12n
0625
(K12n
0625
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 1 10 2 5 12 6 4 9
Solving Sequence
9,12
10
1,5
6 4 3 8 2 7 11
c
9
c
12
c
5
c
4
c
3
c
8
c
2
c
7
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−97u
34
− 1164u
33
+ ··· + 4b − 1732, −239u
34
− 2674u
33
+ ··· + 8a − 4156,
u
35
+ 12u
34
+ ··· + 140u + 8i
I
u
2
= h−3u
24
+ 20u
23
+ ··· + b − 14, 14u
25
− 83u
24
+ ··· + 5a + 15, u
26
− 7u
25
+ ··· − 15u + 5i
I
u
3
= h−38441817751a
5
u
5
− 19856412660u
5
a
4
+ ··· − 2635825958a − 179169756,
4u
5
a
4
+ u
5
a
3
+ ··· + 90a − 272, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 97 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−97u
34
− 1164u
33
+ · · · + 4b − 1732, −239u
34
− 2674u
33
+ · · · +
8a − 4156, u
35
+ 12u
34
+ · · · + 140u + 8i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
5
=
29.8750u
34
+ 334.250u
33
+ ··· + 7861.75u + 519.500
97
4
u
34
+ 291u
33
+ ··· + 6625u + 433
a
6
=
29.8750u
34
+ 344.250u
33
+ ··· + 10823.8u + 713.500
97
4
u
34
+ 281u
33
+ ··· + 3663u + 239
a
4
=
15.6250u
34
+ 177.250u
33
+ ··· + 4392.75u + 280.500
85
4
u
34
+ 243u
33
+ ··· + 4779u + 321
a
3
=
7.37500u
34
+ 71.2500u
33
+ ··· − 4744.25u − 354.500
21
4
u
34
+ 75u
33
+ ··· + 4263u + 263
a
8
=
−
33
8
u
34
−
191
4
u
33
+ ··· −
3645
4
u − 56
−
17
4
u
34
−
97
2
u
33
+ ··· −
2097
2
u − 67
a
2
=
−
125
8
u
34
−
727
4
u
33
+ ··· −
28857
4
u − 491
−
15
4
u
34
−
93
2
u
33
+ ··· +
313
2
u + 7
a
7
=
−40.1250u
34
− 460.250u
33
+ ··· − 12730.8u − 838.500
−
89
4
u
34
− 265u
33
+ ··· − 4561u − 295
a
11
=
5
8
u
34
+
27
4
u
33
+ ··· +
233
4
u + 4
−
1
4
u
34
−
5
2
u
33
+ ··· +
33
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
34
− 40u
33
+ ··· − 3016u − 210
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 17u
34
+ ··· − 3072u + 4096
c
2
, c
7
u
35
− 13u
34
+ ··· − 544u + 64
c
3
u
35
+ 19u
34
+ ··· + 20188u + 1960
c
4
u
35
− 19u
33
+ ··· + 270u − 193
c
5
, c
8
u
35
− 12u
33
+ ··· + 10u − 1
c
6
, c
10
, c
11
u
35
− u
34
+ ··· − 16u
2
+ 1
c
9
, c
12
u
35
− 12u
34
+ ··· + 140u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 3y
34
+ ··· − 250609664y −16777216
c
2
, c
7
y
35
− 17y
34
+ ··· − 3072y −4096
c
3
y
35
− 45y
34
+ ··· + 57342544y −3841600
c
4
y
35
− 38y
34
+ ··· − 208108y −37249
c
5
, c
8
y
35
− 24y
34
+ ··· + 34y −1
c
6
, c
10
, c
11
y
35
− 55y
34
+ ··· + 32y −1
c
9
, c
12
y
35
+ 24y
34
+ ··· + 912y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.099980 + 0.143930I
a = 0.230693 − 0.044757I
b = −1.19145 − 0.89068I
8.07701 + 10.47920I 0
u = −1.099980 − 0.143930I
a = 0.230693 + 0.044757I
b = −1.19145 + 0.89068I
8.07701 − 10.47920I 0
u = −0.176786 + 1.110160I
a = −1.50400 − 0.06191I
b = 0.819836 + 0.909342I
