12n
0815
(K12n
0815
)
A knot diagram
1
Linearized knot diagam
4 6 12 7 10 2 1 12 6 8 4 10
Solving Sequence
2,6
3
7,10
5 4 1 9 12 8 11
c
2
c
6
c
5
c
4
c
1
c
9
c
12
c
8
c
10
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5655077u
11
+ 18192667u
10
+ ··· + 57645040b + 32704792,
4782676u
11
+ 14870711u
10
+ ··· + 28822520a + 7681096,
u
12
+ 4u
11
+ 22u
10
+ 49u
9
+ 124u
8
+ 152u
7
+ 187u
6
+ 152u
5
+ 154u
4
+ 123u
3
+ 84u
2
+ 36u + 8i
I
u
2
= h−u
8
+ u
6
a + u
5
a − 2u
6
+ 2u
4
a − 3u
5
+ 4u
3
a − u
4
+ 3u
2
a − 3u
3
+ 3au − 2u
2
+ b + a,
− u
9
a − 2u
8
a + ··· − 2a − 2, u
10
+ u
9
+ 3u
8
+ 6u
7
+ 7u
6
+ 9u
5
+ 10u
4
+ 8u
3
+ 5u
2
+ 2u + 1i
I
u
3
= h−5028u
7
a − 3060u
7
+ ··· + 87875a + 61205,
− 60170u
7
a − 58983u
7
+ ··· + 1299250a + 839905,
u
8
− 6u
7
+ 24u
6
− 50u
5
+ 73u
4
− 72u
3
+ 61u
2
− 55u + 25i
I
u
4
= hb − u − 1, a, u
2
+ u + 1i
I
u
5
= hu
2
+ 4b + 2u + 5, −2u
2
+ 2a + 3u − 15, u
3
− u
2
+ 7u + 1i
* 5 irreducible components of dim
C
= 0, with total 53 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
= h5.66 × 10
6
u
11
+ 1 .82 × 10
7
u
10
+ · · · + 5.76 × 10
7
b + 3.27 × 10
7
, 4.78 ×
10
6
u
11
+1.49×10
7
u
10
+· · ·+2.88×10
7
a+7.68×10
6
, u
12
+4u
11
+· · ·+36u+8i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
−0.165935u
11
− 0.515941u
10
+ ··· − 3.42377u − 0.266496
−0.0981017u
11
− 0.315598u
10
+ ··· − 1.84222u − 0.567348
a
5
=
0.0555299u
11
+ 0.197961u
10
+ ··· + 1.67411u + 1.16096
−0.0124138u
11
− 0.0591623u
10
+ ··· − 0.874760u − 0.426335
a
4
=
0.0532919u
11
+ 0.200754u
10
+ ··· + 1.69020u + 1.04375
−0.0146517u
11
− 0.0563689u
10
+ ··· − 0.858673u − 0.543549
a
1
=
0.0196973u
11
+ 0.0508957u
10
+ ··· + 1.95987u + 1.74708
−0.0164741u
11
− 0.0773159u
10
+ ··· − 0.265718u − 0.289371
a
9
=
−0.165935u
11
− 0.515941u
10
+ ··· − 3.42377u − 0.266496
−0.0311444u
11
− 0.0537009u
10
+ ··· + 2.15113u + 0.615059
a
12
=
0.0709185u
11
+ 0.185572u
10
+ ··· + 1.74180u + 0.710849
0.0709921u
11
+ 0.228068u
10
+ ··· + 2.74286u + 0.542669
a
8
=
−0.0711186u
11
− 0.224055u
10
+ ··· + 0.618483u + 0.662628
0.00749790u
11
+ 0.0714935u
10
+ ··· + 4.03579u + 0.760724
a
11
=
−0.164351u
11
− 0.516002u
10
+ ··· − 6.02898u − 1.47273
−0.0364474u
11
− 0.0811342u
10
+ ··· + 0.0786132u + 0.481147
