12a
1113
(K12a
1113
)
A knot diagram
1
Linearized knot diagam
4 7 12 8 10 3 11 1 6 5 2 9
Solving Sequence
6,9
10 5
1,11
8 4 2 7 12 3
c
9
c
5
c
10
c
8
c
4
c
1
c
7
c
12
c
3
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.32908 × 10
29
u
40
+ 1.73331 × 10
30
u
39
+ ··· + 3.94562 × 10
29
b + 4.96788 × 10
30
,
6.00345 × 10
29
u
40
+ 4.26908 × 10
30
u
39
+ ··· + 1.97281 × 10
30
a − 8.10812 × 10
30
,
u
41
+ 8u
40
+ ··· + 194u + 20i
I
u
2
= h5.17859 × 10
49
au
52
− 8.79765 × 10
49
u
52
+ ··· + 9.52947 × 10
49
a − 3.28551 × 10
50
,
− 1.62239 × 10
46
au
52
− 9.06685 × 10
45
u
52
+ ··· − 7.15132 × 10
46
a + 1.44688 × 10
46
,
u
53
− 3u
52
+ ··· + 6u − 1i
I
u
3
= h286u
15
a + 870u
15
+ ··· + 412a − 1440, u
15
a − 5u
15
+ ··· − 2a + 3, u
16
− 2u
15
+ ··· + 11u
2
+ 1i
I
u
4
= h−u
12
− 3u
11
− 10u
10
− 19u
9
− 33u
8
− 41u
7
− 45u
6
− 34u
5
− 23u
4
− 7u
3
− 2u
2
+ b + u,
u
12
+ 2u
11
+ 7u
10
+ 9u
9
+ 14u
8
+ 8u
7
+ 4u
6
− 11u
5
− 11u
4
− 16u
3
− 6u
2
+ a − 3u,
u
13
+ 3u
12
+ 11u
11
+ 22u
10
+ 43u
9
+ 60u
8
+ 78u
7
+ 75u
6
+ 68u
5
+ 42u
4
+ 26u
3
+ 9u
2
+ 4u + 1i
* 4 irreducible components of dim
C
= 0, with total 192 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
=
h2.33×10
29
u
40
+1.73×10
30
u
39
+· · ·+3.95×10
29
b+4.97×10
30
, 6.00×10
29
u
40
+
4.27 × 10
30
u
39
+ · · · + 1.97 × 10
30
a − 8.11 × 10
30
, u
41
+ 8u
40
+ · · · + 194u + 20i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
−0.304310u
40
− 2.16396u
39
+ ··· + 7.27239u + 4.10993
−0.590294u
40
− 4.39299u
39
+ ··· − 120.424u − 12.5909
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
0.232767u
40
+ 1.61999u
39
+ ··· + 9.73043u + 0.814296
−0.0989378u
40
− 0.493220u
39
+ ··· + 45.4975u + 5.81510
a
4
=
−0.127456u
40
− 1.18041u
39
+ ··· − 60.6558u − 7.42190
0.0887872u
40
+ 0.841967u
39
+ ··· + 62.8116u + 7.36730
a
2
=
−0.867404u
40
− 6.23818u
39
+ ··· − 84.2089u − 5.14086
−0.686402u
40
− 5.14804u
39
+ ··· − 155.965u − 16.4460
a
7
=
−0.290755u
40
− 2.42498u
39
+ ··· − 97.0747u − 10.9089
0.0561318u
40
+ 0.322093u
39
+ ··· − 19.3335u − 2.67658
a
12
=
−0.894604u
40
− 6.55695u
39
+ ··· − 113.151u − 8.48094
−0.590294u
40
− 4.39299u
39
+ ··· − 120.424u − 12.5909
a
3
=
0.629544u
40
+ 4.44605u
39
+ ··· + 46.3823u + 1.70770
0.599880u
40
+ 4.52470u
39
+ ··· + 165.072u + 17.8921
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.328629u
40
− 0.785952u
39
+ ··· + 308.120u + 23.6438
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
