11a
327
(K11a
327
)
A knot diagram
1
Linearized knot diagam
9 6 1 11 10 2 5 4 3 7 8
Solving Sequence
2,6
3
7,10
11 5 8 4 9 1
c
2
c
6
c
10
c
5
c
7
c
4
c
9
c
1
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4427228u
24
− 51386293u
23
+ ··· + 7423256b + 218726992,
− 5223503u
24
+ 65905467u
23
+ ··· + 14846512a − 424794688, u
25
− 11u
24
+ ··· + 304u − 32i
I
u
2
= h−487u
15
− 1824u
14
+ ··· + 1084b − 1471, 1589u
15
+ 3060u
14
+ ··· + 1084a − 2223,
u
16
+ 2u
15
+ 6u
14
+ 8u
13
+ 10u
12
+ 13u
11
+ 7u
10
+ 15u
9
+ 5u
8
+ 8u
7
+ 9u
6
− 4u
5
+ 12u
4
− 6u
3
+ 7u
2
− u + 1i
I
u
3
= h−232u
41
− 1201u
40
+ ··· + 16b − 31, 31u
41
a + 170u
41
+ ··· − 515a + 1252, u
42
+ 6u
41
+ ··· + 5u − 1i
* 3 irreducible components of dim
C
= 0, with total 125 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
=
h4.43×10
6
u
24
−5.14×10
7
u
23
+· · · +7.42×10
6
b+2.19×10
8
, −5.22×10
6
u
24
+
6.59 × 10
7
u
23
+ · · · + 1.48 × 10
7
a − 4.25 × 10
8
, u
25
− 11u
24
+ · · · + 304u − 32i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
u
a
10
=
0.351834u
24
− 4.43912u
23
+ ··· − 244.548u + 28.6124
−0.596400u
24
+ 6.92234u
23
+ ··· + 262.565u − 29.4651
a
11
=
0.311972u
24
− 4.00378u
23
+ ··· − 299.653u + 35.2367
−0.556538u
24
+ 6.48700u
23
+ ··· + 317.669u − 36.0894
a
5
=
−0.250673u
24
+ 3.42364u
23
+ ··· + 197.791u − 19.2950
0.161063u
24
− 2.76565u
23
+ ··· − 266.465u + 29.3409
a
8
=
−0.277406u
24
+ 3.01578u
23
+ ··· + 199.144u − 23.7794
−0.0363785u
24
+ 0.0499409u
23
+ ··· − 154.341u + 18.2222
a
4
=
0.235672u
24
− 2.80148u
23
+ ··· − 87.9695u + 9.74840
−0.130974u
24
+ 1.51883u
23
+ ··· − 18.7296u + 3.35035
a
9
=
0.920784u
24
− 9.53223u
23
+ ··· − 166.203u + 17.3537
0.207009u
24
− 2.31696u
23
+ ··· − 73.4954u + 7.82611
a
1
=
0.238111u
24
− 2.57557u
23
+ ··· − 106.961u + 13.9134
0.163550u
24
− 1.64723u
23
+ ··· − 42.9394u + 4.26453
a
1
=
0.238111u
24
− 2.57557u
23
+ ··· − 106.961u + 13.9134
0.163550u
24
− 1.64723u
23
+ ··· − 42.9394u + 4.26453
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4915601
1855814
u
24
−
53210001
1855814
u
23
+ ··· −
95751464
927907
u −
19294134
927907
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
25
− 2u
24
+ ··· − 5u + 1
c
2
, c
6
u
25
+ 11u
24
+ ··· + 304u + 32
c
3
, c
7
u
25
− 2u
24
+ ··· − 7u + 1
c
4
, c
8
u
25
− 6u
24
+ ··· + 2u + 1
c
5
, c
9
u
25
− 6u
24
+ ··· + 13u
2
+ 1
c
11
u
25
− 18u
24
+ ··· − 1536u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
25
+ 6y
24
+ ··· − 9y −1
c
2
, c
6
y
25
+ 11y
24
+ ··· − 3328y −1024
c
3
, c
7
y
25
+ 22y
23
+ ··· + 17y −1
c
4
, c
8
y
25
− 2y
24
+ ··· − 16y −1
c
5
, c
9
y
25
+ 4y
24
+ ··· − 26y −1
c
11
y
25
+ 10y
24
+ ··· + 720896y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415596 + 0.889012I
a = −1.53371 + 1.85229I