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
728881
5764504
u
11
+
352229
5764504
u
10
+ ··· +
29077369
1441126
u +
7367045
720563
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
12
− 4u
10
+ 3u
9
+ 13u
8
− 2u
7
− 19u
6
+ 13u
4
− 3u
3
− 2u + 1
c
2
, c
6
u
12
− 4u
11
+ ··· − 36u + 8
c
3
, c
5
, c
9
c
11
u
12
+ 5u
11
+ ··· + 16u + 4
c
7
u
12
− 12u
11
+ ··· − 112u + 16
c
8
u
12
− 13u
11
+ ··· − 2840u + 472
c
10
, c
12
u
12
− u
11
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
12
− 8y
11
+ ··· − 4y + 1
c
2
, c
6
y
12
+ 28y
11
+ ··· + 48y + 64
c
3
, c
5
, c
9
c
11
y
12
− 23y
11
+ ··· + 192y + 16
c
7
y
12
+ 2y
11
+ ··· + 1536y + 256
c
8
y
12
+ 45y
11
+ ··· + 1504672y + 222784
c
10
, c
12
y
12
− y
11
+ ··· + 31y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540143 + 0.761627I
a = −1.69223 + 0.78856I
b = −0.993599 + 0.115131I
−2.97909 + 0.17410I −3.65502 − 0.56316I
u = 0.540143 − 0.761627I
a = −1.69223 − 0.78856I
b = −0.993599 − 0.115131I
−2.97909 − 0.17410I −3.65502 + 0.56316I
u = −0.495932 + 0.959152I
a = 0.436587 − 0.071368I
b = 0.788354 − 0.737396I
−0.33260 − 5.31098I 0.92797 + 6.12254I
u = −0.495932 − 0.959152I
a = 0.436587 + 0.071368I
b = 0.788354 + 0.737396I
−0.33260 + 5.31098I 0.92797 − 6.12254I
u = −0.313071 + 0.674527I
a = −0.261436 + 0.583661I
b = 0.024504 + 0.511749I
−0.252110 − 1.156370I −2.57186 + 6.15407I
u = −0.313071 − 0.674527I
a = −0.261436 − 0.583661I
b = 0.024504 − 0.511749I
−0.252110 + 1.156370I −2.57186 − 6.15407I
u = −0.433831 + 0.256446I
a = 0.396072 − 1.201640I
b = −0.339334 − 0.183220I
1.23387 + 1.55175I 4.02015 − 1.83829I
u = −0.433831 − 0.256446I
a = 0.396072 + 1.201640I
b = −0.339334 + 0.183220I
1.23387 − 1.55175I 4.02015 + 1.83829I
u = −0.29653 + 2.66870I
a = −0.147885 − 0.838892I
b = 0.05531 − 2.12763I
−16.8158 − 1.6628I −7.43215 + 4.58115I
u = −0.29653 − 2.66870I
a = −0.147885 + 0.838892I
b = 0.05531 + 2.12763I
−16.8158 + 1.6628I −7.43215 − 4.58115I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00078 + 2.60205I
a = −0.231108 + 1.220450I
b = −0.03524 + 2.20216I
18.3232 − 12.8945I −2.78911 + 4.52447I
u = −1.00078 − 2.60205I
a = −0.231108 − 1.220450I
b = −0.03524 − 2.20216I
18.3232 + 12.8945I −2.78911 − 4.52447I
6
II.
