12n
0596
(K12n
0596
)
A knot diagram
1
Linearized knot diagam
3 7 10 8 11 2 1 11 4 6 8 5
Solving Sequence
2,7
3 1 8
6,11
5 4 10 9 12
c
2
c
1
c
7
c
6
c
5
c
4
c
10
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
27
+ 23u
26
+ ··· + 2b + 26, 11u
27
+ 49u
26
+ ··· + 4a + 44, u
28
+ 5u
27
+ ··· + 26u + 4i
I
u
2
= h76637u
8
a
3
+ 229871u
8
a
2
+ ··· − 157797a − 344895, −2u
8
a
3
− 2u
8
a
2
+ ··· + a + 9,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h−u
16
− 2u
15
+ ··· + b − 3, −2u
16
− 2u
15
+ ··· + a − 3,
u
17
− 5u
15
+ 12u
13
− 15u
11
+ 9u
9
+ u
7
− 4u
5
− u
4
+ 2u
3
+ 2u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= h5u
27
+ 23u
26
+ · · · + 2b + 26, 11u
27
+ 49u
26
+ · · · + 4a + 44, u
28
+
5u
27
+ · · · + 26u + 4i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
−
11
4
u
27
−
49
4
u
26
+ ··· −
283
4
u − 11
−
5
2
u
27
−
23
2
u
26
+ ··· −
145
2
u − 13
a
5
=
u
27
+
7
2
u
26
+ ··· +
23
2
u +
5
2
7
2
u
27
+
31
2
u
26
+ ··· +
163
2
u + 14
a
4
=
−3u
27
−
19
2
u
26
+ ··· −
15
2
u +
1
2
−
11
2
u
27
−
43
2
u
26
+ ··· −
155
2
u − 12
a
10
=
−
15
4
u
27
−
61
4
u
26
+ ··· −
331
4
u − 13
−
7
2
u
27
−
29
2
u
26
+ ··· −
169
2
u − 15
a
9
=
−3u
27
−
23
2
u
26
+ ··· −
121
2
u −
19
2
−
5
2
u
27
−
19
2
u
26
+ ··· −
113
2
u − 10
a
12
=
5
4
u
27
+
15
4
u
26
+ ··· +
61
4
u + 3
−
1
2
u
27
−
5
2
u
26
+ ··· +
3
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
27
+ 7u
26
+ 11u
25
− 24u
24
− 95u
23
− 48u
22
+ 228u
21
+ 408u
20
−
13u
19
−797u
18
−888u
17
+ 232u
16
+ 1501u
15
+ 1333u
14
−346u
13
−1800u
12
−1511u
11
+
137u
10
+ 1416u
9
+ 1255u
8
+ 153u
7
−670u
6
−686u
5
−222u
4
+ 135u
3
+ 209u
2
+ 110u + 38
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 15u
27
+ ··· + 44u + 16
c
2
, c
6
u
28
− 5u
27
+ ··· − 26u + 4
c
3
, c
5
, c
9
c
10
u
28
+ 9u
26
+ ··· − u + 1
c
4
, c
12
u
28
− u
27
+ ··· − 2u + 1
c
7
u
28
− 15u
27
+ ··· − 2082u + 196
c
8
, c
11
u
28
+ 24u
27
+ ··· + 4608u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 3y
27
+ ··· + 3856y + 256
c
2
, c
6
y
28
− 15y
27
+ ··· − 44y + 16
c
3
, c
5
, c
9
c
10
y
28
+ 18y
27
+ ··· + 13y + 1
c
4
, c
12
y
28
− 39y
27
+ ··· − 42y + 1
c
7
y
28
+ 21y
27
+ ··· + 8244y + 38416
c
8
, c
11
y
28
− 14y
27
+ ··· − 2883584y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929249 + 0.341636I
a = 0.193428 − 0.245481I
b = −0.030096 − 0.588079I
−1.44836 − 1.32384I 0.695067 + 0.255787I
u = 0.929249 − 0.341636I
a = 0.193428 + 0.245481I
b = −0.030096 + 0.588079I
−1.44836 + 1.32384I 0.695067 − 0.255787I
u = −0.660663 + 0.703535I
a = −0.684282 + 0.401431I
b = 0.508694 + 0.182176I
5.08436 − 3.47708I 7.23263 + 2.58361I
u = −0.660663 − 0.703535I
a = −0.684282 − 0.401431I
b = 0.508694 − 0.182176I
5.08436 + 3.47708I 7.23263 − 2.58361I
u = −0.978713 + 0.436112I