b = 1.86263 − 1.68366I
1.61415 − 1.93498I −3.0424 + 31.4661I
u = 0.415596 − 0.889012I
a = −1.53371 − 1.85229I
b = 1.86263 + 1.68366I
1.61415 + 1.93498I −3.0424 − 31.4661I
u = 1.003880 + 0.591915I
a = −0.060664 + 0.510320I
b = −0.283392 − 0.212996I
−2.76859 − 1.48183I −6.65987 − 5.81420I
u = 1.003880 − 0.591915I
a = −0.060664 − 0.510320I
b = −0.283392 + 0.212996I
−2.76859 + 1.48183I −6.65987 + 5.81420I
u = −1.142140 + 0.259514I
a = −0.132195 + 0.169180I
b = −0.170331 + 0.515196I
−1.89203 + 4.73023I −8.60021 − 1.58329I
u = −1.142140 − 0.259514I
a = −0.132195 − 0.169180I
b = −0.170331 − 0.515196I
−1.89203 − 4.73023I −8.60021 + 1.58329I
u = 1.142400 + 0.260296I
a = 0.360462 − 1.041080I
b = 0.382380 + 0.021730I
0.01107 + 12.92330I −4.84732 − 8.19604I
u = 1.142400 − 0.260296I
a = 0.360462 + 1.041080I
b = 0.382380 − 0.021730I
0.01107 − 12.92330I −4.84732 + 8.19604I
u = 0.071145 + 1.245000I
a = −0.926069 + 0.287044I
b = 1.80314 + 0.52501I
6.44614 − 2.45412I 2.40382 + 6.69375I
u = 0.071145 − 1.245000I
a = −0.926069 − 0.287044I
b = 1.80314 − 0.52501I
6.44614 + 2.45412I 2.40382 − 6.69375I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.263360 + 0.222570I
a = −0.217471 + 0.724765I
b = −0.307861 + 0.131345I
−2.66023 + 4.12938I −8.27327 − 5.73297I
u = 1.263360 − 0.222570I
a = −0.217471 − 0.724765I
b = −0.307861 − 0.131345I
−2.66023 − 4.12938I −8.27327 + 5.73297I
u = 0.634694 + 1.156470I
a = 0.870338 − 0.021834I
b = −1.358990 + 0.305406I
−0.75795 − 4.50706I −7.57070 + 5.07072I
u = 0.634694 − 1.156470I
a = 0.870338 + 0.021834I
b = −1.358990 − 0.305406I
−0.75795 + 4.50706I −7.57070 − 5.07072I
u = 0.63878 + 1.29685I
a = −1.205210 + 0.103104I
b = 2.26792 − 0.63100I
3.3047 − 19.2356I −2.92755 + 10.21183I
u = 0.63878 − 1.29685I
a = −1.205210 − 0.103104I
b = 2.26792 + 0.63100I
3.3047 + 19.2356I −2.92755 − 10.21183I
u = 0.20692 + 1.46356I
a = 0.639225 + 0.048922I
b = −1.43216 − 0.66120I
6.31210 + 7.97978I 0.59190 − 6.19914I
u = 0.20692 − 1.46356I
a = 0.639225 − 0.048922I
b = −1.43216 + 0.66120I
6.31210 − 7.97978I 0.59190 + 6.19914I
u = 0.139855 + 0.499323I
a = 0.65973 + 1.57256I
b = 0.321732 − 0.818524I
1.59913 − 1.70507I 2.11756 + 1.16667I
u = 0.139855 − 0.499323I
a = 0.65973 − 1.57256I
b = 0.321732 + 0.818524I
1.59913 + 1.70507I 2.11756 − 1.16667I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64308 + 1.34654I
a = 1.001290 − 0.082426I
b = −2.01357 + 0.55420I
0.99069 − 10.76890I −7.04060 + 8.50753I
u = 0.64308 − 1.34654I
a = 1.001290 + 0.082426I
b = −2.01357 − 0.55420I
0.99069 + 10.76890I −7.04060 − 8.50753I
u = 0.25168 + 1.49957I
a = −0.606065 + 0.151895I
b = 1.59013 + 0.08120I
3.88935 − 1.44009I −9.35211 + 8.90381I
u = 0.25168 − 1.49957I
a = −0.606065 − 0.151895I
b = 1.59013 − 0.08120I