I
u
2
= h−u
8
+u
6
a+· · ·+b+a, −u
9
a−2u
8
a+· · ·−2a−2, u
10
+u
9
+· · ·+2u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
a
u
8
− u
6
a + ··· − 3au − a
a
5
=
u
9
a + u
9
+ ··· − a + 2u
u
9
a + u
9
+ ··· + a + 2
a
4
=
u
9
a + u
9
+ ··· − 2a + 2u
u
9
a + u
9
+ ··· + 5u + 2
a
1
=
−u
9
a − u
9
+ ··· − 6u − 1
−u
9
a − u
9
+ ··· − 4u − 1
a
9
=
a
u
8
− u
6
a + ··· − 3au − a
a
12
=
−u
9
a − 2u
9
+ ··· + a − 2
−u
7
a − u
8
+ ··· − 4u − 2
a
8
=
u
8
a + 3u
9
+ ··· − au + 6u
u
8
a + u
9
+ ··· + 6u + 2
a
11
=
−u
9
a − 2u
9
+ ··· + 2a − 1
−u
7
a − 2u
8
+ ··· + a − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
9
+ u
8
+ 9u
7
+ 17u
6
+ 17u
5
+ 31u
4
+ 34u
3
+ 19u
2
+ 15u + 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 7u
19
+ ··· − 7u + 1
c
2
(u
10
+ u
9
+ 3u
8
+ 6u
7
+ 7u
6
+ 9u
5
+ 10u
4
+ 8u
3
+ 5u
2
+ 2u + 1)
2
c
3
, c
9
u
20
+ 4u
19
+ ··· + 24u + 4
c
5
, c
11
u
20
− 4u
19
+ ··· − 24u + 4
c
6
(u
10
− u
9
+ 3u
8
− 6u
7
+ 7u
6
− 9u
5
+ 10u
4
− 8u
3
+ 5u
2
− 2u + 1)
2
c
7
(u
10
− 4u
8
+ 10u
6
− 2u
5
− 9u
4
− 12u
3
+ 15u
2
+ 2u + 4)
2
c
8
(u
10
+ 2u
9
− 4u
8
− 4u
7
+ 14u
6
+ 6u
5
− 14u
4
− 4u
3
+ 12u
2
+ 6u + 1)
2
c
10
, c
12
u
20
− 7u
19
+ ··· − 6u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− y
19
+ ··· − 9y + 1
c
2
, c
6
(y
10
+ 5y
9
+ 11y
8
+ 8y
7
− 5y
6
− 9y
5
+ 8y
4
+ 14y
3
+ 13y
2
+ 6y + 1)
2
c
3
, c
5
, c
9
c
11
y
20
+ 2y
19
+ ··· + 64y + 16
c
7
(y
10
− 8y
9
+ ··· + 116y + 16)
2
c
8
(y
10
− 12y
9
+ ··· − 12y + 1)
2
c
10
, c
12
y
20
− 9y
19
+ ··· − 8y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014310 + 0.256691I
a = 0.964180 − 0.567184I
b = −0.172201 − 1.125270I
−2.82507 − 0.01586I −5.03096 + 0.40672I
u = −1.014310 + 0.256691I
a = 0.842936 + 0.896392I
b = −0.089370 + 1.110650I
−2.82507 − 0.01586I −5.03096 + 0.40672I
u = −1.014310 − 0.256691I
a = 0.964180 + 0.567184I
b = −0.172201 + 1.125270I
−2.82507 + 0.01586I −5.03096 − 0.40672I
u = −1.014310 − 0.256691I
a = 0.842936 − 0.896392I
b = −0.089370 − 1.110650I
−2.82507 + 0.01586I −5.03096 − 0.40672I
u = −0.494190 + 0.650032I
a = 0.701854 − 0.119057I
b = 0.93649 − 2.03449I
−1.80674 − 6.46947I −1.01128 + 9.30231I
u = −0.494190 + 0.650032I
a = −0.366624 − 1.277610I
b = 0.159063 − 0.249786I
−1.80674 − 6.46947I −1.01128 + 9.30231I
u = −0.494190 − 0.650032I
a = 0.701854 + 0.119057I
b = 0.93649 + 2.03449I
−1.80674 + 6.46947I −1.01128 − 9.30231I
u = −0.494190 − 0.650032I
a = −0.366624 + 1.277610I
