12n
0697
(K12n
0697
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 10 9 11 3 12 5 7 6
Solving Sequence
5,10 2,6
4 1 12 9 7 3 8 11
c
5
c
4
c
1
c
12
c
9
c
6
c
3
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.62104 × 10
19
u
20
+ 1.26138 × 10
19
u
19
+ ··· + 4.08630 × 10
20
b + 4.01944 × 10
20
,
− 1.37856 × 10
21
u
20
− 8.38333 × 10
20
u
19
+ ··· + 5.72082 × 10
21
a − 9.06403 × 10
21
, u
21
− 3u
19
+ ··· − u + 1i
I
u
2
= hb + 1, −u
3
− u
2
+ 2a − u + 1, u
4
+ u
2
− u + 1i
I
u
3
= h−2u
11
+ u
10
− 5u
9
+ 10u
8
+ 5u
7
+ 22u
6
+ 17u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ b + 6u + 2,
− 4u
12
+ 5u
11
− 12u
10
+ 28u
9
− 6u
8
+ 41u
7
+ 12u
5
− 5u
4
− 5u
3
− 9u
2
+ a − 6u − 5,
u
13
+ 3u
11
− 4u
10
− 3u
9
− 16u
8
− 16u
7
− 22u
6
− 18u
5
− 16u
4
− 11u
3
− 7u
2
− 3u − 1i
I
u
4
= hb + 1, u
5
+ 2u
3
+ a + u + 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
u
5
= h−31240024u
11
− 108045960u
10
+ ··· + 16035124397b + 4787221942,
− 2479067476388u
11
− 7672762434312u
10
+ ··· + 189470000096321a − 300611169358247,
u
12
+ 2u
11
− u
10
+ 24u
8
+ 24u
7
− 42u
6
+ 142u
5
− 296u
4
+ 168u
3
− 248u
2
+ 192u − 79i
* 5 irreducible components of dim
C
= 0, with total 56 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−3.62×10
19
u
20
+1.26×10
19
u
19
+· · ·+4.09×10
20
b+4.02×10
20
, −1.38×
10
21
u
20
−8.38×10
20
u
19
+· · ·+5.72×10
21
a−9.06×10
21
, u
21
−3u
19
+· · ·−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
0.240973u
20
+ 0.146541u
19
+ ··· + 0.630949u + 1.58439
0.0886140u
20
− 0.0308685u
19
+ ··· + 0.687354u − 0.983638
a
6
=
1
u
2
a
4
=
0.569574u
20
+ 0.221291u
19
+ ··· − 0.866797u + 0.435171
−0.376569u
20
− 0.348821u
19
+ ··· + 2.18805u + 0.671636
a
1
=
−0.0422288u
20
− 0.00485208u
19
+ ··· − 0.760876u + 0.127899
−0.411664u
20
− 0.138444u
19
+ ··· + 3.07667u + 1.14698
a
12
=
0.367023u
20
+ 0.127899u
19
+ ··· − 3.80016u − 1.01423
−0.367023u
20
− 0.127899u
19
+ ··· + 2.80016u + 1.01423
a
9
=
0.410427u
20
+ 0.0856689u
19
+ ··· − 1.95365u − 1.18436
−0.368198u
20
− 0.0808168u
19
+ ··· + 2.71453u + 1.05646
a
7
=
−1.01423u
20
− 0.367023u
19
+ ··· + 4.62375u + 3.81439
1.01423u
20
+ 0.367023u
19
+ ··· − 4.62375u − 2.81439
a
3
=
0.152359u
20
+ 0.177409u
19
+ ··· − 0.0564046u + 2.56803
0.0886140u
20
− 0.0308685u
19
+ ··· + 0.687354u − 0.983638
a
8
=
1.01423u
20
+ 0.367023u
19
+ ··· − 4.62375u − 3.81439
−1.01423u
20
− 0.367023u
19
+ ··· + 4.62375u + 2.81439
a
11
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
41331710946122587570789
11441642780167527166456
u
20
−
13713223367732965094891
11441642780167527166456
u
19
+ ··· +
62252584059208509594863
2860410695041881791614
u +
24448772877532289945923
5720821390083763583228