−0.154709 + 0.705431I 0
u = −0.176786 − 1.110160I
a = −1.50400 + 0.06191I
b = 0.819836 − 0.909342I
−0.154709 − 0.705431I 0
u = −1.148150 + 0.105837I
a = −0.218382 + 0.022702I
b = 1.266830 + 0.573062I
9.98543 + 3.73790I 0
u = −1.148150 − 0.105837I
a = −0.218382 − 0.022702I
b = 1.266830 − 0.573062I
9.98543 − 3.73790I 0
u = −0.156742 + 1.187670I
a = 1.74113 − 0.29318I
b = −1.21323 − 0.79801I
4.43767 + 2.72692I 0
u = −0.156742 − 1.187670I
a = 1.74113 + 0.29318I
b = −1.21323 + 0.79801I
4.43767 − 2.72692I 0
u = −0.080256 + 1.203320I
a = 1.32268 − 0.52185I
b = −1.066100 − 0.381230I
5.03943 + 0.52910I 0
u = −0.080256 − 1.203320I
a = 1.32268 + 0.52185I
b = −1.066100 + 0.381230I
5.03943 − 0.52910I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.180648 + 1.194610I
a = −1.91566 + 0.20321I
b = 1.28335 + 0.96670I
2.44479 + 7.71496I 0
u = −0.180648 − 1.194610I
a = −1.91566 − 0.20321I
b = 1.28335 − 0.96670I
2.44479 − 7.71496I 0
u = −0.027618 + 1.240640I
a = −1.043420 + 0.623249I
b = 0.946278 + 0.141646I
3.62037 − 4.19606I 0
u = −0.027618 − 1.240640I
a = −1.043420 − 0.623249I
b = 0.946278 − 0.141646I
3.62037 + 4.19606I 0
u = 0.393608 + 0.616666I
a = −0.541312 − 0.331797I
b = 0.128387 + 0.276430I
0.073195 − 1.283670I 0.53283 + 5.86961I
u = 0.393608 − 0.616666I
a = −0.541312 + 0.331797I
b = 0.128387 − 0.276430I
0.073195 + 1.283670I 0.53283 − 5.86961I
u = −1.33744
a = 0.212540
b = −0.842391
1.80982 0
u = −0.382949 + 0.400086I
a = 1.077350 + 0.149282I
b = 0.262290 − 0.775953I
−2.26874 + 1.67313I 1.23489 − 1.13105I
u = −0.382949 − 0.400086I
a = 1.077350 − 0.149282I
b = 0.262290 + 0.775953I
−2.26874 − 1.67313I 1.23489 + 1.13105I
u = −0.48137 + 1.41511I
a = 1.87041 − 0.11510I
b = −1.51506 − 1.07641I
12.9957 + 16.0498I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.48137 − 1.41511I
a = 1.87041 + 0.11510I
b = −1.51506 + 1.07641I
12.9957 − 16.0498I 0
u = −0.50191 + 1.42077I
a = −1.72676 + 0.32922I
b = 1.55368 + 0.82547I
14.8329 + 9.5367I 0
u = −0.50191 − 1.42077I
a = −1.72676 − 0.32922I
b = 1.55368 − 0.82547I
14.8329 − 9.5367I 0
u = 1.08815 + 1.05620I
a = 0.209018 + 0.062343I
b = −0.1172880 − 0.0788852I
−5.12951 − 4.01720I 0
u = 1.08815 − 1.05620I
a = 0.209018 − 0.062343I
b = −0.1172880 + 0.0788852I
−5.12951 + 4.01720I 0
u = −0.67357 + 1.36899I
a = 0.486870 − 0.931148I
b = −1.050210 + 0.441181I
11.70210 − 4.12793I 0
u = −0.67357 − 1.36899I
a = 0.486870 + 0.931148I
b = −1.050210 − 0.441181I
11.70210 + 4.12793I 0
u = −0.61726 + 1.41428I
a = −0.858106 + 0.838071I
b = 1.257250 − 0.123309I
14.0234 + 2.6592I 0
u = −0.61726 − 1.41428I
a = −0.858106 − 0.838071I
b = 1.257250 + 0.123309I
14.0234 − 2.6592I 0
u = −0.412094 + 0.136239I
a = 1.48498 − 0.11016I