b = 0.159063 + 0.249786I
−1.80674 + 6.46947I −1.01128 − 9.30231I
u = 0.382212 + 1.255980I
a = 0.293033 − 1.100270I
b = 0.11581 − 2.62267I
−3.73684 + 4.80030I −9.38054 − 3.15587I
u = 0.382212 + 1.255980I
a = −0.519971 + 0.035643I
b = −0.588255 + 0.303305I
−3.73684 + 4.80030I −9.38054 − 3.15587I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382212 − 1.255980I
a = 0.293033 + 1.100270I
b = 0.11581 + 2.62267I
−3.73684 − 4.80030I −9.38054 + 3.15587I
u = 0.382212 − 1.255980I
a = −0.519971 − 0.035643I
b = −0.588255 − 0.303305I
−3.73684 − 4.80030I −9.38054 + 3.15587I
u = 0.068366 + 0.610240I
a = −0.187485 + 1.399550I
b = 0.909534 − 0.136013I
−0.72327 − 2.84641I −2.67521 + 3.01300I
u = 0.068366 + 0.610240I
a = −1.41876 + 0.52381I
b = −0.061464 + 1.381430I
−0.72327 − 2.84641I −2.67521 + 3.01300I
u = 0.068366 − 0.610240I
a = −0.187485 − 1.399550I
b = 0.909534 + 0.136013I
−0.72327 + 2.84641I −2.67521 − 3.01300I
u = 0.068366 − 0.610240I
a = −1.41876 − 0.52381I
b = −0.061464 − 1.381430I
−0.72327 + 2.84641I −2.67521 − 3.01300I
u = 0.55792 + 1.34043I
a = 0.830798 + 0.641959I
b = −0.21457 + 2.05660I
5.80206 + 1.85988I 11.59799 + 1.32723I
u = 0.55792 + 1.34043I
a = −1.139960 − 0.180068I
b = −0.495038 − 0.305606I
5.80206 + 1.85988I 11.59799 + 1.32723I
u = 0.55792 − 1.34043I
a = 0.830798 − 0.641959I
b = −0.21457 − 2.05660I
5.80206 − 1.85988I 11.59799 − 1.32723I
u = 0.55792 − 1.34043I
a = −1.139960 + 0.180068I
b = −0.495038 + 0.305606I
5.80206 − 1.85988I 11.59799 − 1.32723I
11
III. I
u
3
= h−5028u
7
a − 3060u
7
+ · · · + 87875a + 61205, −6.02 × 10
4
au
7
−
5.90 × 10
4
u
7
+ · · · + 1.30 × 10
6
a + 8.40 × 10
5
, u
8
− 6u
7
+ · · · − 55u + 25i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
a
0.208156au
7
+ 0.126682u
7
+ ··· − 3.63796a − 2.53384
a
5
=
0.0470296au
7
+ 0.0807038u
7
+ ··· − 2.49100a − 2.44185
−0.0371352au
7
+ 0.0705030u
7
+ ··· + 0.0672739a − 0.0987373
a
4
=
0.00269095au
7
+ 0.0452660u
7
+ ··· − 0.454150a − 2.52258
−0.0814738au
7
+ 0.0350652u
7
+ ··· + 2.10412a − 0.179466
a
1
=
−0.0475678au
7
− 0.0396357u
7
+ ··· − 1.21817a + 2.58775
−0.0475678au
7
− 0.0895467u
7
+ ··· − 1.21817a + 2.46657
a
9
=
a
0.208156au
7
+ 0.126682u
7
+ ··· − 3.63796a − 2.53384
a
12
=
−0.145519au
7
− 0.0181660u
7
+ ··· + 2.71290a + 0.0474022
0.192548au
7
+ 0.0841648u
7
+ ··· − 5.20389a − 2.55827
a
8
=
0.128379au
7
+ 0.0664376u
7
+ ··· − 1.68185a − 0.471083
0.128379au
7