3.88935 + 1.44009I −9.35211 − 8.90381I
u = 0.461512
a = 1.30067
b = −0.323241
−0.923370 −10.5990
7
II. I
u
2
= h−487u
15
− 1824u
14
+ · · · + 1084b − 1471, 1589u
15
+ 3060u
14
+
· · · + 1084a − 2223, u
16
+ 2u
15
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
u
a
10
=
−1.46587u
15
− 2.82288u
14
+ ··· − 8.94373u + 2.05074
0.449262u
15
+ 1.68266u
14
+ ··· + 2.15959u + 1.35701
a
11
=
−2.16513u
15
− 4.00554u
14
+ ··· − 10.8533u + 2.94373
1.14852u
15
+ 2.86531u
14
+ ··· + 4.06919u + 0.464022
a
5
=
−1.54520u
15
− 1.93727u
14
+ ··· − 11.4124u + 3.55443
1.44557u
15
+ 2.59594u
14
+ ··· + 5.70756u + 0.392066
a
8
=
0.904982u
15
+ 0.642066u
14
+ ··· + 6.23524u − 5.72232
−1.47325u
15
− 2.99631u
14
+ ··· − 6.84779u + 1.12085
a
4
=
1.52768u
15
+ 4.90037u
14
+ ··· + 2.14022u + 5.48708
0.885609u
15
+ 0.811808u
14
+ ··· + 5.48708u − 2.41328
a
9
=
−1.35701u
15
− 2.26476u
14
+ ··· − 8.35886u + 3.51661
0.892989u
15
+ 2.48524u
14
+ ··· + 2.39114u + 1.01661
a
1
=
−0.758303u
15
− 2.07011u
14
+ ··· + 2.85793u − 3.04613
−0.258303u
15
− 0.0701107u
14
+ ··· − 3.64207u + 0.453875
a
1
=
−0.758303u
15
− 2.07011u
14
+ ··· + 2.85793u − 3.04613
−0.258303u
15
− 0.0701107u
14
+ ··· − 3.64207u + 0.453875
(ii) Obstruction class = 1
(iii) Cusp Shapes =
883
271
u
15
+
7393
1084
u
14
+ ··· +
7220
271
u −
8893
1084
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
16
+ 2u
15
+ ··· + 4u + 12
c
2
u
16
+ 2u
15
+ ··· − u + 1
c
3
, c
7
u
16
+ 2u
15
+ ··· + 8u + 4
c
4
, c
8
4(4u
16
+ 14u
14
+ ··· − 3u + 1)
c
5
, c
9
4(4u
16
+ 10u
14
+ ··· − 5u + 1)
c
6
u
16
− 2u
15
+ ··· + u + 1
c
11
u
16
+ 5u
15
+ ··· − 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
− 2y
15
+ ··· − 352y + 144
c
2
, c
6
y
16
+ 8y
15
+ ··· + 13y + 1
c
3
, c
7
y
16
+ 4y
15
+ ··· + 48y + 16
c
4
, c
8
16(16y
16
+ 112y
15
+ ··· + 15y + 1)
c
5
, c
9
16(16y
16
+ 80y
15
+ ··· − 7y + 1)
c
11
y
16
+ 7y
15
+ ··· − 22y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.127924 + 0.951196I
a = 1.199100 + 0.627565I
b = −1.66156 + 0.95514I
1.55850 − 0.57188I −4.03325 + 0.08278I
u = 0.127924 − 0.951196I
a = 1.199100 − 0.627565I
b = −1.66156 − 0.95514I
1.55850 + 0.57188I −4.03325 − 0.08278I
u = 0.576501 + 0.749960I
a = 0.038226 + 0.569336I
b = −0.906045 + 0.258948I
−2.90623 − 2.39320I −11.15335 + 3.39673I
u = 0.576501 − 0.749960I
a = 0.038226 − 0.569336I
b = −0.906045 − 0.258948I
−2.90623 + 2.39320I −11.15335 − 3.39673I
u = −0.236683 + 1.046650I
a = −1.215370 − 0.028025I
b = 1.56644 − 0.63415I
6.29877 + 0.99707I 2.79381 − 0.26391I
u = −0.236683 − 1.046650I
a = −1.215370 + 0.028025I
b = 1.56644 + 0.63415I
6.29877 − 0.99707I 2.79381 + 0.26391I
u = 0.677411 + 0.413884I
a = −0.426400 + 0.321010I
b = −0.724338 − 0.105805I
−2.89915 − 2.26107I −9.33280 + 4.93182I
u = 0.677411 − 0.413884I