a = −0.573780 + 0.856820I
b = −0.23105 + 1.41378I
−0.59221 + 3.85896I 5.41585 − 8.89544I
u = −0.978713 − 0.436112I
a = −0.573780 − 0.856820I
b = −0.23105 − 1.41378I
−0.59221 − 3.85896I 5.41585 + 8.89544I
u = −0.893353 + 0.642807I
a = 0.439255 − 0.143317I
b = 0.481145 − 1.329810I
4.40206 + 8.59519I 6.36570 − 7.75404I
u = −0.893353 − 0.642807I
a = 0.439255 + 0.143317I
b = 0.481145 + 1.329810I
4.40206 − 8.59519I 6.36570 + 7.75404I
u = −0.181084 + 0.864099I
a = 2.35580 + 0.19920I
b = 0.657053 − 0.345268I
0.30413 − 10.11890I 5.46914 + 5.28623I
u = −0.181084 − 0.864099I
a = 2.35580 − 0.19920I
b = 0.657053 + 0.345268I
0.30413 + 10.11890I 5.46914 − 5.28623I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.390931 + 0.790393I
a = 0.553034 − 0.988547I
b = −0.088477 − 0.180368I
3.66685 + 0.77577I 5.01952 − 3.31127I
u = −0.390931 − 0.790393I
a = 0.553034 + 0.988547I
b = −0.088477 + 0.180368I
3.66685 − 0.77577I 5.01952 + 3.31127I
u = −0.046181 + 0.865065I
a = −1.71050 − 0.23913I
b = −0.600654 + 0.312900I
−5.04513 − 2.20112I 6.66836 + 3.09691I
u = −0.046181 − 0.865065I
a = −1.71050 + 0.23913I
b = −0.600654 − 0.312900I
−5.04513 + 2.20112I 6.66836 − 3.09691I
u = 1.194960 + 0.139644I
a = 0.479609 − 0.801194I
b = 0.64008 − 1.70137I
−1.55027 − 3.30862I 0.08727 + 3.64392I
u = 1.194960 − 0.139644I
a = 0.479609 + 0.801194I
b = 0.64008 + 1.70137I
−1.55027 + 3.30862I 0.08727 − 3.64392I
u = −1.104270 + 0.595120I
a = −0.695565 + 0.302010I
b = −1.190600 + 0.700335I
1.56113 + 4.41097I 1.00210 − 1.17558I
u = −1.104270 − 0.595120I
a = −0.695565 − 0.302010I
b = −1.190600 − 0.700335I
1.56113 − 4.41097I 1.00210 + 1.17558I
u = 1.251710 + 0.341500I
a = 0.02594 − 1.65411I
b = −0.77011 − 2.56071I
−4.19391 + 6.08731I 0.85731 − 2.80136I
u = 1.251710 − 0.341500I
a = 0.02594 + 1.65411I
b = −0.77011 + 2.56071I
−4.19391 − 6.08731I 0.85731 + 2.80136I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.206160 + 0.542493I
a = −0.15086 + 2.22381I
b = −0.02581 + 3.45703I
−2.7661 + 15.2558I 2.52297 − 8.38664I
u = −1.206160 − 0.542493I
a = −0.15086 − 2.22381I
b = −0.02581 − 3.45703I
−2.7661 − 15.2558I 2.52297 + 8.38664I
u = 1.251980 + 0.436921I
a = −0.149674 + 1.280100I
b = 0.44752 + 1.88854I
−8.98786 − 2.38473I 3.28316 + 0.77142I
u = 1.251980 − 0.436921I
a = −0.149674 − 1.280100I
b = 0.44752 − 1.88854I
−8.98786 + 2.38473I 3.28316 − 0.77142I
u = −1.237260 + 0.486713I
a = 0.03375 − 1.83518I
b = −0.13153 − 2.67194I
−8.62321 + 7.05383I 4.15719 − 6.57682I
u = −1.237260 − 0.486713I
a = 0.03375 + 1.83518I
b = −0.13153 + 2.67194I
−8.62321 − 7.05383I 4.15719 + 6.57682I
u = −0.429297 + 0.384695I
a = 1.133840 + 0.097257I
b = 0.333840 − 0.315853I
0.916737 − 0.202146I 11.22373 + 1.78332I
u = −0.429297 − 0.384695I
a = 1.133840 − 0.097257I