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
21
− 5u
20
+ ··· − 176u + 64
c
3
, c
8
u
21
+ u
20
+ ··· + 3328u + 1024
c
5
, c
7
, c
10
c
11
u
21
− 3u
19
+ ··· − u + 1
c
6
, c
12
u
21
+ u
20
+ ··· + 26u
2
+ 1
c
9
u
21
+ 7u
20
+ ··· + 32u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
21
− 25y
20
+ ··· + 9472y −4096
c
3
, c
8
y
21
− 27y
20
+ ··· − 1769472y −1048576
c
5
, c
7
, c
10
c
11
y
21
− 6y
20
+ ··· + 9y −1
c
6
, c
12
y
21
+ 13y
20
+ ··· − 52y −1
c
9
y
21
− 5y
20
+ ··· + 440y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749636 + 0.488902I
a = 0.469897 + 0.044424I
b = 0.341636 + 0.425477I
−1.45186 + 0.85737I −6.38463 − 1.62097I
u = −0.749636 − 0.488902I
a = 0.469897 − 0.044424I
b = 0.341636 − 0.425477I
−1.45186 − 0.85737I −6.38463 + 1.62097I
u = −0.139166 + 0.781262I
a = −0.73889 + 1.22004I
b = 1.375930 − 0.218020I
−3.48621 + 5.01960I −12.50321 + 2.57874I
u = −0.139166 − 0.781262I
a = −0.73889 − 1.22004I
b = 1.375930 + 0.218020I
−3.48621 − 5.01960I −12.50321 − 2.57874I
u = −0.099594 + 0.653522I
a = 0.28465 − 1.42599I
b = −0.166654 + 0.606297I
1.43705 + 2.05574I −1.84211 − 3.02644I
u = −0.099594 − 0.653522I
a = 0.28465 + 1.42599I
b = −0.166654 − 0.606297I
1.43705 − 2.05574I −1.84211 + 3.02644I
u = 0.713665 + 1.142840I
a = 0.257213 − 0.050637I
b = 0.917606 − 0.416133I
1.15190 − 6.95574I −3.07603 + 1.63596I
u = 0.713665 − 1.142840I
a = 0.257213 + 0.050637I
b = 0.917606 + 0.416133I
1.15190 + 6.95574I −3.07603 − 1.63596I
u = 0.118860 + 0.511212I
a = 0.21443 + 2.11251I
b = −1.120560 − 0.176119I
−1.29818 − 0.86925I −5.22327 − 0.45664I
u = 0.118860 − 0.511212I
a = 0.21443 − 2.11251I
b = −1.120560 + 0.176119I
−1.29818 + 0.86925I −5.22327 + 0.45664I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396570 + 0.053595I
a = 0.127913 − 0.750550I
b = 0.872784 + 0.806219I
4.27603 − 3.00281I −0.00709 − 9.01951I
u = 0.396570 − 0.053595I
a = 0.127913 + 0.750550I
b = 0.872784 − 0.806219I
4.27603 + 3.00281I −0.00709 + 9.01951I
u = −0.322867
a = 1.20351
b = −0.565313
−0.896054 −11.8310
u = 1.14110 + 1.36056I
a = 0.796386 − 0.921717I
b = 1.89575 + 0.52604I
−18.0940 − 7.3272I −7.63094 + 2.78873I
u = 1.14110 − 1.36056I
a = 0.796386 + 0.921717I
b = 1.89575 − 0.52604I
−18.0940 + 7.3272I −7.63094 − 2.78873I
u = 1.83772 + 0.22825I
a = −0.768356 + 0.189539I
b = −1.69775 − 1.08714I
−7.41133 + 0.52434I −8.70349 − 1.08333I
u = 1.83772 − 0.22825I
a = −0.768356 − 0.189539I
b = −1.69775 + 1.08714I
−7.41133 − 0.52434I −8.70349 + 1.08333I
u = −1.86654 + 0.63952I
a = −0.678604 − 0.317967I
b = −1.55087 + 1.33931I
−7.05646 + 5.93668I −8.04055 − 3.74874I
u = −1.86654 − 0.63952I
a = −0.678604 + 0.317967I
b = −1.55087 − 1.33931I