b = 0.870960 − 0.623172I
−0.69807 − 5.41461I 4.99900 + 9.86847I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412094 − 0.136239I
a = 1.48498 + 0.11016I
b = 0.870960 + 0.623172I
−0.69807 + 5.41461I 4.99900 − 9.86847I
u = −0.53677 + 1.49180I
a = 1.111360 − 0.251453I
b = −1.054110 − 0.475748I
6.80622 + 6.65686I 0
u = −0.53677 − 1.49180I
a = 1.111360 + 0.251453I
b = −1.054110 + 0.475748I
6.80622 − 6.65686I 0
u = −0.336936 + 0.095632I
a = −1.58311 − 0.02068I
b = −0.760213 + 0.327462I
1.31189 − 0.75210I 6.86398 + 3.34403I
u = −0.336936 − 0.095632I
a = −1.58311 + 0.02068I
b = −0.760213 − 0.327462I
1.31189 + 0.75210I 6.86398 − 3.34403I
8
II. I
u
2
= h−3u
24
+ 20u
23
+ · · · + b − 14, 14u
25
− 83u
24
+ · · · + 5a + 15, u
26
−
7u
25
+ · · · − 15u + 5i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
5
=
−
14
5
u
25
+
83
5
u
24
+ ··· +
1
5
u − 3
3u
24
− 20u
23
+ ··· − 31u + 14
a
6
=
1
5
u
25
−
17
5
u
24
+ ··· +
71
5
u − 3
−3u
25
+ 23u
24
+ ··· − 45u + 14
a
4
=
−
4
5
u
25
+
28
5
u
24
+ ··· +
1
5
u − 2
−2u
22
+ 11u
21
+ ··· + 4u − 1
a
3
=
−
21
5
u
25
+
152
5
u
24
+ ··· −
181
5
u + 5
8u
25
− 54u
24
+ ··· + 50u − 9
a
8
=
9
5
u
25
−
53
5
u
24
+ ··· −
11
5
u + 5
u
25
− 8u
24
+ ··· + 32u − 14
a
2
=
−
9
5
u
25
+
93
5
u
24
+ ··· −
259
5
u + 17
6u
25
− 47u
24
+ ··· + 88u − 26
a
7
=
1
5
u
25
−
7
5
u
24
+ ··· +
1
5
u + 1
2u
24
− 13u
23
+ ··· − 15u + 4
a
11
=
6
5
u
25
−
42
5
u
24
+ ··· +
11
5
u − 1
−u
25
+ 6u
24
+ ··· + 11u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 2u
25
+ 9u
24
−77u
23
+ 407u
22
−1373u
21
+ 3767u
20
−8362u
19
+ 15938u
18
−25873u
17
+
36425u
16
− 43673u
15
+ 43799u
14
− 33927u
13
+ 14898u
12
+ 8887u
11
− 30580u
10
+
44036u
9
−46418u
8
+ 39264u
7
−27167u
6
+ 15123u
5
−6437u
4
+ 1785u
3
−99u
2
−150u + 45
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 16u
25
+ ··· − 115u + 9
c
2
u
26
− 8u
24
+ ··· + 5u + 3
c
3
u
26
+ 22u
25
+ ··· + 3110u + 473
c
4
u
26
− 9u
24
+ ··· − u − 3
c
5
, c
8
u
26
+ 2u
24
+ ··· − 7u − 1
c
6
, c
11
u
26
− u
25
+ ··· + u − 1
c
7
u
26
− 8u
24
+ ··· − 5u + 3
c
9
u
26
− 7u
25
+ ··· − 15u + 5
c
10
u
26
+ u
25
+ ··· − u − 1
c
12
u
26
+ 7u
25
+ ··· + 15u + 5
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 4y
24
+ ··· − 211y + 81
c
2
, c
7
y
26
− 16y
25
+ ··· − 115y + 9
c
3
y
26
− 34y
25
+ ··· − 2510880y + 223729
c
4
y
26
− 18y
25
+ ··· + 47y + 9
c
5
, c
8
y
26
+ 4y
25
+ ··· − 27y + 1
c
6
, c
10
, c
11
y
26
− 19y
25
+ ··· + 15y + 1
c
9
, c
12
y
26
+ 19y
25
+ ··· − 365y + 25
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994612
a = 0.638284
b = −0.318280
0.856397 −2.32000
u = −0.212241 + 1.020190I
a = 1.23563 − 1.37216I
b = −0.081295 + 1.211700I
9.42472 − 2.04416I 6.12450 + 2.23947I
