12n
0707
(K12n
0707
)
A knot diagram
1
Linearized knot diagam
4 11 12 10 11 3 4 12 1 5 7 9
Solving Sequence
9,12
1
4,10
5 3 8 7 6 11 2
c
12
c
9
c
4
c
3
c
8
c
7
c
6
c
11
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−114u
14
− 108u
13
+ ··· + 299b − 79, 310u
14
+ 215u
13
+ ··· + 299a − 593,
u
15
− 8u
13
+ 25u
11
− 33u
9
+ 2u
7
− u
6
+ 37u
5
+ 2u
4
− 27u
3
− u
2
+ u + 1i
I
u
2
= h1.65560 × 10
32
u
39
+ 3.59685 × 10
32
u
38
+ ··· + 2.03419 × 10
33
b + 3.23849 × 10
33
,
− 2.30658 × 10
33
u
39
− 2.80492 × 10
33
u
38
+ ··· + 1.42393 × 10
34
a − 3.27516 × 10
34
, u
40
− u
39
+ ··· + 2u − 7i
I
u
3
= hu
3
+ b − 2u, u
4
− u
3
− 2u
2
+ a + u, u
5
− 3u
3
+ 2u − 1i
I
u
4
= hu
7
− 4u
5
− u
4
+ 3u
3
+ 3u
2
+ b + u − 1, −3u
7
+ 14u
5
+ 2u
4
− 17u
3
− 7u
2
+ a + 4u + 6,
u
8
− 5u
6
− u
5
+ 7u
4
+ 4u
3
− 2u
2
− 4u − 1i
* 4 irreducible components of dim
C
= 0, with total 68 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−114u
14
− 108u
13
+ · · · + 299b − 79, 310u
14
+ 215u
13
+ · · · + 299a −
593, u
15
− 8u
13
+ · · · + u + 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−1.03679u
14
− 0.719064u
13
+ ··· − 0.645485u + 1.98328
0.381271u
14
+ 0.361204u
13
+ ··· − 2.40134u + 0.264214
a
10
=
u
−u
3
+ u
a
5
=
−1.03679u
14
− 0.719064u
13
+ ··· − 0.645485u + 1.98328
0.381271u
14
+ 0.361204u
13
+ ··· − 2.40134u + 0.264214
a
3
=
−0.655518u
14
− 0.357860u
13
+ ··· − 3.04682u + 2.24749
0.381271u
14
+ 0.361204u
13
+ ··· − 2.40134u + 0.264214
a
8
=
−u
u
a
7
=
−0.277592u
14
+ 0.210702u
13
+ ··· − 4.23411u − 0.762542
−0.571906u
14
− 0.541806u
13
+ ··· + 0.602007u + 0.103679
a
6
=
−0.381271u
14
− 0.361204u
13
+ ··· + 2.40134u − 1.26421
0.224080u
14
+ 0.107023u
13
+ ··· + 1.65886u − 0.625418
a
11
=
−0.719064u
14
− 1.41806u
13
+ ··· + 4.02007u + 1.03679
0.361204u
14
+ 0.605351u
13
+ ··· + 0.882943u − 0.381271
a
2
=
−0.625418u
14
− 0.224080u
13
+ ··· − 2.97324u + 1.71572
0.518395u
14
+ 0.859532u
13
+ ··· − 3.17726u − 0.491639
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1039
299
u
14
−
465
299
u
13
+ ··· +
3706
299
u +
1512
299
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 12u
14
+ ··· + 352u − 16
c
2
, c
7
u
15
− u
14
+ ··· − 9u + 1
c
3
, c
6
u
15
− 6u
13
+ ··· − 2u + 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u
15
− 8u
13
+ 25u
11
− 33u
9
+ 2u
7
− u
6
+ 37u
5
+ 2u
4
− 27u
3
− u
2
+ u + 1
c
11
u
15
+ 8u
14
+ ··· + 2u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 2y
14
+ ··· + 81824y − 256
c
2
, c
7
y
15
+ 15y
14
+ ··· + 13y − 1
c
3
, c
6
y
15
− 12y
14
+ ··· + 38y − 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
15
− 16y
14
+ ··· + 3y − 1
c
11
y
15
− 2y
14
+ ··· + 332y − 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012566 + 0.990836I