+ 0.313310u
7
+ ··· − 1.68185a − 5.53860
a
11
=
0.106189au
7
+ 0.234602u
7
+ ··· − 3.84455a − 1.23660
−0.228648au
7
+ 0.0835438u
7
+ ··· + 4.32726a + 2.00807
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2475
4831
u
7
−
58067
24155
u
6
+
218393
24155
u
5
−
326712
24155
u
4
+
446026
24155
u
3
−
285694
24155
u
2
+
252936
24155
u −
68757
4831
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
16
− 5u
15
+ ··· − 137u + 103
c
2
, c
6
(u
8
+ 6u
7
+ 24u
6
+ 50u
5
+ 73u
4
+ 72u
3
+ 61u
2
+ 55u + 25)
2
c
3
, c
5
, c
9
c
11
u
16
− 4u
15
+ ··· + 8104u + 8557
c
7
(u
4
+ 2u
3
− 3u − 1)
4
c
8
(u
8
+ 4u
7
+ ··· + 1636u + 709)
2
c
10
, c
12
u
16
+ 5u
15
+ ··· + 1490u + 631
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
16
− 3y
15
+ ··· − 68415y + 10609
c
2
, c
6
(y
8
+ 12y
7
+ 122y
6
+ 262y
5
+ 447y
4
− 578y
3
− 549y
2
+ 25y + 625)
2
c
3
, c
5
, c
9
c
11
y
16
− 42y
15
+ ··· + 743954296y + 73222249
c
7
(y
4
− 4y
3
+ 10y
2
− 9y + 1)
4
c
8
(y
8
+ 110y
7
+ ··· + 929478y + 502681)
2
c
10
, c
12
y
16
− 17y
15
+ ··· + 2691604y + 398161
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356173 + 0.922051I
a = −1.45726 − 0.66205I
b = −0.571202 + 0.124651I
−2.60769 + 5.61159I −4.01448 − 3.52119I
u = −0.356173 + 0.922051I
a = 0.58952 − 1.50850I
b = −0.46449 − 2.42477I
−2.60769 + 5.61159I −4.01448 − 3.52119I
u = −0.356173 − 0.922051I
a = −1.45726 + 0.66205I
b = −0.571202 − 0.124651I
−2.60769 − 5.61159I −4.01448 + 3.52119I
u = −0.356173 − 0.922051I
a = 0.58952 + 1.50850I
b = −0.46449 + 2.42477I
−2.60769 − 5.61159I −4.01448 + 3.52119I
u = 0.976606 + 0.152571I
a = −1.248430 − 0.212849I
b = 0.444438 − 0.330170I
−2.60769 − 1.55182I −4.60507 + 3.15648I
u = 0.976606 + 0.152571I
a = −0.065632 + 0.390479I
b = 0.386763 + 1.198400I
−2.60769 − 1.55182I −4.60507 + 3.15648I
u = 0.976606 − 0.152571I
a = −1.248430 + 0.212849I
b = 0.444438 + 0.330170I
−2.60769 + 1.55182I −4.60507 − 3.15648I
u = 0.976606 − 0.152571I
a = −0.065632 − 0.390479I
b = 0.386763 − 1.198400I
−2.60769 + 1.55182I −4.60507 − 3.15648I
u = 0.82072 + 1.42153I
a = 0.883685 + 0.700209I
b = −0.16909 + 1.79182I
5.45104 + 2.02988I −7.20164 − 6.73627I
u = 0.82072 + 1.42153I
a = 1.150180 + 0.122308I
b = 0.512857 + 0.312984I
5.45104 + 2.02988I −7.20164 − 6.73627I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.82072 − 1.42153I
a = 0.883685 − 0.700209I
b = −0.16909 − 1.79182I
5.45104 − 2.02988I −7.20164 + 6.73627I