a = −0.426400 − 0.321010I
b = −0.724338 + 0.105805I
−2.89915 + 2.26107I −9.33280 − 4.93182I
u = −1.320930 + 0.057937I
a = −0.246952 + 0.504969I
b = −0.055825 + 0.235863I
−1.55964 + 5.26639I −1.17081 − 11.68071I
u = −1.320930 − 0.057937I
a = −0.246952 − 0.504969I
b = −0.055825 − 0.235863I
−1.55964 − 5.26639I −1.17081 + 11.68071I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475337 + 1.308180I
a = 0.992931 + 0.359393I
b = −1.97006 − 0.64060I
3.22523 + 10.87130I −2.52543 − 9.79507I
u = −0.475337 − 1.308180I
a = 0.992931 − 0.359393I
b = −1.97006 + 0.64060I
3.22523 − 10.87130I −2.52543 + 9.79507I
u = −0.001694 + 0.451366I
a = 0.26545 − 2.71413I
b = 1.166390 + 0.676954I
−1.17125 − 8.19000I −3.99419 + 8.09299I
u = −0.001694 − 0.451366I
a = 0.26545 + 2.71413I
b = 1.166390 − 0.676954I
−1.17125 + 8.19000I −3.99419 − 8.09299I
u = −0.34720 + 1.51741I
a = −0.606987 − 0.107433I
b = 1.58500 − 0.00976I
4.03350 + 1.05064I −2.08398 + 8.23407I
u = −0.34720 − 1.51741I
a = −0.606987 + 0.107433I
b = 1.58500 + 0.00976I
4.03350 − 1.05064I −2.08398 − 8.23407I
12
III. I
u
3
= h−232u
41
− 1201u
40
+ · · · + 16b − 31, 31u
41
a + 170u
41
+ · · · −
515a + 1252, u
42
+ 6u
41
+ · · · + 5u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
−u
u
a
10
=
a
14.5000u
41
+ 75.0625u
40
+ ··· − 41.8750u + 1.93750
a
11
=
37
8
u
41
+
115
8
u
40
+ ··· + a +
191
16
79
8
u
41
+
971
16
u
40
+ ··· +
517
16
u − 10
a
5
=
−14.5000au
41
− 4.25000u
41
+ ··· − 1.93750a − 10.6250
4.62500au
41
+ 4.68750u
41
+ ··· + 11.9375a − 0.0625000
a
8
=
10.2500au
41
− 0.562500u
41
+ ··· − 3.93750a + 20.2500
−4.43750au
41
− 0.687500u
41
+ ··· + 3.68750a − 1.31250
a
4
=
−9.87500au
41
+ 2.43750u
41
+ ··· + 9.25000a − 24.5000
9u
41
a −
93
16
u
41
+ ··· +
7
8
a −
21
16
a
9
=
29
2
u
41
+
1201
16
u
40
+ ··· + a +
31
16
79
8
u
41
+
971
16
u
40
+ ··· +
517
16
u − 10
a
1
=
−13.3750au
41
+ 2.56250u
41
+ ··· + 4.62500a + 11.3750
8.31250au
41
+ 4.25000u
41
+ ··· − 5.25000a − 4.06250
a
1
=
−13.3750au
41
+ 2.56250u
41
+ ··· + 4.62500a + 11.3750
8.31250au
41
+ 4.25000u
41
+ ··· − 5.25000a − 4.06250
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
19
4
u
41
−
29
2
u
40
+ ··· + 101u −
91
4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
84
− 3u
83
+ ··· + 3176u + 2356
c
2
, c
6
(u
42
− 6u
41
+ ··· − 5u − 1)
2
c
3
, c
7
u
84
− 9u
83
+ ··· − 35640u + 2484
c
4
, c
8
4(4u
84
− 12u
83
+ ··· + 1046u + 469)
c
5
, c
9
4(4u
84
− 4u
83
+ ··· − 1099480u + 136525)
c
11
(u
42
+ 10u
41
+ ··· + 8u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
84
− 17y
83
+ ··· − 109199184y + 5550736
c
2
, c
6
(y
42
+ 26y
41
+ ··· − 119y + 1)
2
c
3
, c
7
y
84
+ 23y
83
+ ··· + 232799184y + 6170256
c
4
, c
8
16(16y
84
+ 96y
83
+ ··· + 1.50976 × 10
7
y + 219961)
c
5
, c
9
16(16y
84
+ 288y