a = −0.211019 + 0.142592I
b = −1.41460 + 0.28782I
−8.15802 + 4.15828I 1.85862 − 2.84983I
u = 0.012566 − 0.990836I
a = −0.211019 − 0.142592I
b = −1.41460 − 0.28782I
−8.15802 − 4.15828I 1.85862 + 2.84983I
u = 1.169430 + 0.063677I
a = 0.64821 + 2.11508I
b = −0.920632 − 0.865411I
3.87319 − 2.68365I 10.95805 + 3.07423I
u = 1.169430 − 0.063677I
a = 0.64821 − 2.11508I
b = −0.920632 + 0.865411I
3.87319 + 2.68365I 10.95805 − 3.07423I
u = −1.246380 + 0.258821I
a = 0.538407 − 0.957075I
b = −0.644440 + 0.812972I
6.72141 − 1.91087I 13.27233 + 1.33121I
u = −1.246380 − 0.258821I
a = 0.538407 + 0.957075I
b = −0.644440 − 0.812972I
6.72141 + 1.91087I 13.27233 − 1.33121I
u = −1.43453
a = 0.152509
b = −1.16134
8.30719 10.1930
u = −1.45450 + 0.38452I
a = −0.85460 − 1.15788I
b = 1.122180 + 0.164567I
1.22162 − 5.77031I 7.48274 + 3.55671I
u = −1.45450 − 0.38452I
a = −0.85460 + 1.15788I
b = 1.122180 − 0.164567I
1.22162 + 5.77031I 7.48274 − 3.55671I
u = 1.45202 + 0.46014I
a = −0.49137 + 1.50243I
b = 1.44823 − 0.69051I
1.2931 + 14.7754I 9.28197 − 7.69335I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45202 − 0.46014I
a = −0.49137 − 1.50243I
b = 1.44823 + 0.69051I
1.2931 − 14.7754I 9.28197 + 7.69335I
u = 1.54559
a = −0.962536
b = 0.336815
14.2541 21.6380
u = 0.391264
a = 0.943881
b = −0.200615
0.640876 15.5990
u = −0.184294 + 0.258098I
a = 1.80344 − 0.62550I
b = 0.921833 − 0.474362I
−1.74796 + 1.39281I −0.06858 − 4.56854I
u = −0.184294 − 0.258098I
a = 1.80344 + 0.62550I
b = 0.921833 + 0.474362I
−1.74796 − 1.39281I −0.06858 + 4.56854I
6
II.
I
u
2
= h1.66×10
32
u
39
+3.60×10
32
u
38
+· · ·+2.03×10
33
b+3.24×10
33
, −2.31×
10
33
u
39
−2.80×10
33
u
38
+· · ·+1.42×10
34
a−3.28×10
34
, u
40
−u
39
+· · ·+2u−7i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
0.161987u
39
+ 0.196985u
38
+ ··· − 3.44398u + 2.30009
−0.0813887u
39
− 0.176820u
38
+ ··· − 0.179851u − 1.59203
a
10
=
u
−u
3
+ u
a
5
=
−0.163111u
39
+ 0.121091u
38
+ ··· − 2.45449u − 0.157285
0.0118001u
39
− 0.161041u
38
+ ··· + 2.28334u − 1.24246
a
3
=
0.0805980u
39
+ 0.0201647u
38
+ ··· − 3.62383u + 0.708055
−0.0813887u
39
− 0.176820u
38
+ ··· − 0.179851u − 1.59203
a
8
=
−u
u
a
7
=
−0.686240u
39
+ 0.165773u
38
+ ··· − 8.36308u − 2.07268
−0.124536u
39
− 0.0137535u
38
+ ··· + 3.30823u − 1.30076
a
6
=
−0.264297u
39
+ 0.208180u
38
+ ··· − 8.40248u + 1.25906
−0.0917954u
39
− 0.149519u
38
+ ··· + 1.01878u − 1.41043
a
11
=
0.362372u
39
− 0.240314u
38
+ ··· + 6.14938u − 0.500854
0.0561169u
39
+ 0.187756u
38
+ ··· − 1.78765u + 1.85008
a
2
=
0.606180u
39
+ 0.0186776u
38
+ ··· + 5.88374u + 4.45545
0.100110u
39
− 0.0338163u
38
+ ··· − 1.25499u − 0.588358
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.718225u
39
+ 0.557029u
38
+ ··· − 30.2068u + 28.6614