b = 0.333840 + 0.315853I
0.916737 + 0.202146I 11.22373 − 1.78332I
7
II. I
u
2
= h7.66 × 10
4
a
3
u
8
+ 2.30 × 10
5
a
2
u
8
+ · · · − 1.58 × 10
5
a − 3.45 ×
10
5
, −2u
8
a
3
−2u
8
a
2
+· · · + a + 9, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u +1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
a
−0.348260a
3
u
8
− 1.04460a
2
u
8
+ ··· + 0.717073a + 1.56730
a
5
=
0.0201175a
3
u
8
− 0.189537a
2
u
8
+ ··· + 0.953476a + 0.606425
1.18312a
3
u
8
+ 0.607006a
2
u
8
+ ··· − 0.223129a − 0.845472
a
4
=
0.102078a
3
u
8
+ 0.780534a
2
u
8
+ ··· + 0.252298a + 2.71609
1.10786a
3
u
8
+ 0.872901a
2
u
8
+ ··· + 0.474304a + 0.368532
a
10
=
0.574324a
3
u
8
+ 0.498198a
2
u
8
+ ··· + 1.36008a − 1.45711
0.226064a
3
u
8
− 0.546399a
2
u
8
+ ··· + 1.07715a + 0.110190
a
9
=
−0.946496a
3
u
8
− 0.481503a
2
u
8
+ ··· + 1.29709a + 0.301795
−1.23084a
3
u
8
− 0.992111a
2
u
8
+ ··· − 0.666073a + 0.450292
a
12
=
0.704404a
3
u
8
+ 0.679020a
2
u
8
+ ··· + 1.31993a − 0.641679
−0.0950072a
3
u
8
− 0.862513a
2
u
8
+ ··· + 1.36519a + 2.02857
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
+ 4u
4
+ 8u
3
− 4u
2
+ 4u + 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
c
2
, c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
4
c
3
, c
5
, c
9
c
10
u
36
+ u
35
+ ··· − 1540u − 431
c
4
, c
12
u
36
− u
35
+ ··· − 2656u − 751
c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
4
c
8
, c
11
(u
2
− u − 1)
18
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
4
c
2
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
4
c
3
, c
5
, c
9
c
10
y
36
+ 15y
35
+ ··· + 409212y + 185761
c
4
, c
12
y
36
− 21y
35
+ ··· − 3861084y + 564001
c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
4
c
8
, c
11
(y
2
− 3y + 1)
18
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0.151267 + 0.887525I
b = −0.12420 + 2.14410I
5.73128 − 2.09337I 8.51499 + 4.16283I
u = 0.772920 + 0.510351I
a = 0.862183 − 0.856156I
b = 1.057480 − 0.208017I
−2.16441 − 2.09337I 8.51499 + 4.16283I
u = 0.772920 + 0.510351I
a = −0.325403 + 0.538567I
b = −0.954335 − 0.596353I
−2.16441 − 2.09337I 8.51499 + 4.16283I
u = 0.772920 + 0.510351I
a = −1.55657 − 0.05607I
b = −0.145829 − 0.038232I
5.73128 − 2.09337I 8.51499 + 4.16283I
u = 0.772920 − 0.510351I
a = 0.151267 − 0.887525I
b = −0.12420 − 2.14410I
5.73128 + 2.09337I 8.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = 0.862183 + 0.856156I
b = 1.057480 + 0.208017I
−2.16441 + 2.09337I 8.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = −0.325403 − 0.538567I
b = −0.954335 + 0.596353I
−2.16441 + 2.09337I 8.51499 − 4.16283I
u = 0.772920 − 0.510351I
a = −1.55657 + 0.05607I
b = −0.145829 + 0.038232I
5.73128 + 2.09337I 8.51499 − 4.16283I
u = −0.825933
a = −0.970502 + 0.221821I
b = −0.77881 + 1.87106I