83
+ ··· + 6.61960 × 10
10
y + 1.86391 × 10
10
)
c
11
(y
42
− 10y
41
+ ··· − 30y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325948 + 0.949697I
a = −0.964750 − 0.436121I
b = 2.40317 + 1.11984I
−0.63873 + 10.04910I −4.01954 − 9.88636I
u = −0.325948 + 0.949697I
a = 0.45071 + 1.85178I
b = 0.059181 − 0.978397I
−0.63873 + 10.04910I −4.01954 − 9.88636I
u = −0.325948 − 0.949697I
a = −0.964750 + 0.436121I
b = 2.40317 − 1.11984I
−0.63873 − 10.04910I −4.01954 + 9.88636I
u = −0.325948 − 0.949697I
a = 0.45071 − 1.85178I
b = 0.059181 + 0.978397I
−0.63873 − 10.04910I −4.01954 + 9.88636I
u = 0.112450 + 0.998802I
a = 0.200694 + 0.455272I
b = 0.52750 + 2.80905I
1.74133 − 0.33747I 2.7137 − 43.4048I
u = 0.112450 + 0.998802I
a = −3.26809 + 0.46049I
b = 3.54766 − 1.43933I
1.74133 − 0.33747I 2.7137 − 43.4048I
u = 0.112450 − 0.998802I
a = 0.200694 − 0.455272I
b = 0.52750 − 2.80905I
1.74133 + 0.33747I 2.7137 + 43.4048I
u = 0.112450 − 0.998802I
a = −3.26809 − 0.46049I
b = 3.54766 + 1.43933I
1.74133 + 0.33747I 2.7137 + 43.4048I
u = 0.538797 + 0.860840I
a = −0.171556 + 1.119860I
b = −0.545075 − 0.528944I
−1.79973 − 4.25346I −6.96363 + 7.82606I
u = 0.538797 + 0.860840I
a = −0.330198 + 0.277066I
b = 0.948270 − 0.886884I
−1.79973 − 4.25346I −6.96363 + 7.82606I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538797 − 0.860840I
a = −0.171556 − 1.119860I
b = −0.545075 + 0.528944I
−1.79973 + 4.25346I −6.96363 − 7.82606I
u = 0.538797 − 0.860840I
a = −0.330198 − 0.277066I
b = 0.948270 + 0.886884I
−1.79973 + 4.25346I −6.96363 − 7.82606I
u = −0.298007 + 0.971824I
a = 0.853265 + 0.008147I
b = −2.06211 − 1.01872I
−1.71171 + 3.49501I −4.54786 − 6.62152I
u = −0.298007 + 0.971824I
a = 0.101215 − 1.406540I
b = −0.639103 + 0.318059I
−1.71171 + 3.49501I −4.54786 − 6.62152I
u = −0.298007 − 0.971824I
a = 0.853265 − 0.008147I
b = −2.06211 + 1.01872I
−1.71171 − 3.49501I −4.54786 + 6.62152I
u = −0.298007 − 0.971824I
a = 0.101215 + 1.406540I
b = −0.639103 − 0.318059I
−1.71171 − 3.49501I −4.54786 + 6.62152I
u = 0.257956 + 0.918905I
a = −0.857753 + 1.032860I
b = 1.50278 − 1.12038I
1.73911 − 1.92391I 0.68192 + 8.36291I
u = 0.257956 + 0.918905I
a = −0.465729 + 1.311450I
b = 0.910902 − 0.719132I
1.73911 − 1.92391I 0.68192 + 8.36291I
u = 0.257956 − 0.918905I
a = −0.857753 − 1.032860I
b = 1.50278 + 1.12038I
1.73911 + 1.92391I 0.68192 − 8.36291I
u = 0.257956 − 0.918905I
a = −0.465729 − 1.311450I
b = 0.910902 + 0.719132I
1.73911 + 1.92391I 0.68192 − 8.36291I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895252 + 0.152881I
a = −0.470894 − 1.244210I
b = 0.074629 + 0.157299I
2.24777 − 5.28258I −1.79836 + 5.79106I
u = −0.895252 + 0.152881I
a = 0.663629 + 1.226450I
b = 0.240307 − 0.269247I
2.24777 − 5.28258I −1.79836 + 5.79106I