−7.05646 − 5.93668I −8.04055 + 3.74874I
u = −1.19154 + 1.65776I
a = 0.683607 + 0.829952I
b = 1.91479 − 0.63403I
−16.9669 + 14.7114I −6.79810 − 5.93574I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19154 − 1.65776I
a = 0.683607 − 0.829952I
b = 1.91479 + 0.63403I
−16.9669 − 14.7114I −6.79810 + 5.93574I
7
II. I
u
2
= hb + 1, −u
3
− u
2
+ 2a − u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
1
2
u
3
+
1
2
u
2
+
1
2
u −
1
2
−1
a
6
=
1
u
2
a
4
=
1
2
u
3
+
1
2
u
2
+
1
2
u +
1
2
−1
a
1
=
−1
0
a
12
=
−u
2
− 1
u
2
− u + 1
a
9
=
−u
3
− u
2
u
3
+ u
2
+ 1
a
7
=
−u
3
u
3
+ 1
a
3
=
1
2
u
3
+
1
2
u
2
+
1
2
u +
1
2
−1
a
8
=
−u
3
− u
2
u
3
+ u
2
+ 1
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
19
4
u
3
+
13
2
u
2
−
5
2
u −
37
4
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
− u + 1
c
6
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
10
, c
11
u
4
+ u
2
+ u + 1
c
12
u
4
− 2u
3
+ 3u
2
− u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.447562 + 0.776246I
b = −1.00000
−2.62503 − 1.39709I −12.79646 + 4.25046I
u = 0.547424 − 0.585652I
a = −0.447562 − 0.776246I
b = −1.00000
−2.62503 + 1.39709I −12.79646 − 4.25046I
u = −0.547424 + 1.120870I
a = −0.302438 − 0.253422I
b = −1.00000
0.98010 + 7.64338I −5.07854 − 12.68142I
u = −0.547424 − 1.120870I
a = −0.302438 + 0.253422I
b = −1.00000
0.98010 − 7.64338I −5.07854 + 12.68142I
11
III.
I
u
3
= h−2u
11
+u
10
+· · ·+b+2, −4u
12
+5u
11
+· · ·+a−5, u
13
+3u
11
+· · ·−3u−1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
4u
12
− 5u
11
+ ··· + 6u + 5
2u
11
− u
10
+ ··· − 6u − 2
a
6
=
1
u
2
a
4
=
3u
11
− u
10
+ ··· − 8u − 3
−u
12
− 2u
11
+ ··· + 12u + 4
a
1
=
u
11
+ 2u
9
− 4u
8
− 5u
7
− 12u
6
− 11u
5
− 10u
4
− 7u
3
− 6u
2
− 5u − 1
−u
12
− u
11
+ ··· + 9u + 4
a
12
=
u
12
+ u
11
+ ··· − 11u − 4
−u
12
− u
11
+ ··· + 10u + 4
a
9
=
−4u
12
− 3u
11
+ ··· + 24u + 7
4u
12
+ 2u
11
+ ··· − 19u − 6
a
7
=
−4u
12
+ u
11
+ ··· + 11u + 2
4u
12
− u
11
+ ··· − 11u − 3
a
3
=
4u
12
− 7u
11
+ ··· + 12u + 7
2u
11
− u
10
+ ··· − 6u − 2
a
8
=
−4u
12
+ u
11
+ ··· + 11u + 2
4u
12
− u
11
+ ··· − 11u − 3
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
11
+ 12u
10
− 13u
9
+ 34u
8
− 65u
7
+ 2u
6
− 99u
5
− 27u
4
− 41u
3
− 6u
2
− 17u − 7
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
13
+ 6u
12
+ ··· − 3u + 1
c
3
u
13
+ 3u
12
+ ··· − 3u + 1
c
4
u
13
− 6u
12
+ ··· − 3u − 1
c
5
, c
11
u
13
+ 3u
11
+ ··· − 3u − 1
c
6
, c
12
u
13
+ 3u
12
+ ··· − 6u − 1
c
7
, c
10
u
13
+ 3u
11
+ ··· − 3u + 1
c
8
u
13
− 3u
12
+ ··· − 3u − 1
c
9
u
13
+ 5u
12
+ ··· + 7u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
13
− 16y
12
+ ··· − y −1
c
3
, c
8
y
13
− 15y
12
+ ··· + 7y −1
c
5
, c
7
, c
10
c
11
y
13
+ 6y
12