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 7u
19
+ ··· − 3u − 1)
2
c
2
, c
7
u
40
− 2u
39
+ ··· − 26u − 61
c
3
, c
6
u
40
+ 2u
39
+ ··· − 228u − 23
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u
40
− u
39
+ ··· + 2u − 7
c
11
(u
20
− 3u
19
+ ··· + 3u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 3y
19
+ ··· + 13y + 1)
2
c
2
, c
7
y
40
+ 30y
39
+ ··· + 71304y + 3721
c
3
, c
6
y
40
− 28y
39
+ ··· − 27282y + 529
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
40
− 31y
39
+ ··· − 144y + 49
c
11
(y
20
− y
19
+ ··· + 5y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172284 + 0.930618I
a = 0.563522 − 0.356753I
b = 0.782168 + 0.436510I
2.10225 − 1.91320I 12.94560 + 2.54574I
u = 0.172284 − 0.930618I
a = 0.563522 + 0.356753I
b = 0.782168 − 0.436510I
2.10225 + 1.91320I 12.94560 − 2.54574I
u = −0.244911 + 1.046600I
a = −0.233171 + 0.381855I
b = −1.38627 − 0.42735I
−4.04482 − 9.38865I 5.79523 + 6.34367I
u = −0.244911 − 1.046600I
a = −0.233171 − 0.381855I
b = −1.38627 + 0.42735I
−4.04482 + 9.38865I 5.79523 − 6.34367I
u = 1.066340 + 0.174534I
a = 0.33370 − 1.70053I
b = 0.655937 + 0.084213I
2.98449 + 4.45164I 7.31119 − 2.95218I
u = 1.066340 − 0.174534I
a = 0.33370 + 1.70053I
b = 0.655937 − 0.084213I
2.98449 − 4.45164I 7.31119 + 2.95218I
u = 0.233487 + 0.859274I
a = −0.065996 − 0.829336I
b = −1.398940 − 0.116446I
−4.18215 + 1.22248I 3.92149 − 1.39446I
u = 0.233487 − 0.859274I
a = −0.065996 + 0.829336I
b = −1.398940 + 0.116446I
−4.18215 − 1.22248I 3.92149 + 1.39446I
u = −1.14094
a = −0.265310
b = 1.65585
9.37112 7.59830
u = 1.104630 + 0.381776I
a = −0.560979 + 1.119390I
b = 1.63716 − 0.52448I
−1.57771 + 3.26749I 7.04002 − 3.73668I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.104630 − 0.381776I
a = −0.560979 − 1.119390I
b = 1.63716 + 0.52448I
−1.57771 − 3.26749I 7.04002 + 3.73668I
u = −1.156520 + 0.322107I
a = 0.14951 + 1.66461I
b = −1.029110 − 0.644604I
1.13469 − 4.44881I 7.43323 + 7.56778I
u = −1.156520 − 0.322107I
a = 0.14951 − 1.66461I
b = −1.029110 + 0.644604I
1.13469 + 4.44881I 7.43323 − 7.56778I
u = 1.207880 + 0.090529I
a = 0.50967 − 1.69237I
b = −0.68428 + 1.42821I
2.10225 + 1.91320I 12.94560 − 2.54574I
u = 1.207880 − 0.090529I
a = 0.50967 + 1.69237I
b = −0.68428 − 1.42821I
2.10225 − 1.91320I 12.94560 + 2.54574I
u = 1.223790 + 0.228666I
a = 0.77947 − 1.20408I
b = −1.28524 + 0.61663I
1.41622 + 1.68884I 7.49070 + 2.96681I
u = 1.223790 − 0.228666I
a = 0.77947 + 1.20408I
b = −1.28524 − 0.61663I
1.41622 − 1.68884I 7.49070 − 2.96681I
u = 0.441449 + 0.571825I
a = 1.29994 − 0.84693I
b = 0.259428 − 0.080723I
1.41622 − 1.68884I 7.49070 − 2.96681I
u = 0.441449 − 0.571825I
a = 1.29994 + 0.84693I
b = 0.259428 + 0.080723I
1.41622 + 1.68884I 7.49070 + 2.96681I