u = −0.212241 − 1.020190I
a = 1.23563 + 1.37216I
b = −0.081295 − 1.211700I
9.42472 + 2.04416I 6.12450 − 2.23947I
u = 0.690336 + 0.610624I
a = 0.076479 − 0.614284I
b = 0.774243 + 0.308106I
1.035900 − 0.601010I 6.74042 + 0.76556I
u = 0.690336 − 0.610624I
a = 0.076479 + 0.614284I
b = 0.774243 − 0.308106I
1.035900 + 0.601010I 6.74042 − 0.76556I
u = −0.149267 + 1.091680I
a = −1.79375 + 0.98935I
b = 0.54342 − 1.31617I
9.80770 + 3.58067I 6.57697 − 2.52937I
u = −0.149267 − 1.091680I
a = −1.79375 − 0.98935I
b = 0.54342 + 1.31617I
9.80770 − 3.58067I 6.57697 + 2.52937I
u = 0.389539 + 1.134620I
a = −1.302210 − 0.416528I
b = 1.108030 − 0.626702I
2.91227 − 3.60504I 3.99685 + 3.76042I
u = 0.389539 − 1.134620I
a = −1.302210 + 0.416528I
b = 1.108030 + 0.626702I
2.91227 + 3.60504I 3.99685 − 3.76042I
u = 0.797638 + 0.055469I
a = −0.141851 − 0.260115I
b = −0.182422 − 1.114170I
−3.82284 − 1.29938I −2.97334 + 4.45756I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797638 − 0.055469I
a = −0.141851 + 0.260115I
b = −0.182422 + 1.114170I
−3.82284 + 1.29938I −2.97334 − 4.45756I
u = 0.332677 + 1.187440I
a = 1.67027 + 0.23671I
b = −1.22101 + 0.91742I
1.60214 − 8.49569I 1.29011 + 9.18149I
u = 0.332677 − 1.187440I
a = 1.67027 − 0.23671I
b = −1.22101 − 0.91742I
1.60214 + 8.49569I 1.29011 − 9.18149I
u = 0.663432 + 0.362819I
a = −0.524336 + 0.422708I
b = −0.822418 − 0.618568I
−1.08880 + 4.74486I −0.32078 − 1.84995I
u = 0.663432 − 0.362819I
a = −0.524336 − 0.422708I
b = −0.822418 + 0.618568I
−1.08880 − 4.74486I −0.32078 + 1.84995I
u = −0.084221 + 1.248750I
a = −1.63024 − 0.11402I
b = 1.036010 − 0.675543I
7.45067 + 1.13341I 10.54209 + 2.52582I
u = −0.084221 − 1.248750I
a = −1.63024 + 0.11402I
b = 1.036010 + 0.675543I
7.45067 − 1.13341I 10.54209 − 2.52582I
u = 0.352829 + 1.277260I
a = 1.49620 − 0.38804I
b = −0.78216 + 1.19766I
0.00872 − 2.80461I 3.16243 + 0.29385I
u = 0.352829 − 1.277260I
a = 1.49620 + 0.38804I
b = −0.78216 − 1.19766I
0.00872 + 2.80461I 3.16243 − 0.29385I
u = −0.158743 + 1.367070I
a = 1.055280 + 0.122047I
b = −0.726480 + 0.371188I
6.12252 + 3.91786I 6.46603 − 4.94923I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158743 − 1.367070I
a = 1.055280 − 0.122047I
b = −0.726480 − 0.371188I
6.12252 − 3.91786I 6.46603 + 4.94923I
u = 0.391414 + 1.325100I
a = −1.115120 + 0.491333I
b = 0.489745 − 1.045650I
0.54950 − 5.62615I 3.66832 + 10.11722I
u = 0.391414 − 1.325100I
a = −1.115120 − 0.491333I
b = 0.489745 + 1.045650I
0.54950 + 5.62615I 3.66832 − 10.11722I
u = 1.10193 + 1.08460I
a = 0.207377 + 0.156851I
b = −0.368539 + 0.019205I
−4.99593 − 4.04910I 27.6398 + 11.5463I
u = 1.10193 − 1.08460I
a = 0.207377 − 0.156851I
b = −0.368539 − 0.019205I