+ ··· − 5y −1
c
6
, c
12
y
13
− 15y
12
+ ··· + 2y −1
c
9
y
13
− 3y
12
+ ··· + 31y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210034 + 0.823435I
a = −0.96478 + 1.20909I
b = 1.383880 − 0.179213I
−3.30762 + 5.36054I −2.9630 − 14.9223I
u = −0.210034 − 0.823435I
a = −0.96478 − 1.20909I
b = 1.383880 + 0.179213I
−3.30762 − 5.36054I −2.9630 + 14.9223I
u = 0.433075 + 0.722389I
a = −5.11247 + 2.19335I
b = −1.017580 + 0.097497I
0.24289 − 2.63834I −11.1688 + 22.2580I
u = 0.433075 − 0.722389I
a = −5.11247 − 2.19335I
b = −1.017580 − 0.097497I
0.24289 + 2.63834I −11.1688 − 22.2580I
u = −0.332363 + 0.723799I
a = 1.22666 − 1.54731I
b = −0.195461 + 0.299951I
1.73250 + 3.31191I 2.30285 − 9.65242I
u = −0.332363 − 0.723799I
a = 1.22666 + 1.54731I
b = −0.195461 − 0.299951I
1.73250 − 3.31191I 2.30285 + 9.65242I
u = −0.221139 + 1.245340I
a = 0.195961 + 0.001466I
b = 1.47371 + 0.23975I
−1.70123 − 3.58519I −8.08868 + 2.57007I
u = −0.221139 − 1.245340I
a = 0.195961 − 0.001466I
b = 1.47371 − 0.23975I
−1.70123 + 3.58519I −8.08868 − 2.57007I
u = −0.561559 + 0.310550I
a = 0.299162 + 0.039936I
b = 0.757557 − 0.861161I
4.16689 + 3.30359I −8.3931 − 13.8587I
u = −0.561559 − 0.310550I
a = 0.299162 − 0.039936I
b = 0.757557 + 0.861161I
4.16689 − 3.30359I −8.3931 + 13.8587I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10456 + 1.52728I
a = 0.865689 + 0.511270I
b = −0.619685 − 0.390992I
5.01404 − 0.65957I −7.51619 + 8.70514I
u = −0.10456 − 1.52728I
a = 0.865689 − 0.511270I
b = −0.619685 + 0.390992I
5.01404 + 0.65957I −7.51619 − 8.70514I
u = 1.99317
a = 0.979535
b = 2.43517
−15.5848 −10.3460
16
IV. I
u
4
= hb + 1, u
5
+ 2u
3
+ a + u + 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−u
5
− 2u
3
− u − 1
−1
a
6
=
1
u
2
a
4
=
−u
5
− 2u
3
− u
−1
a
1
=
−1
0
a
12
=
−u
2
− 1
−u
4
a
9
=
−u
5
− 2u
3
− u
−1
a
7
=
−2u
5
− 3u
3
− u
2
− 2u − 1
u
5
+ u
3
+ u
2
+ u
a
3
=
−u
5
− 2u
3
− u
−1
a
8
=
−u
5
− 2u
3
− u
−1
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
+ 4u − 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
(u
3
+ u
2
− 1)
2
c
10
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
12
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
9
(y
3
− y
2
+ 2y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.039862 + 0.693124I
b = −1.00000
−1.37919 − 2.82812I −7.50976 + 2.97945I
u = 0.498832 − 1.001300I
a = −0.039862 − 0.693124I
b = −1.00000
−1.37919 + 2.82812I −7.50976 − 2.97945I
u = −0.284920 + 1.115140I
a = −0.877439 + 0.479689I
b = −1.00000
2.75839 −6 − 0.980489 + 0.10I
u = −0.284920 − 1.115140I
a = −0.877439 − 0.479689I
b = −1.00000
2.75839 −6 − 0.980489 + 0.10I
u = −0.713912 + 0.305839I
a = −0.08270 − 1.43799I
b = −1.00000