u = −0.895252 − 0.152881I
a = −0.470894 + 1.244210I
b = 0.074629 − 0.157299I
2.24777 + 5.28258I −1.79836 − 5.79106I
u = −0.895252 − 0.152881I
a = 0.663629 − 1.226450I
b = 0.240307 + 0.269247I
2.24777 + 5.28258I −1.79836 − 5.79106I
u = −1.083120 + 0.207022I
a = −0.396667 − 0.804873I
b = −0.262157 − 0.314734I
−2.65956 − 4.72365I −10.86372 + 6.28405I
u = −1.083120 + 0.207022I
a = 0.416341 + 0.464688I
b = 0.082718 − 0.451135I
−2.65956 − 4.72365I −10.86372 + 6.28405I
u = −1.083120 − 0.207022I
a = −0.396667 + 0.804873I
b = −0.262157 + 0.314734I
−2.65956 + 4.72365I −10.86372 − 6.28405I
u = −1.083120 − 0.207022I
a = 0.416341 − 0.464688I
b = 0.082718 + 0.451135I
−2.65956 + 4.72365I −10.86372 − 6.28405I
u = 1.102180 + 0.313402I
a = −0.195443 − 0.871124I
b = 0.796667 − 0.423906I
0.59757 − 5.16280I −2.48880 + 8.90244I
u = 1.102180 + 0.313402I
a = −0.509959 − 0.475402I
b = −0.298579 + 0.138256I
0.59757 − 5.16280I −2.48880 + 8.90244I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.102180 − 0.313402I
a = −0.195443 + 0.871124I
b = 0.796667 + 0.423906I
0.59757 + 5.16280I −2.48880 − 8.90244I
u = 1.102180 − 0.313402I
a = −0.509959 + 0.475402I
b = −0.298579 − 0.138256I
0.59757 + 5.16280I −2.48880 − 8.90244I
u = 0.075659 + 0.844181I
a = 0.457368 − 0.528326I
b = −2.83732 + 0.20631I
0.946887 + 0.000924I −0.489674 − 0.600771I
u = 0.075659 + 0.844181I
a = 0.53699 − 3.00985I
b = −0.47574 + 1.85018I
0.946887 + 0.000924I −0.489674 − 0.600771I
u = 0.075659 − 0.844181I
a = 0.457368 + 0.528326I
b = −2.83732 − 0.20631I
0.946887 − 0.000924I −0.489674 + 0.600771I
u = 0.075659 − 0.844181I
a = 0.53699 + 3.00985I
b = −0.47574 − 1.85018I
0.946887 − 0.000924I −0.489674 + 0.600771I
u = −0.359732 + 1.156400I
a = 0.803632 + 0.179500I
b = −1.40145 + 0.77758I
6.25056 + 3.50676I 0
u = −0.359732 + 1.156400I
a = −1.45348 − 0.04951I
b = 2.21108 + 0.40433I
6.25056 + 3.50676I 0
u = −0.359732 − 1.156400I
a = 0.803632 − 0.179500I
b = −1.40145 − 0.77758I
6.25056 − 3.50676I 0
u = −0.359732 − 1.156400I
a = −1.45348 + 0.04951I
b = 2.21108 − 0.40433I
6.25056 − 3.50676I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.382825 + 0.638516I
a = −1.38881 − 0.77315I
b = 1.25297 + 1.46432I
−1.54662 − 6.94396I −6.14826 + 1.80846I
u = −0.382825 + 0.638516I
a = 0.20384 + 1.86406I
b = −0.167271 + 0.004343I
−1.54662 − 6.94396I −6.14826 + 1.80846I
u = −0.382825 − 0.638516I
a = −1.38881 + 0.77315I
b = 1.25297 − 1.46432I
−1.54662 + 6.94396I −6.14826 − 1.80846I
u = −0.382825 − 0.638516I
a = 0.20384 − 1.86406I
b = −0.167271 − 0.004343I
−1.54662 + 6.94396I −6.14826 − 1.80846I
u = 0.512878 + 0.535469I
a = 1.267690 + 0.182619I
b = −1.156610 + 0.534850I
−2.62567 + 0.01437I −9.66321 + 0.05333I
u = 0.512878 + 0.535469I
a = 1.110440 − 0.853009I
b = −0.110157 − 0.142346I