−5.14629 −0.652350
u = −0.825933
a = −0.970502 − 0.221821I
b = −0.77881 − 1.87106I
−5.14629 −0.652350
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825933
a = 2.42255
b = 1.04146
2.74940 −0.652350
u = −0.825933
a = 2.65906
b = 3.03642
2.74940 −0.652350
u = −1.173910 + 0.391555I
a = 0.445118 + 0.708986I
b = −0.33086 + 1.41743I
−8.31919 + 1.33617I 0.715907 − 0.701750I
u = −1.173910 + 0.391555I
a = 0.535426 + 1.090460I
b = 1.55838 + 1.72349I
−0.423507 + 1.336170I 0.715907 − 0.701750I
u = −1.173910 + 0.391555I
a = −0.43835 − 2.05384I
b = 0.07636 − 3.23541I
−8.31919 + 1.33617I 0.715907 − 0.701750I
u = −1.173910 + 0.391555I
a = −0.55315 + 2.43040I
b = −0.89210 + 3.03603I
−0.423507 + 1.336170I 0.715907 − 0.701750I
u = −1.173910 − 0.391555I
a = 0.445118 − 0.708986I
b = −0.33086 − 1.41743I
−8.31919 − 1.33617I 0.715907 + 0.701750I
u = −1.173910 − 0.391555I
a = 0.535426 − 1.090460I
b = 1.55838 − 1.72349I
−0.423507 − 1.336170I 0.715907 + 0.701750I
u = −1.173910 − 0.391555I
a = −0.43835 + 2.05384I
b = 0.07636 + 3.23541I
−8.31919 − 1.33617I 0.715907 + 0.701750I
u = −1.173910 − 0.391555I
a = −0.55315 − 2.43040I
b = −0.89210 − 3.03603I
−0.423507 − 1.336170I 0.715907 + 0.701750I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 + 0.739668I
a = 1.54638 + 0.14856I
b = 0.175596 + 0.706856I
−4.56478 + 2.45442I 5.67208 − 2.91298I
u = 0.141484 + 0.739668I
a = 0.41836 + 1.61589I
b = 0.122312 − 0.331093I
3.33090 + 2.45442I 5.67208 − 2.91298I
u = 0.141484 + 0.739668I
a = 2.42721 − 0.66480I
b = 1.130180 − 0.397277I
3.33090 + 2.45442I 5.67208 − 2.91298I
u = 0.141484 + 0.739668I
a = −2.63329 − 0.51185I
b = −0.654005 − 0.428643I
−4.56478 + 2.45442I 5.67208 − 2.91298I
u = 0.141484 − 0.739668I
a = 1.54638 − 0.14856I
b = 0.175596 − 0.706856I
−4.56478 − 2.45442I 5.67208 + 2.91298I
u = 0.141484 − 0.739668I
a = 0.41836 − 1.61589I
b = 0.122312 + 0.331093I
3.33090 − 2.45442I 5.67208 + 2.91298I
u = 0.141484 − 0.739668I
a = 2.42721 + 0.66480I
b = 1.130180 + 0.397277I
3.33090 − 2.45442I 5.67208 + 2.91298I
u = 0.141484 − 0.739668I
a = −2.63329 + 0.51185I
b = −0.654005 + 0.428643I
−4.56478 − 2.45442I 5.67208 + 2.91298I
u = 1.172470 + 0.500383I
a = −0.674403 + 0.060775I
b = −1.92502 + 0.14461I
0.34972 − 7.08493I 2.42320 + 5.91335I
u = 1.172470 + 0.500383I
a = −0.64734 − 1.39577I
b = −0.38514 − 2.29252I
−7.54597 − 7.08493I 2.42320 + 5.91335I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172470 + 0.500383I
a = 0.61611 + 2.25592I
b = 0.86666 + 3.45374I
−7.54597 − 7.08493I 2.42320 + 5.91335I
u = 1.172470 + 0.500383I
a = 0.75615 − 2.31269I
b = 0.66439 − 3.18473I
0.34972 − 7.08493I 2.42320 + 5.91335I
u = 1.172470 − 0.500383I
a = −0.674403 − 0.060775I
b = −1.92502 − 0.14461I
0.34972 + 7.08493I 2.42320 − 5.91335I
u = 1.172470 − 0.500383I