u = −1.068460 + 0.761321I
a = −0.426555 − 0.520491I
b = 1.176790 − 0.196349I
−1.57771 + 3.26749I 7.04002 − 3.73668I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068460 − 0.761321I
a = −0.426555 + 0.520491I
b = 1.176790 + 0.196349I
−1.57771 − 3.26749I 7.04002 + 3.73668I
u = −1.313800 + 0.233184I
a = −0.19963 + 1.86651I
b = 0.01842 − 1.57786I
5.71544 − 7.22344I 12.4528 + 8.0152I
u = −1.313800 − 0.233184I
a = −0.19963 − 1.86651I
b = 0.01842 + 1.57786I
5.71544 + 7.22344I 12.4528 − 8.0152I
u = −0.615450 + 0.236917I
a = 0.579816 + 1.206680I
b = 0.497229 + 0.198466I
−2.02990 − 1.39321I 1.85435 + 4.74860I
u = −0.615450 − 0.236917I
a = 0.579816 − 1.206680I
b = 0.497229 − 0.198466I
−2.02990 + 1.39321I 1.85435 − 4.74860I
u = −1.310930 + 0.483541I
a = −0.52543 − 1.34527I
b = 1.53654 + 0.62806I
−4.04482 − 9.38865I 6.00000 + 6.34367I
u = −1.310930 − 0.483541I
a = −0.52543 + 1.34527I
b = 1.53654 − 0.62806I
−4.04482 + 9.38865I 6.00000 − 6.34367I
u = 1.303490 + 0.504837I
a = −0.10836 − 1.48082I
b = −0.964074 + 0.616530I
5.71544 + 7.22344I 12.4528 − 8.0152I
u = 1.303490 − 0.504837I
a = −0.10836 + 1.48082I
b = −0.964074 − 0.616530I
5.71544 − 7.22344I 12.4528 + 8.0152I
u = 0.094199 + 0.593079I
a = 0.485794 + 0.531586I
b = 1.262160 − 0.290729I
−2.02990 + 1.39321I 1.85435 − 4.74860I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094199 − 0.593079I
a = 0.485794 − 0.531586I
b = 1.262160 + 0.290729I
−2.02990 − 1.39321I 1.85435 + 4.74860I
u = 1.300120 + 0.527949I
a = −0.636468 + 0.928959I
b = 1.152670 − 0.013361I
−4.18215 + 1.22248I 6.00000 + 0.I
u = 1.300120 − 0.527949I
a = −0.636468 − 0.928959I
b = 1.152670 + 0.013361I
−4.18215 − 1.22248I 6.00000 + 0.I
u = −1.40763 + 0.26008I
a = 0.90351 + 1.65797I
b = −1.28489 − 0.83804I
2.98449 − 4.45164I 0
u = −1.40763 − 0.26008I
a = 0.90351 − 1.65797I
b = −1.28489 + 0.83804I
2.98449 + 4.45164I 0
u = 0.166400 + 0.503509I
a = −0.865523 + 0.582383I
b = 0.297685 − 1.021220I
1.13469 + 4.44881I 7.43323 − 7.56778I
u = 0.166400 − 0.503509I
a = −0.865523 − 0.582383I
b = 0.297685 + 1.021220I
1.13469 − 4.44881I 7.43323 + 7.56778I
u = −0.461471
a = 3.17311
b = −0.944216
7.33107 23.9120
u = −1.58819
a = 0.0220772
b = −0.324173
7.33107 0
u = 1.79789
a = 0.675888
b = −0.874248
9.37112 0
13
III. I
u
3
= hu
3
+ b − 2u, u
4
− u
3
− 2u
2
+ a + u, u
5
− 3u
3
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
−u
4
+ u
3
+ 2u
2
− u
−u
3
+ 2u
a
10
=
u
−u
3
+ u
a
5
=
−u
4
+ u
3
+ 3u
2
− u
−u
4
− u
3
+ u
2
+ 2u
a
3
=
−u
4
+ 2u
2
+ u
−u
3
+ 2u
a
8
=
−u
u
a
7
=
−u
2
u
4
− 2u
2
+ 1
a
6
=
−u
4
− u
3
+ 2u
2
+ 2u − 1
u + 1
a
11
=
−u
4
+ u
2
− u + 1
u
4
+ u
3
− 2u
2
− u + 1
a
2
=
−u
4
+ 2u
3
+ u
2
− u + 1
−2u
3
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
− 4u
2
− 9u + 13
