693I
b = 0.40384 − 2.31431I
−3.42686 − 8.95499I 4.97585 + 5.84784I
u = −0.646907 + 0.309141I
a = −1.50508 − 0.65497I
b = −0.59498 − 1.52441I
6.67515 + 2.06052I 11.02279 − 4.27827I
u = −0.646907 + 0.309141I
a = −1.00812 − 2.23459I
b = 0.043192 + 0.359954I
6.67515 + 2.06052I 11.02279 − 4.27827I
u = −0.646907 − 0.309141I
a = −1.50508 + 0.65497I
b = −0.59498 + 1.52441I
6.67515 − 2.06052I 11.02279 + 4.27827I
u = −0.646907 − 0.309141I
a = −1.00812 + 2.23459I
b = 0.043192 − 0.359954I
6.67515 − 2.06052I 11.02279 + 4.27827I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 9u
16
+ ··· − 4u + 1)(u
18
+ 9u
17
+ ··· + u + 1)
2
· (u
36
+ 18u
35
+ ··· + 11u + 4)
c
2
(u
17
− u
16
+ ··· − 2u + 1)(u
18
+ u
17
+ ··· + u + 1)
2
· (u
36
− 6u
35
+ ··· − 11u + 2)
c
3
(u
17
+ u
16
+ ··· + 2u + 5)(u
18
− u
17
+ ··· − u + 5)
2
· (u
36
+ 6u
35
+ ··· + 721u + 74)
c
4
, c
12
(u
17
− 2u
16
+ ··· − 3u + 1)(u
36
− 28u
34
+ ··· + u + 1)
· (u
36
+ u
35
+ ··· − 4000u + 889)
c
5
, c
9
(u
17
− 8u
15
+ ··· − u + 1)(u
36
− 8u
34
+ ··· − 19u + 23)
· (u
36
+ u
35
+ ··· − 84188u + 25097)
c
6
(u
17
+ u
16
+ ··· − 2u − 1)(u
18
+ u
17
+ ··· + u + 1)
2
· (u
36
− 6u
35
+ ··· − 11u + 2)
c
7
, c
10
(u
17
− 3u
16
+ ··· + 2u + 1)(u
36
− 15u
35
+ ··· − 340u + 25)
· (u
36
− 3u
35
+ ··· − 4u + 1)
c
8
(u
17
+ 14u
16
+ ··· + 23u + 5)(u
18
− 15u
17
+ ··· + 29u + 3)
2
· (u
36
+ 17u
35
+ ··· − 1495u + 160)
c
11
(u
17
− 14u
16
+ ··· + 23u − 5)(u
18
− 15u
17
+ ··· + 29u + 3)
2
· (u
36
+ 17u
35
+ ··· − 1495u + 160)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ y
16
+ ··· − 8y −1)(y
18
+ y
17
+ ··· + 9y + 1)
2
· (y
36
+ 2y
35
+ ··· + 415y + 16)
c
2
, c
6
(y
17
+ 9y
16
+ ··· − 4y −1)(y
18
+ 9y
17
+ ··· + y + 1)
2
· (y
36
+ 18y
35
+ ··· + 11y + 4)
c
3
(y
17
− 13y
16
+ ··· − 86y −25)(y
18
− 7y
17
+ ··· − 91y + 25)
2
· (y
36
− 20y
35
+ ··· − 111805y + 5476)
c
4
, c
12
(y
17
− 16y
16
+ ··· − 3y −1)(y
36
− 56y
35
+ ··· − y + 1)
· (y
36
− 45y
35
+ ··· − 11217180y + 790321)
c
5
, c
9
(y
17
− 16y
16
+ ··· + 9y −1)
· (y
36
− 25y
35
+ ··· − 7934994452y + 629859409)
· (y
36
− 16y
35
+ ··· − 5421y + 529)
c
7
, c
10
(y
17
− 7y
16
+ ··· + 4y −1)(y
36
− 9y
35
+ ··· + 14100y + 625)
· (y
36
+ 9y
35
+ ··· + 16y + 1)
c
8
, c
11
(y
17
− 18y
16
+ ··· − 371y −25)(y
18
− 35y
17
+ ··· − 211y + 9)
2
· (y
36
− 29y
35
+ ··· − 1047185y + 25600)
22