u = 0.82072 − 1.42153I
a = 1.150180 − 0.122308I
b = 0.512857 − 0.312984I
5.45104 − 2.02988I −7.20164 + 6.73627I
u = 1.55884 + 2.70000I
a = 0.40664 − 1.37969I
b = 0.37568 − 2.03120I
19.5035 + 2.0299I −3.67881 − 0.69325I
u = 1.55884 + 2.70000I
a = 0.14130 + 1.51086I
b = −0.01496 + 2.22431I
19.5035 + 2.0299I −3.67881 − 0.69325I
u = 1.55884 − 2.70000I
a = 0.40664 + 1.37969I
b = 0.37568 + 2.03120I
19.5035 − 2.0299I −3.67881 + 0.69325I
u = 1.55884 − 2.70000I
a = 0.14130 − 1.51086I
b = −0.01496 − 2.22431I
19.5035 − 2.0299I −3.67881 + 0.69325I
16
IV. I
u
4
= hb − u − 1, a, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
7
=
u
u
a
10
=
0
u + 1
a
5
=
0
u
a
4
=
1
u + 1
a
1
=
−u
−u
a
9
=
0
u + 1
a
12
=
−u
1
a
8
=
u
u
a
11
=
−u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
7
c
9
, c
11
u
2
c
8
(u + 1)
2
c
10
, c
12
(u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
7
c
9
, c
11
y
2
c
8
, c
10
, c
12
(y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 0. + 3.46410I
u = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 0. − 3.46410I
20
V. I
u
5
= hu
2
+ 4b + 2u + 5, −2u
2
+ 2a + 3u − 15, u
3
− u
2
+ 7u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
u
2
−
3
2
u +
15
2
−
1
4
u
2
−
1
2
u −
5
4
a
5
=
−
5
4
u
2
+
1
2
u −
33
4
−u + 1
a
4
=
−u
2
+ u − 8
1
4
u
2
−
1
2
u +
5
4
a
1
=
3
2
u
2
− 2u +
23
2
−
1
4
u
2
−
7
4
a
9
=
u
2
−
3
2
u +
15
2
−
1
4
u
2
− 3u −
7
4
a
12
=
5
4
u
2
−
3
2
u +
33
4
1
4
u
2
−
5
4
a
8
=
13
4
u
2
− 3u +
87
4
−
1
4
u
2
+
3
2
u −
13
4
a
11
=
11
4
u
2
−
7
2
u +
67
4
1
4
u
2
−
1
2
u −
11
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3
2
u
2
+ 2u −
23
2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
3
− u − 1
c
2
u
3
− u
2
+ 7u + 1
c
3
, c
9
u
3
− 4u
2
+ u + 7
c
5
, c
11
u
3
+ 4u
2
+ u − 7
c
6
u
3
+ u
2
+ 7u − 1
c
7
u
3
− u
2
+ 2u − 7
c
8
u
3
− 3u
2
+ 18u − 27
c
10
, c
12
u
3
+ 2u
2
+ 3u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− 2y
2
+ y −1
c
2
, c
6
y
3
+ 13y
2
+ 51y −1
c
3
, c
5
, c
9
c
11
y
3
− 14y
2
+ 57y −49
c
7
y
3
+ 3y
2
− 10y −49
c
8
y
3
+ 27y
2
+ 162y −729
c
10
, c
12
y
3
+ 2y
2
+ 5y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139681
a = 7.72903
b = −1.18504
−4.20933 −11.8090
u = 0.56984 + 2.61428I
a = 0.135484 − 0.941977I
b = 0.09252 − 2.05200I
−15.9896 + 0.9427I −0.595686 + 0.759395I
u = 0.56984 − 2.61428I
a = 0.135484 + 0.941977I
b = 0.09252 + 2.05200I
−15.9896 − 0.9427I −0.595686 − 0.759395I