−4.99593 + 4.04910I 27.6398 − 11.5463I
u = −0.236035
a = −4.10573
b = 0.784035
3.63799 13.4930
14
III. I
u
3
= h−3.84 × 10
10
a
5
u
5
− 1.99 × 10
10
a
4
u
5
+ · · · − 2.64 × 10
9
a − 1.79 ×
10
8
, 4u
5
a
4
+ u
5
a
3
+ · · · + 90a − 272, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
5
=
a
22.7375a
5
u
5
+ 11.7446a
4
u
5
+ ··· + 1.55903a + 0.105975
a
6
=
17.4024a
5
u
5
+ 8.90807a
4
u
5
+ ··· + 2.70752a − 0.0801194
5.33502a
5
u
5
+ 2.83654a
4
u
5
+ ··· − 0.148487a + 0.186094
a
4
=
−22.7375a
5
u
5
− 11.7446a
4
u
5
+ ··· − 0.559030a − 0.105975
5.33502a
5
u
5
+ 2.83654a
4
u
5
+ ··· − 0.148487a + 0.186094
a
3
=
−16.3123a
5
u
5
− 8.46656a
4
u
5
+ ··· − 1.43971a + 0.213592
7.29620a
5
u
5
+ 3.87826a
4
u
5
+ ··· + 1.28149a + 0.523558
a
8
=
−6.24783a
5
u
5
− 6.05457a
4
u
5
+ ··· − 0.986241a + 0.330441
−4.85306a
5
u
5
− 4.50211a
4
u
5
+ ··· − 1.02272a + 0.683110
a
2
=
−14.6689a
5
u
5
− 14.1906a
4
u
5
+ ··· − 2.29063a + 0.459585
3.56796a
5
u
5
+ 3.63393a
4
u
5
+ ··· + 0.281670a + 0.553965
a
7
=
−9.54626a
5
u
5
− 4.90520a
4
u
5
+ ··· − 1.28745a + 0.352817
0.530130a
5
u
5
+ 0.316901a
4
u
5
+ ··· + 1.12923a + 0.384333
a
11
=
−15.2075a
5
u
5
− 14.4298a
4
u
5
+ ··· − 2.17959a + 0.280254
−1.77366a
5
u
5
− 1.96756a
4
u
5
+ ··· − 0.0617525a − 0.267275
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
12578180552
1690682787
a
5
u
5
−
35048362616
1690682787
u
5
a
4
+ ···−
6976030156
1690682787
a −
3021249058
1690682787
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
12
c
2
, c
7
(u
3
+ u
2
− 1)
12
c
3
(u
6
− 5u
5
+ 7u
4
− 2u
2
− 3u − 1)
6
c
4
u
36
+ u
35
+ ··· − 1508790u − 544009
c
5
, c
8
u
36
− 5u
35
+ ··· − 4368u − 383
c
6
, c
10
, c
11
u
36
− u
35
+ ··· + 36176u − 62927
c
9
, c
12
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
12
c
2
, c
7
(y
3
− y
2
+ 2y −1)
12
c
3
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
6
c
4
y
36
− 33y
35
+ ··· − 2168864044260y + 295945792081
c
5
, c
8
y
36
+ 3y
35
+ ··· − 23130032y + 146689
c
6
, c
10
, c
11
y
36
− 45y
35
+ ··· − 4582417224y + 3959807329
c
9
, c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = 0.046621 + 0.560350I
b = 0.946484 + 0.058547I
0.29884 + 2.82812I 3.24026 − 2.97945I
u = 0.873214
a = 0.046621 − 0.560350I
b = 0.946484 − 0.058547I
0.29884 − 2.82812I 3.24026 + 2.97945I
u = 0.873214
a = −0.216714 + 0.473383I
b = −0.867194 − 0.540430I
0.29884 + 2.82812I 3.24026 − 2.97945I
u = 0.873214
a = −0.216714 − 0.473383I
b = −0.867194 + 0.540430I
0.29884 − 2.82812I 3.24026 + 2.97945I
u = 0.873214
a = −0.225325 + 0.158182I
b = 0.105037 + 1.089450I
−3.83874 −3.28901 + 0.I
u = 0.873214
a = −0.225325 − 0.158182I
b = 0.105037 − 1.089450I
−3.83874 −3.28901 + 0.I
u = −0.138835 + 1.234450I