−2.62567 + 0.01437I −9.66321 + 0.05333I
u = 0.512878 − 0.535469I
a = 1.267690 − 0.182619I
b = −1.156610 − 0.534850I
−2.62567 − 0.01437I −9.66321 − 0.05333I
u = 0.512878 − 0.535469I
a = 1.110440 + 0.853009I
b = −0.110157 + 0.142346I
−2.62567 − 0.01437I −9.66321 − 0.05333I
u = −0.230795 + 1.303580I
a = 0.814037 + 0.666476I
b = −0.995505 − 0.929146I
3.16694 − 0.26769I 0
u = −0.230795 + 1.303580I
a = −0.496678 + 0.044530I
b = 1.90104 − 0.68178I
3.16694 − 0.26769I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230795 − 1.303580I
a = 0.814037 − 0.666476I
b = −0.995505 + 0.929146I
3.16694 + 0.26769I 0
u = −0.230795 − 1.303580I
a = −0.496678 − 0.044530I
b = 1.90104 + 0.68178I
3.16694 + 0.26769I 0
u = −0.378608 + 1.274890I
a = −0.858200 + 0.272003I
b = 1.60611 − 0.48936I
6.70547 − 0.94792I 0
u = −0.378608 + 1.274890I
a = 0.674687 − 0.144148I
b = −1.117200 + 0.759402I
6.70547 − 0.94792I 0
u = −0.378608 − 1.274890I
a = −0.858200 − 0.272003I
b = 1.60611 + 0.48936I
6.70547 + 0.94792I 0
u = −0.378608 − 1.274890I
a = 0.674687 + 0.144148I
b = −1.117200 − 0.759402I
6.70547 + 0.94792I 0
u = −0.543373 + 1.232310I
a = 1.225940 + 0.209319I
b = −2.23920 − 0.34704I
5.50034 + 10.51420I 0
u = −0.543373 + 1.232310I
a = −1.359110 − 0.228250I
b = 2.28106 + 0.70236I
5.50034 + 10.51420I 0
u = −0.543373 − 1.232310I
a = 1.225940 − 0.209319I
b = −2.23920 + 0.34704I
5.50034 − 10.51420I 0
u = −0.543373 − 1.232310I
a = −1.359110 + 0.228250I
b = 2.28106 − 0.70236I
5.50034 − 10.51420I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311468 + 0.567237I
a = 1.292270 − 0.168197I
b = −1.33812 − 0.86681I
−2.83797 − 0.65564I −8.38135 − 1.81835I
u = −0.311468 + 0.567237I
a = −0.12822 − 1.67182I
b = −0.254835 − 0.364369I
−2.83797 − 0.65564I −8.38135 − 1.81835I
u = −0.311468 − 0.567237I
a = 1.292270 + 0.168197I
b = −1.33812 + 0.86681I
−2.83797 + 0.65564I −8.38135 + 1.81835I
u = −0.311468 − 0.567237I
a = −0.12822 + 1.67182I
b = −0.254835 + 0.364369I
−2.83797 + 0.65564I −8.38135 + 1.81835I
u = 0.396691 + 1.332610I
a = 1.197580 − 0.251128I
b = −2.06300 + 0.81742I
5.77239 − 9.91992I 0
u = 0.396691 + 1.332610I
a = 0.669581 − 0.093528I
b = −1.79454 − 0.63699I
5.77239 − 9.91992I 0
u = 0.396691 − 1.332610I
a = 1.197580 + 0.251128I
b = −2.06300 − 0.81742I
5.77239 + 9.91992I 0
u = 0.396691 − 1.332610I
a = 0.669581 + 0.093528I
b = −1.79454 + 0.63699I
5.77239 + 9.91992I 0
u = −0.595370
a = 0.55085 + 1.47940I
b = 0.523221 − 0.356395I
2.99475 −0.888110
u = −0.595370
a = 0.55085 − 1.47940I
b = 0.523221 + 0.356395I
2.99475 −0.888110
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592284 + 1.279270I
a = 1.012450 + 0.084454I
b = −2.22219 − 0.61915I
0.72340 + 10.65260I 0
u = −0.592284 + 1.279270I
a = −0.971424 − 0.369796I
b = 1.39630 + 0.70236I