−1.37919 − 2.82812I −7.50976 + 2.97945I
u = −0.713912 − 0.305839I
a = −0.08270 + 1.43799I
b = −1.00000
−1.37919 + 2.82812I −7.50976 − 2.97945I
20
V. I
u
5
=
h−3.12×10
7
u
11
−1.08×10
8
u
10
+· · ·+1.60×10
10
b+4.79×10
9
, −2.48×10
12
u
11
−
7.67 × 10
12
u
10
+ · · · + 1.89 × 10
14
a − 3.01 × 10
14
, u
12
+ 2u
11
+ · · · + 192u − 79i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
0.0130842u
11
+ 0.0404959u
10
+ ··· − 3.54067u + 1.58659
0.00194822u
11
+ 0.00673808u
10
+ ··· − 0.189616u − 0.298546
a
6
=
1
u
2
a
4
=
0.00262893u
11
+ 0.00748102u
10
+ ··· − 1.18530u + 1.48618
−0.00389645u
11
− 0.0134762u
10
+ ··· + 0.379232u − 0.402908
a
1
=
0.00720608u
11
+ 0.0217001u
10
+ ··· − 2.56022u + 0.673821
−0.00779290u
11
− 0.0269523u
10
+ ··· + 0.758463u − 0.805816
a
12
=
0.0155775u
11
+ 0.0393443u
10
+ ··· − 4.14869u + 2.05539
−0.00417591u
11
− 0.0144212u
10
+ ··· + 1.24677u − 0.734617
a
9
=
−0.0130842u
11
− 0.0404959u
10
+ ··· + 3.54067u − 0.586590
−0.00194822u
11
− 0.00673808u
10
+ ··· + 0.189616u + 0.298546
a
7
=
0.0107154u
11
+ 0.0306105u
10
+ ··· − 2.36500u − 0.00933523
−0.00613825u
11
− 0.0163914u
10
+ ··· + 0.990078u − 0.803027
a
3
=
0.0111360u
11
+ 0.0337578u
10
+ ··· − 3.35105u + 1.88514
0.00194822u
11
+ 0.00673808u
10
+ ··· − 0.189616u − 0.298546
a
8
=
−0.00847360u
11
− 0.0276953u
10
+ ··· + 1.75415u + 0.409455
0.00389645u
11
+ 0.0134762u
10
+ ··· − 0.379232u + 0.402908
a
11
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
78562652888
2398354431599
u
11
−
197375077140
2398354431599
u
10
+ ··· +
8974663966792
2398354431599
u −
21399328621852
2398354431599
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
2
− 2u − 1)
6
c
3
, c
8
(u
2
− 4u + 2)
6
c
5
, c
7
, c
10
c
11
u
12
+ 2u
11
+ ··· + 192u − 79
c
6
, c
12
u
12
+ 6u
11
+ ··· + 92u + 161
c
9
(u
3
− u
2
+ 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
2
− 6y + 1)
6
c
3
, c
8
(y
2
− 12y + 4)
6
c
5
, c
7
, c
10
c
11
y
12
− 6y
11
+ ··· + 2320y + 6241
c
6
, c
12
y
12
+ 2y
11
+ ··· − 31648y + 25921
c
9
(y
3
− y
2
+ 2y −1)
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374272 + 0.913197I
a = 2.14288 − 0.70393I
b = −0.414214
1.08821 + 2.82812I −7.50976 − 2.97945I
u = −0.374272 − 0.913197I
a = 2.14288 + 0.70393I
b = −0.414214
1.08821 − 2.82812I −7.50976 + 2.97945I
u = 1.30635
a = 1.43621
b = 2.41421
−14.5134 −0.980490
u = 0.463361 + 0.371761I
a = −0.09457 − 1.94281I
b = −0.414214
1.08821 − 2.82812I −7.50976 + 2.97945I
u = 0.463361 − 0.371761I
a = −0.09457 + 1.94281I
b = −0.414214
1.08821 + 2.82812I −7.50976 − 2.97945I
u = 0.11802 + 1.46261I
a = 1.031230 − 0.387086I
b = −0.414214
5.22579 −6 − 0.980489 + 0.10I
u = 0.11802 − 1.46261I
a = 1.031230 + 0.387086I
b = −0.414214