a = −0.64734 + 1.39577I
b = −0.38514 + 2.29252I
−7.54597 + 7.08493I 2.42320 − 5.91335I
u = 1.172470 − 0.500383I
a = 0.61611 − 2.25592I
b = 0.86666 − 3.45374I
−7.54597 + 7.08493I 2.42320 − 5.91335I
u = 1.172470 − 0.500383I
a = 0.75615 + 2.31269I
b = 0.66439 + 3.18473I
0.34972 + 7.08493I 2.42320 − 5.91335I
14
III. I
u
3
=
h−u
16
−2u
15
+· · · +b−3, −2u
16
−2u
15
+· · · +a−3, u
17
−5u
15
+· · · +2u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
2u
16
+ 2u
15
+ ··· + 3u + 3
u
16
+ 2u
15
+ ··· + 2u + 3
a
5
=
−u
16
− u
15
+ ··· − 2u − 2
−u
16
+ 5u
14
+ ··· − u
2
− 2u
a
4
=
−u
16
− u
15
+ ··· − 3u − 2
−u
16
+ 5u
14
+ ··· − 3u − 1
a
10
=
3u
16
+ 2u
15
+ ··· + 4u + 3
2u
16
+ 2u
15
+ ··· + 3u + 3
a
9
=
4u
16
+ 2u
15
+ ··· + 7u + 4
3u
16
+ u
15
+ ··· + 5u + 3
a
12
=
2u
16
+ u
15
+ ··· + 2u + 3
u
16
+ u
15
+ ··· + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
16
+ 2u
15
− 36u
14
− 10u
13
+ 76u
12
+ 22u
11
− 72u
10
− 24u
9
+
16u
8
+ 10u
7
+ 35u
6
+ 4u
5
− 18u
4
− 11u
3
+ u
2
+ 11u + 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 10u
16
+ ··· + 4u − 1
c
2
u
17
− 5u
15
+ 12u
13
− 15u
11
+ 9u
9
+ u
7
− 4u
5
− u
4
+ 2u
3
+ 2u
2
− 1
c
3
, c
10
u
17
+ 5u
15
+ ··· − u − 1
c
4
, c
12
u
17
− u
16
+ ··· + 5u
2
+ 1
c
5
, c
9
u
17
+ 5u
15
+ ··· − u + 1
c
6
u
17
− 5u
15
+ 12u
13
− 15u
11
+ 9u
9
+ u
7
− 4u
5
+ u
4
+ 2u
3
− 2u
2
+ 1
c
7
u
17
+ 7u
15
+ ··· − 3u
2
+ 1
c
8
u
17
+ 7u
16
+ ··· − u + 1
c
11
u
17
− 7u
16
+ ··· − u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 2y
16
+ ··· + 4y −1
c
2
, c
6
y
17
− 10y
16
+ ··· + 4y −1
c
3
, c
5
, c
9
c
10
y
17
+ 10y
16
+ ··· + 7y −1
c
4
, c
12
y
17
− 7y
16
+ ··· − 10y −1
c
7
y
17
+ 14y
16
+ ··· + 6y −1
c
8
, c
11
y
17
− 11y
16
+ ··· − 51y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806464 + 0.504400I
a = −0.748785 + 0.704425I
b = −1.238150 − 0.257225I
−3.19864 − 2.06883I −1.36600 + 3.80945I
u = 0.806464 − 0.504400I
a = −0.748785 − 0.704425I
b = −1.238150 + 0.257225I
−3.19864 + 2.06883I −1.36600 − 3.80945I
u = −0.876293 + 0.240637I
a = 0.609471 + 0.505981I
b = 0.11865 + 1.93872I
−4.91029 + 1.12432I 2.42540 − 5.99697I
u = −0.876293 − 0.240637I
a = 0.609471 − 0.505981I
b = 0.11865 − 1.93872I
−4.91029 − 1.12432I 2.42540 + 5.99697I
u = 1.099480 + 0.356702I
a = 0.45815 − 1.72821I
b = 1.06242 − 2.07706I
1.14190 − 2.14869I 6.17290 + 4.05530I
u = 1.099480 − 0.356702I
a = 0.45815 + 1.72821I
b = 1.06242 + 2.07706I
1.14190 + 2.14869I 6.17290 − 4.05530I
u = 0.079653 + 0.818924I
a = −2.03854 − 0.16466I
b = −0.547172 − 0.515255I
−6.40236 + 1.87076I −0.340060 − 0.880617I
u = 0.079653 − 0.818924I
a = −2.03854 + 0.16466I
b = −0.547172 + 0.515255I
−6.40236 − 1.87076I −0.340060 + 0.880617I
u = −1.094930 + 0.535891I
a = −0.394976 + 0.616533I
b = −0.916412 + 0.497599I