a = −0.710924 − 0.211504I
b = 0.177665 − 0.836176I
6.78159 + 1.97241I 4.40477 − 3.68478I
u = −0.138835 + 1.234450I
a = −0.96909 + 1.81374I
b = 1.14994 − 2.52852I
10.91920 − 0.85571I 10.93403 − 0.70533I
u = −0.138835 + 1.234450I
a = 2.05223 − 0.44593I
b = −1.36734 + 0.51282I
6.78159 + 1.97241I 4.40477 − 3.68478I
u = −0.138835 + 1.234450I
a = 1.53377 − 1.76635I
b = −1.76314 + 2.25582I
10.91920 + 4.80053I 10.93403 − 6.66423I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138835 + 1.234450I
a = −2.53558 − 1.55858I
b = 0.572383 + 0.351094I
10.91920 + 4.80053I 10.93403 − 6.66423I
u = −0.138835 + 1.234450I
a = 2.98342 + 1.01491I
b = −0.857247 − 0.322484I
10.91920 − 0.85571I 10.93403 − 0.70533I
u = −0.138835 − 1.234450I
a = −0.710924 + 0.211504I
b = 0.177665 + 0.836176I
6.78159 − 1.97241I 4.40477 + 3.68478I
u = −0.138835 − 1.234450I
a = −0.96909 − 1.81374I
b = 1.14994 + 2.52852I
10.91920 + 0.85571I 10.93403 + 0.70533I
u = −0.138835 − 1.234450I
a = 2.05223 + 0.44593I
b = −1.36734 − 0.51282I
6.78159 − 1.97241I 4.40477 + 3.68478I
u = −0.138835 − 1.234450I
a = 1.53377 + 1.76635I
b = −1.76314 − 2.25582I
10.91920 − 4.80053I 10.93403 + 6.66423I
u = −0.138835 − 1.234450I
a = −2.53558 + 1.55858I
b = 0.572383 − 0.351094I
10.91920 − 4.80053I 10.93403 + 6.66423I
u = −0.138835 − 1.234450I
a = 2.98342 − 1.01491I
b = −0.857247 + 0.322484I
10.91920 + 0.85571I 10.93403 + 0.70533I
u = 0.408802 + 1.276380I
a = 1.006520 − 0.502701I
b = −0.515095 + 1.191540I
0.12577 − 4.59213I 0.39935 + 3.20482I
u = 0.408802 + 1.276380I
a = 0.833561 + 1.021450I
b = −0.858564 + 0.199511I
4.26335 − 1.76400I 6.92862 + 0.22537I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.408802 + 1.276380I
a = −1.40776 + 0.27165I
b = 0.678316 − 0.908842I
0.12577 − 4.59213I 0.39935 + 3.20482I
u = 0.408802 + 1.276380I
a = −1.51500 − 0.18826I
b = 1.56863 − 0.46722I
4.26335 − 1.76400I 6.92862 + 0.22537I
u = 0.408802 + 1.276380I
a = −1.37419 − 0.89571I
b = 1.055710 − 0.493186I
4.26335 − 7.42025I 6.92862 + 6.18427I
u = 0.408802 + 1.276380I
a = 1.75274 − 0.11189I
b = −1.64256 + 0.97429I
4.26335 − 7.42025I 6.92862 + 6.18427I
u = 0.408802 − 1.276380I
a = 1.006520 + 0.502701I
b = −0.515095 − 1.191540I
0.12577 + 4.59213I 0.39935 − 3.20482I
u = 0.408802 − 1.276380I
a = 0.833561 − 1.021450I
b = −0.858564 − 0.199511I
4.26335 + 1.76400I 6.92862 − 0.22537I
u = 0.408802 − 1.276380I
a = −1.40776 − 0.27165I
b = 0.678316 + 0.908842I
0.12577 + 4.59213I 0.39935 − 3.20482I
u = 0.408802 − 1.276380I
a = −1.51500 + 0.18826I
b = 1.56863 + 0.46722I
4.26335 + 1.76400I 6.92862 − 0.22537I
u = 0.408802 − 1.276380I
a = −1.37419 + 0.89571I
b = 1.055710 + 0.493186I
4.26335 + 7.42025I 6.92862 − 6.18427I