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 7u
4
+ 23u
3
− 41u
2
+ 36u − 13
c
2
, c
7
u
5
+ u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
3
, c
6
u
5
− u
3
+ u
2
+ u − 1
c
4
, c
5
, c
8
c
9
u
5
− 3u
3
+ 2u + 1
c
10
, c
12
u
5
− 3u
3
+ 2u − 1
c
11
u
5
− 3u
4
+ 3u
3
− 3u
2
+ 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 3y
4
+ 27y
3
− 207y
2
+ 230y − 169
c
2
, c
7
y
5
+ 5y
4
+ 7y
3
+ y
2
− 2y − 1
c
3
, c
6
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y − 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y − 1
c
11
y
5
− 3y
4
− 5y
3
− 3y
2
− 2y − 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.297630 + 0.272489I
a = 0.53019 + 1.94593I
b = −0.699311 − 0.811268I
4.27168 − 5.69445I 10.65653 + 5.80129I
u = −1.297630 − 0.272489I
a = 0.53019 − 1.94593I
b = −0.699311 + 0.811268I
4.27168 + 5.69445I 10.65653 − 5.80129I
u = 0.516079 + 0.312340I
a = −0.116662 + 0.442697I
b = 1.045750 + 0.405588I
−1.28936 − 0.85728I 7.62581 − 3.22423I
u = 0.516079 − 0.312340I
a = −0.116662 − 0.442697I
b = 1.045750 − 0.405588I
−1.28936 + 0.85728I 7.62581 + 3.22423I
u = 1.56310
a = 1.17294
b = −0.692872
13.7746 4.43530
17
IV. I
u
4
= hu
7
− 4u
5
− u
4
+ 3u
3
+ 3u
2
+ b + u − 1, −3u
7
+ 14u
5
+ · · · + a +
6, u
8
− 5u
6
− u
5
+ 7u
4
+ 4u
3
− 2u
2
− 4u − 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
3u
7
− 14u
5
− 2u
4
+ 17u
3
+ 7u
2
− 4u − 6
−u
7
+ 4u
5
+ u
4
− 3u
3
− 3u
2
− u + 1
a
10
=
u
−u
3
+ u
a
5
=
2u
7
− 10u
5
− u
4
+ 13u
3
+ 4u
2
− 3u − 5
−u
7
+ 5u
5
+ u
4
− 6u
3
− 3u
2
+ u + 2
a
3
=
2u
7
− 10u
5
− u
4
+ 14u
3
+ 4u
2
− 5u − 5
−u
7
+ 4u
5
+ u
4
− 3u
3
− 3u
2
− u + 1
a
8
=
−u
u
a
7
=
−2u
7
+ u
6
+ 9u
5
− 3u
4
− 11u
3
− u
2
+ 3u + 6
u
7
− 4u
5
− u
4
+ 4u
3
+ 3u
2
− u − 2
a
6
=
−3u
7
+ u
6
+ 15u
5
− 2u
4
− 22u
3
− 5u
2
+ 9u + 10
u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 3u − 3
a
11
=
3u
7
− u
6
− 14u
5
+ u
4
+ 18u
3
+ 7u
2
− 6u − 9
−u
7
+ 5u
5
+ u
4
− 7u
3
− 3u
2
+ 2u + 3
a
2
=
2u
7
+ u
6
− 9u
5
− 5u
4
+ 10u
3
+ 7u
2
− 2u − 3
−u
7
− u
6
+ 4u
5
+ 4u
4
− 2u
3
− 4u
2
− 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
7
− 32u
5
− 8u
4
+ 32u
3
+ 24u
2
− 8u − 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ u − 1)
2
c
2
, c
7
u
8
− u
7
+ 5u
5
− 4u
4
− u
3
+ 4u
2
− 4u − 1
c
3
, c
6
u
8
− 3u
7
+ u
6
+ 6u
5
− 5u
4
− 5u
3
+ 3u
2
+ 2u − 1
c
4
, c
5
, c
8
c
9
u
8
− 5u
6
+ u
5
+ 7u
4
− 4u
3
− 2u
2
+ 4u − 1
c
10
, c
12
u
8
− 5u
6
− u
5
+ 7u
4
+ 4u
3
− 2u
2
− 4u − 1
c
11
(u
4
+ u
3
− u
2
− u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ y
3
+ y
2
− 3y + 1)
2
c
2
, c
7
y
8
− y
7
+ 2y
6
− 19y
5
+ 16y
4
+ 7y
3
+ 16y
2
− 24y + 1
c
3
, c
6
y
8
− 7y
7
+ 27y
6
− 70y
5
+ 101y
4
− 81y
3
+ 39y
2
− 10y + 1
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y