2.45035 + 5.14369I 6.48699 − 5.37235I
u = −1.094930 − 0.535891I
a = −0.394976 − 0.616533I
b = −0.916412 − 0.497599I
2.45035 − 5.14369I 6.48699 + 5.37235I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.226240 + 0.422738I
a = −0.36893 − 1.44794I
b = 0.26202 − 2.28019I
−10.28250 + 2.44785I −3.93694 − 2.30757I
u = −1.226240 − 0.422738I
a = −0.36893 + 1.44794I
b = 0.26202 + 2.28019I
−10.28250 − 2.44785I −3.93694 + 2.30757I
u = 0.701228
a = 3.47594
b = 2.25858
3.41691 14.8210
u = −0.354453 + 0.603484I
a = 0.284538 − 1.027620I
b = 0.675649 − 0.146534I
4.57912 − 0.58290I 8.48530 + 0.03334I
u = −0.354453 − 0.603484I
a = 0.284538 + 1.027620I
b = 0.675649 + 0.146534I
4.57912 + 0.58290I 8.48530 − 0.03334I
u = 1.215700 + 0.495120I
a = 0.46110 + 1.90414I
b = 0.45370 + 2.86772I
−9.76009 − 6.65732I −3.33785 + 4.07802I
u = 1.215700 − 0.495120I
a = 0.46110 − 1.90414I
b = 0.45370 − 2.86772I
−9.76009 + 6.65732I −3.33785 − 4.07802I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
· (u
17
− 10u
16
+ ··· + 4u − 1)(u
28
+ 15u
27
+ ··· + 44u + 16)
c
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
4
· (u
17
− 5u
15
+ 12u
13
− 15u
11
+ 9u
9
+ u
7
− 4u
5
− u
4
+ 2u
3
+ 2u
2
− 1)
· (u
28
− 5u
27
+ ··· − 26u + 4)
c
3
, c
10
(u
17
+ 5u
15
+ ··· − u − 1)(u
28
+ 9u
26
+ ··· − u + 1)
· (u
36
+ u
35
+ ··· − 1540u − 431)
c
4
, c
12
(u
17
− u
16
+ ··· + 5u
2
+ 1)(u
28
− u
27
+ ··· − 2u + 1)
· (u
36
− u
35
+ ··· − 2656u − 751)
c
5
, c
9
(u
17
+ 5u
15
+ ··· − u + 1)(u
28
+ 9u
26
+ ··· − u + 1)
· (u
36
+ u
35
+ ··· − 1540u − 431)
c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
4
· (u
17
− 5u
15
+ 12u
13
− 15u
11
+ 9u
9
+ u
7
− 4u
5
+ u
4
+ 2u
3
− 2u
2
+ 1)
· (u
28
− 5u
27
+ ··· − 26u + 4)
c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
4
· (u
17
+ 7u
15
+ ··· − 3u
2
+ 1)(u
28
− 15u
27
+ ··· − 2082u + 196)
c
8
((u
2
− u − 1)
18
)(u
17
+ 7u
16
+ ··· − u + 1)
· (u
28
+ 24u
27
+ ··· + 4608u + 512)
c
11
((u
2
− u − 1)
18
)(u
17
− 7u
16
+ ··· − u − 1)
· (u
28
+ 24u
27
+ ··· + 4608u + 512)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
4
· (y
17
− 2y
16
+ ··· + 4y −1)(y
28
− 3y
27
+ ··· + 3856y + 256)
c
2
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
4
· (y
17
− 10y
16
+ ··· + 4y −1)(y
28
− 15y
27
+ ··· − 44y + 16)
c
3
, c
5
, c
9
c
10
(y
17
+ 10y
16
+ ··· + 7y −1)(y
28
+ 18y
27
+ ··· + 13y + 1)
· (y
36
+ 15y
35
+ ··· + 409212y + 185761)
c
4
, c
12
(y
17
− 7y
16
+ ··· − 10y −1)(y
28
− 39y
27
+ ··· − 42y + 1)
· (y
36
− 21y
35
+ ··· − 3861084y + 564001)
c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
4
· (y
17
+ 14y
16
+ ··· + 6y −1)(y
28
+ 21y
27
+ ··· + 8244y + 38416)
c
8
, c
11
((y
2
− 3y + 1)
18
)(y
17
− 11y
16
+ ··· − 51y −1)
· (y
28
− 14y
27
+ ··· − 2883584y + 262144)
21