u = 0.408802 − 1.276380I
a = 1.75274 + 0.11189I
b = −1.64256 − 0.97429I
4.26335 + 7.42025I 6.92862 − 6.18427I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413150
a = 1.28447
b = −1.08768
3.08250 −4.43630
u = −0.413150
a = −2.71395
b = 0.0813039
3.08250 −4.43630
u = −0.413150
a = 2.75916 + 1.87870I
b = −1.07546 + 1.08432I
7.22008 + 2.82812I 2.09298 − 2.97945I
u = −0.413150
a = 2.75916 − 1.87870I
b = −1.07546 − 1.08432I
7.22008 − 2.82812I 2.09298 + 2.97945I
u = −0.413150
a = −3.29870 + 1.40034I
b = 0.695621 + 1.224170I
7.22008 + 2.82812I 2.09298 − 2.97945I
u = −0.413150
a = −3.29870 − 1.40034I
b = 0.695621 − 1.224170I
7.22008 − 2.82812I 2.09298 + 2.97945I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
12
)(u
26
− 16u
25
+ ··· − 115u + 9)
· (u
35
+ 17u
34
+ ··· − 3072u + 4096)
c
2
((u
3
+ u
2
− 1)
12
)(u
26
− 8u
24
+ ··· + 5u + 3)
· (u
35
− 13u
34
+ ··· − 544u + 64)
c
3
((u
6
− 5u
5
+ 7u
4
− 2u
2
− 3u − 1)
6
)(u
26
+ 22u
25
+ ··· + 3110u + 473)
· (u
35
+ 19u
34
+ ··· + 20188u + 1960)
c
4
(u
26
− 9u
24
+ ··· − u − 3)(u
35
− 19u
33
+ ··· + 270u − 193)
· (u
36
+ u
35
+ ··· − 1508790u − 544009)
c
5
, c
8
(u
26
+ 2u
24
+ ··· − 7u − 1)(u
35
− 12u
33
+ ··· + 10u − 1)
· (u
36
− 5u
35
+ ··· − 4368u − 383)
c
6
, c
11
(u
26
− u
25
+ ··· + u − 1)(u
35
− u
34
+ ··· − 16u
2
+ 1)
· (u
36
− u
35
+ ··· + 36176u − 62927)
c
7
((u
3
+ u
2
− 1)
12
)(u
26
− 8u
24
+ ··· − 5u + 3)
· (u
35
− 13u
34
+ ··· − 544u + 64)
c
9
((u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
)(u
26
− 7u
25
+ ··· − 15u + 5)
· (u
35
− 12u
34
+ ··· + 140u − 8)
c
10
(u
26
+ u
25
+ ··· − u − 1)(u
35
− u
34
+ ··· − 16u
2
+ 1)
· (u
36
− u
35
+ ··· + 36176u − 62927)
c
12
((u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
)(u
26
+ 7u
25
+ ··· + 15u + 5)
· (u
35
− 12u
34
+ ··· + 140u − 8)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
12
)(y
26
− 4y
24
+ ··· − 211y + 81)
· (y
35
+ 3y
34
+ ··· − 250609664y −16777216)
c
2
, c
7
((y
3
− y
2
+ 2y −1)
12
)(y
26
− 16y
25
+ ··· − 115y + 9)
· (y
35
− 17y
34
+ ··· − 3072y −4096)
c
3
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
6
· (y
26
− 34y
25
+ ··· − 2510880y + 223729)
· (y
35
− 45y
34
+ ··· + 57342544y −3841600)
c
4
(y
26
− 18y
25
+ ··· + 47y + 9)(y
35
− 38y
34
+ ··· − 208108y −37249)
· (y
36
− 33y
35
+ ··· − 2168864044260y + 295945792081)
c
5
, c
8
(y
26
+ 4y
25
+ ··· − 27y + 1)(y
35
− 24y
34
+ ··· + 34y −1)
· (y
36
+ 3y
35
+ ··· − 23130032y + 146689)
c
6
, c
10
, c
11
(y
26
− 19y
25
+ ··· + 15y + 1)(y
35
− 55y
34
+ ··· + 32y −1)
· (y
36
− 45y
35
+ ··· − 4582417224y + 3959807329)
c
9
, c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
6
· (y
26
+ 19y
25
+ ··· − 365y + 25)(y
35
+ 24y
34
+ ··· + 912y −64)
23