8
− 10y
7
+ 39y
6
− 75y
5
+ 75y
4
− 42y
3
+ 22y
2
− 12y + 1
c
11
(y
4
− 3y
3
+ y
2
+ y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.220530 + 0.143929I
a = 0.91993 − 1.73081I
b = −1.36577 + 1.02316I
1.21622 + 2.52742I 5.33661 − 5.36615I
u = 1.220530 − 0.143929I
a = 0.91993 + 1.73081I
b = −1.36577 − 1.02316I
1.21622 − 2.52742I 5.33661 + 5.36615I
u = −0.475131 + 0.605600I
a = 1.42534 + 0.16678I
b = 0.698689 − 0.352393I
1.21622 + 2.52742I 5.33661 − 5.36615I
u = −0.475131 − 0.605600I
a = 1.42534 − 0.16678I
b = 0.698689 + 0.352393I
1.21622 − 2.52742I 5.33661 + 5.36615I
u = −1.26429
a = 0.514662
b = −1.67103
10.2678 17.4300
u = −1.63636
a = 0.469455
b = −0.596060
7.03897 −4.10300
u = −0.313425
a = −4.55992
b = 1.10894
7.03897 −4.10300
u = 1.72328
a = −0.114719
b = −0.507696
10.2678 17.4300
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ u − 1)
2
(u
5
− 7u
4
+ 23u
3
− 41u
2
+ 36u − 13)
· (u
15
− 12u
14
+ ··· + 352u − 16)(u
20
+ 7u
19
+ ··· − 3u − 1)
2
c
2
, c
7
(u
5
+ u
4
+ 3u
3
+ 3u
2
+ 2u + 1)(u
8
− u
7
+ ··· − 4u − 1)
· (u
15
− u
14
+ ··· − 9u + 1)(u
40
− 2u
39
+ ··· − 26u − 61)
c
3
, c
6
(u
5
− u
3
+ u
2
+ u − 1)(u
8
− 3u
7
+ ··· + 2u − 1)
· (u
15
− 6u
13
+ ··· − 2u + 1)(u
40
+ 2u
39
+ ··· − 228u − 23)
c
4
, c
5
, c
8
c
9
(u
5
− 3u
3
+ 2u + 1)(u
8
− 5u
6
+ u
5
+ 7u
4
− 4u
3
− 2u
2
+ 4u − 1)
· (u
15
− 8u
13
+ 25u
11
− 33u
9
+ 2u
7
− u
6
+ 37u
5
+ 2u
4
− 27u
3
− u
2
+ u + 1)
· (u
40
− u
39
+ ··· + 2u − 7)
c
10
, c
12
(u
5
− 3u
3
+ 2u − 1)(u
8
− 5u
6
− u
5
+ 7u
4
+ 4u
3
− 2u
2
− 4u − 1)
· (u
15
− 8u
13
+ 25u
11
− 33u
9
+ 2u
7
− u
6
+ 37u
5
+ 2u
4
− 27u
3
− u
2
+ u + 1)
· (u
40
− u
39
+ ··· + 2u − 7)
c
11
(u
4
+ u
3
− u
2
− u − 1)
2
(u
5
− 3u
4
+ 3u
3
− 3u
2
+ 2u − 1)
· (u
15
+ 8u
14
+ ··· + 2u − 4)(u
20
− 3u
19
+ ··· + 3u − 1)
2
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ y
3
+ y
2
− 3y + 1)
2
(y
5
− 3y
4
+ 27y
3
− 207y
2
+ 230y − 169)
· (y
15
− 2y
14
+ ··· + 81824y − 256)(y
20
+ 3y
19
+ ··· + 13y + 1)
2
c
2
, c
7
(y
5
+ 5y
4
+ 7y
3
+ y
2
− 2y − 1)
· (y
8
− y
7
+ 2y
6
− 19y
5
+ 16y
4
+ 7y
3
+ 16y
2
− 24y + 1)
· (y
15
+ 15y
14
+ ··· + 13y − 1)(y
40
+ 30y
39
+ ··· + 71304y + 3721)
c
3
, c
6
(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y − 1)
· (y
8
− 7y
7
+ 27y
6
− 70y
5
+ 101y
4
− 81y
3
+ 39y
2
− 10y + 1)
· (y
15
− 12y
14
+ ··· + 38y − 1)(y
40
− 28y
39
+ ··· − 27282y + 529)
c
4
, c
5
, c
8
c
9
, c
10
, c
12
(y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y − 1)
· (y
8
− 10y
7
+ 39y
6
− 75y
5
+ 75y
4
− 42y
3
+ 22y
2
− 12y + 1)
· (y
15
− 16y
14
+ ··· + 3y − 1)(y
40
− 31y
39
+ ··· − 144y + 49)
c
11
(y
4
− 3y
3
+ y
2
+ y + 1)
2
(y
5
− 3y
4
− 5y
3
− 3y
2
− 2y − 1)
· (y
15
− 2y
14
+ ··· + 332y − 16)(y
20
− y
19
+ ··· + 5y + 1)
2
23