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)(u
3
− u − 1)
· (u
12
− 4u
10
+ 3u
9
+ 13u
8
− 2u
7
− 19u
6
+ 13u
4
− 3u
3
− 2u + 1)
· (u
16
− 5u
15
+ ··· − 137u + 103)(u
20
− 7u
19
+ ··· − 7u + 1)
c
2
(u
2
+ u + 1)(u
3
− u
2
+ 7u + 1)
· (u
8
+ 6u
7
+ 24u
6
+ 50u
5
+ 73u
4
+ 72u
3
+ 61u
2
+ 55u + 25)
2
· (u
10
+ u
9
+ 3u
8
+ 6u
7
+ 7u
6
+ 9u
5
+ 10u
4
+ 8u
3
+ 5u
2
+ 2u + 1)
2
· (u
12
− 4u
11
+ ··· − 36u + 8)
c
3
, c
9
u
2
(u
3
− 4u
2
+ u + 7)(u
12
+ 5u
11
+ ··· + 16u + 4)
· (u
16
− 4u
15
+ ··· + 8104u + 8557)(u
20
+ 4u
19
+ ··· + 24u + 4)
c
5
, c
11
u
2
(u
3
+ 4u
2
+ u − 7)(u
12
+ 5u
11
+ ··· + 16u + 4)
· (u
16
− 4u
15
+ ··· + 8104u + 8557)(u
20
− 4u
19
+ ··· − 24u + 4)
c
6
(u
2
− u + 1)(u
3
+ u
2
+ 7u − 1)
· (u
8
+ 6u
7
+ 24u
6
+ 50u
5
+ 73u
4
+ 72u
3
+ 61u
2
+ 55u + 25)
2
· (u
10
− u
9
+ 3u
8
− 6u
7
+ 7u
6
− 9u
5
+ 10u
4
− 8u
3
+ 5u
2
− 2u + 1)
2
· (u
12
− 4u
11
+ ··· − 36u + 8)
c
7
u
2
(u
3
− u
2
+ 2u − 7)(u
4
+ 2u
3
− 3u − 1)
4
· (u
10
− 4u
8
+ 10u
6
− 2u
5
− 9u
4
− 12u
3
+ 15u
2
+ 2u + 4)
2
· (u
12
− 12u
11
+ ··· − 112u + 16)
c
8
((u + 1)
2
)(u
3
− 3u
2
+ 18u − 27)(u
8
+ 4u
7
+ ··· + 1636u + 709)
2
· (u
10
+ 2u
9
− 4u
8
− 4u
7
+ 14u
6
+ 6u
5
− 14u
4
− 4u
3
+ 12u
2
+ 6u + 1)
2
· (u
12
− 13u
11
+ ··· − 2840u + 472)
c
10
, c
12
((u − 1)
2
)(u
3
+ 2u
2
+ 3u + 1)(u
12
− u
11
+ ··· − u + 1)
· (u
16
+ 5u
15
+ ··· + 1490u + 631)(u
20
− 7u
19
+ ··· − 6u + 1)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
3
− 2y
2
+ y −1)(y
12
− 8y
11
+ ··· − 4y + 1)
· (y
16
− 3y
15
+ ··· − 68415y + 10609)(y
20
− y
19
+ ··· − 9y + 1)
c
2
, c
6
(y
2
+ y + 1)(y
3
+ 13y
2
+ 51y −1)
· (y
8
+ 12y
7
+ 122y
6
+ 262y
5
+ 447y
4
− 578y
3
− 549y
2
+ 25y + 625)
2
· (y
10
+ 5y
9
+ 11y
8
+ 8y
7
− 5y
6
− 9y
5
+ 8y
4
+ 14y
3
+ 13y
2
+ 6y + 1)
2
· (y
12
+ 28y
11
+ ··· + 48y + 64)
c
3
, c
5
, c
9
c
11
y
2
(y
3
− 14y
2
+ 57y −49)(y
12
− 23y
11
+ ··· + 192y + 16)
· (y
16
− 42y
15
+ ··· + 743954296y + 73222249)
· (y
20
+ 2y
19
+ ··· + 64y + 16)
c
7
y
2
(y
3
+ 3y
2
− 10y −49)(y
4
− 4y
3
+ 10y
2
− 9y + 1)
4
· ((y
10
− 8y
9
+ ··· + 116y + 16)
2
)(y
12
+ 2y
11
+ ··· + 1536y + 256)
c
8
(y −1)
2
(y
3
+ 27y
2
+ 162y −729)
· (y
8
+ 110y
7
+ ··· + 929478y + 502681)
2
· (y
10
− 12y
9
+ ··· − 12y + 1)
2
· (y
12
+ 45y
11
+ ··· + 1504672y + 222784)
c
10
, c
12
((y −1)
2
)(y
3
+ 2y
2
+ 5y −1)(y
12
− y
11
+ ··· + 31y + 1)
· (y
16
− 17y
15
+ ··· + 2691604y + 398161)(y
20
− 9y
19
+ ··· − 8y + 1)
26