0.72340 + 10.65260I 0
u = −0.592284 − 1.279270I
a = 1.012450 − 0.084454I
b = −2.22219 + 0.61915I
0.72340 − 10.65260I 0
u = −0.592284 − 1.279270I
a = −0.971424 + 0.369796I
b = 1.39630 − 0.70236I
0.72340 − 10.65260I 0
u = −0.83407 + 1.17304I
a = −0.846452 + 0.470033I
b = 1.91783 + 0.40306I
3.47473 + 3.59921I 0
u = −0.83407 + 1.17304I
a = 0.698535 − 0.136771I
b = −0.897515 + 0.111127I
3.47473 + 3.59921I 0
u = −0.83407 − 1.17304I
a = −0.846452 − 0.470033I
b = 1.91783 − 0.40306I
3.47473 − 3.59921I 0
u = −0.83407 − 1.17304I
a = 0.698535 + 0.136771I
b = −0.897515 − 0.111127I
3.47473 − 3.59921I 0
u = 0.49310 + 1.49129I
a = −0.750144 − 0.060457I
b = 2.06938 − 0.32915I
4.60778 − 1.63835I 0
u = 0.49310 + 1.49129I
a = −0.494383 + 0.168172I
b = 1.011680 + 0.088282I
4.60778 − 1.63835I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49310 − 1.49129I
a = −0.750144 + 0.060457I
b = 2.06938 + 0.32915I
4.60778 + 1.63835I 0
u = 0.49310 − 1.49129I
a = −0.494383 − 0.168172I
b = 1.011680 − 0.088282I
4.60778 + 1.63835I 0
u = 0.0869009
a = 11.17620 + 5.82018I
b = −0.886821 + 0.549732I
0.204160 −5.26330
u = 0.0869009
a = 11.17620 − 5.82018I
b = −0.886821 − 0.549732I
0.204160 −5.26330
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
16
+ 2u
15
+ ··· + 4u + 12)(u
25
− 2u
24
+ ··· − 5u + 1)
· (u
84
− 3u
83
+ ··· + 3176u + 2356)
c
2
(u
16
+ 2u
15
+ ··· − u + 1)(u
25
+ 11u
24
+ ··· + 304u + 32)
· (u
42
− 6u
41
+ ··· − 5u − 1)
2
c
3
, c
7
(u
16
+ 2u
15
+ ··· + 8u + 4)(u
25
− 2u
24
+ ··· − 7u + 1)
· (u
84
− 9u
83
+ ··· − 35640u + 2484)
c
4
, c
8
16(4u
16
+ 14u
14
+ ··· − 3u + 1)(u
25
− 6u
24
+ ··· + 2u + 1)
· (4u
84
− 12u
83
+ ··· + 1046u + 469)
c
5
, c
9
16(4u
16
+ 10u
14
+ ··· − 5u + 1)(u
25
− 6u
24
+ ··· + 13u
2
+ 1)
· (4u
84
− 4u
83
+ ··· − 1099480u + 136525)
c
6
(u
16
− 2u
15
+ ··· + u + 1)(u
25
+ 11u
24
+ ··· + 304u + 32)
· (u
42
− 6u
41
+ ··· − 5u − 1)
2
c
11
(u
16
+ 5u
15
+ ··· − 2u + 1)(u
25
− 18u
24
+ ··· − 1536u + 256)
· (u
42
+ 10u
41
+ ··· + 8u + 1)
2
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
16
− 2y
15
+ ··· − 352y + 144)(y
25
+ 6y
24
+ ··· − 9y −1)
· (y
84
− 17y
83
+ ··· − 109199184y + 5550736)
c
2
, c
6
(y
16
+ 8y
15
+ ··· + 13y + 1)(y
25
+ 11y
24
+ ··· − 3328y −1024)
· (y
42
+ 26y
41
+ ··· − 119y + 1)
2
c
3
, c
7
(y
16
+ 4y
15
+ ··· + 48y + 16)(y
25
+ 22y
23
+ ··· + 17y −1)
· (y
84
+ 23y
83
+ ··· + 232799184y + 6170256)
c
4
, c
8
256(16y
16
+ 112y
15
+ ··· + 15y + 1)(y
25
− 2y
24
+ ··· − 16y −1)
· (16y
84
+ 96y
83
+ ··· + 15097640y + 219961)
c
5
, c
9
256(16y
16
+ 80y
15
+ ··· − 7y + 1)(y
25
+ 4y
24
+ ··· − 26y −1)
· (16y
84
+ 288y
83
+ ··· + 66196030900y + 18639075625)
c
11
(y
16
+ 7y
15
+ ··· − 22y + 1)(y
25
+ 10y
24
+ ··· + 720896y −65536)
· (y
42
− 10y
41
+ ··· − 30y + 1)
2
26