5.22579 −6 − 0.980489 + 0.10I
u = 1.49364 + 1.50456I
a = 0.633916 − 0.506378I
b = 2.41421
−18.6510 − 2.8281I −7.50976 + 2.97945I
u = 1.49364 − 1.50456I
a = 0.633916 + 0.506378I
b = 2.41421
−18.6510 + 2.8281I −7.50976 − 2.97945I
u = −2.01289 + 1.65116I
a = 0.617702 + 0.335790I
b = 2.41421
−18.6510 − 2.8281I −7.50976 + 2.97945I
24
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −2.01289 − 1.65116I
a = 0.617702 − 0.335790I
b = 2.41421
−18.6510 + 2.8281I −7.50976 − 2.97945I
u = −2.68206
a = 0.787537
b = 2.41421
−14.5134 −0.980490
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
10
)(u
2
− 2u − 1)
6
(u
13
+ 6u
12
+ ··· − 3u + 1)
· (u
21
− 5u
20
+ ··· − 176u + 64)
c
3
u
10
(u
2
− 4u + 2)
6
(u
13
+ 3u
12
+ ··· − 3u + 1)
· (u
21
+ u
20
+ ··· + 3328u + 1024)
c
4
((u + 1)
10
)(u
2
− 2u − 1)
6
(u
13
− 6u
12
+ ··· − 3u − 1)
· (u
21
− 5u
20
+ ··· − 176u + 64)
c
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
12
+ 2u
11
+ ··· + 192u − 79)(u
13
+ 3u
11
+ ··· − 3u − 1)
· (u
21
− 3u
19
+ ··· − u + 1)
c
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
12
+ 6u
11
+ ··· + 92u + 161)(u
13
+ 3u
12
+ ··· − 6u − 1)
· (u
21
+ u
20
+ ··· + 26u
2
+ 1)
c
7
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
12
+ 2u
11
+ ··· + 192u − 79)(u
13
+ 3u
11
+ ··· − 3u + 1)
· (u
21
− 3u
19
+ ··· − u + 1)
c
8
u
10
(u
2
− 4u + 2)
6
(u
13
− 3u
12
+ ··· − 3u − 1)
· (u
21
+ u
20
+ ··· + 3328u + 1024)
c
9
(u
3
− u
2
+ 1)
4
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· (u
13
+ 5u
12
+ ··· + 7u + 1)(u
21
+ 7u
20
+ ··· + 32u + 4)
c
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
12
+ 2u
11
+ ··· + 192u − 79)(u
13
+ 3u
11
+ ··· − 3u + 1)
· (u
21
− 3u
19
+ ··· − u + 1)
c
11
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
12
+ 2u
11
+ ··· + 192u − 79)(u
13
+ 3u
11
+ ··· − 3u − 1)
· (u
21
− 3u
19
+ ··· − u + 1)
c
12
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
12
+ 6u
11
+ ··· + 92u + 161)(u
13
+ 3u
12
+ ··· − 6u − 1)
· (u
21
+ u
20
+ ··· + 26u
2
+ 1)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
10
)(y
2
− 6y + 1)
6
(y
13
− 16y
12
+ ··· − y −1)
· (y
21
− 25y
20
+ ··· + 9472y −4096)
c
3
, c
8
y
10
(y
2
− 12y + 4)
6
(y
13
− 15y
12
+ ··· + 7y −1)
· (y
21
− 27y
20
+ ··· − 1769472y −1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
12
− 6y
11
+ ··· + 2320y + 6241)(y
13
+ 6y
12
+ ··· − 5y −1)
· (y
21
− 6y
20
+ ··· + 9y −1)
c
6
, c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
12
+ 2y
11
+ ··· − 31648y + 25921)(y
13
− 15y
12
+ ··· + 2y −1)
· (y
21
+ 13y
20
+ ··· − 52y −1)
c
9
((y
3
− y
2
+ 2y −1)
6
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
13
− 3y
12
+ ··· + 31y −1)
· (y
21
− 5y
20
+ ··· + 440y −16)
27