41
− u
40
+ ··· + 7u + 1
c
2
, c
6
, c
8
c
12
u
41
+ u
40
+ ··· + 16u + 8
c
3
u
41
+ 24u
40
+ ··· + 23118u + 1748
c
4
, c
7
u
41
+ u
40
+ ··· − 11u + 1
c
5
, c
9
, c
10
u
41
+ 8u
40
+ ··· + 194u + 20
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
41
+ 21y
40
+ ··· − 3y −1
c
2
, c
6
, c
8
c
12
y
41
+ 35y
40
+ ··· + 384y −64
c
3
y
41
+ 4y
40
+ ··· + 11912284y −3055504
c
4
, c
7
y
41
+ 37y
40
+ ··· + 29y −1
c
5
, c
9
, c
10
y
41
+ 40y
40
+ ··· − 484y −400
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.296481 + 0.899852I
a = 0.47000 + 1.47415I
b = 0.239416 − 0.465715I
−1.07101 − 1.40379I −24.1033 − 2.2010I
u = 0.296481 − 0.899852I
a = 0.47000 − 1.47415I
b = 0.239416 + 0.465715I
−1.07101 + 1.40379I −24.1033 + 2.2010I
u = −0.949933 + 0.547761I
a = −1.019870 − 0.650432I
b = −0.51711 + 1.38075I
7.5075 + 14.6287I −6.64605 − 9.04000I
u = −0.949933 − 0.547761I
a = −1.019870 + 0.650432I
b = −0.51711 − 1.38075I
7.5075 − 14.6287I −6.64605 + 9.04000I
u = −0.836872 + 0.326614I
a = 1.123520 + 0.469004I
b = 0.041114 − 1.137190I
6.37687 − 0.34568I −3.90013 + 0.61025I
u = −0.836872 − 0.326614I
a = 1.123520 − 0.469004I
b = 0.041114 + 1.137190I
6.37687 + 0.34568I −3.90013 − 0.61025I
u = −0.123273 + 1.152850I
a = −0.948871 + 0.267902I
b = 0.280654 − 0.908325I
8.03704 + 3.95126I 0
u = −0.123273 − 1.152850I
a = −0.948871 − 0.267902I
b = 0.280654 + 0.908325I
8.03704 − 3.95126I 0
u = −0.531136 + 0.588460I
a = 0.37159 + 1.46239I
b = 0.167628 − 1.242120I
7.61357 + 4.79301I −1.03971 − 6.50667I
u = −0.531136 − 0.588460I
a = 0.37159 − 1.46239I
b = 0.167628 + 1.242120I
7.61357 − 4.79301I −1.03971 + 6.50667I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.943969 + 0.763974I
a = −0.284764 − 0.405342I
b = 0.37025 + 1.38725I
8.03931 − 8.34303I 0
u = −0.943969 − 0.763974I
a = −0.284764 + 0.405342I
b = 0.37025 − 1.38725I
8.03931 + 8.34303I 0
u = 0.698688 + 1.035400I
a = 0.625759 − 0.631852I
b = −0.095443 + 1.262590I
4.65670 − 2.14457I 0
u = 0.698688 − 1.035400I
a = 0.625759 + 0.631852I
b = −0.095443 − 1.262590I
4.65670 + 2.14457I 0
u = 0.706973 + 0.226894I
a = 0.900475 − 0.017853I
b = 0.318501 + 1.110170I
2.64938 − 2.74377I −9.97316 + 2.99890I
u = 0.706973 − 0.226894I
a = 0.900475 + 0.017853I
b = 0.318501 − 1.110170I
2.64938 + 2.74377I −9.97316 − 2.99890I
u = −0.576720 + 0.444424I
a = −0.400332 − 0.410197I
b = −0.877603 − 0.143803I
−0.34799 + 3.97887I −12.7101 − 6.2808I
u = −0.576720 − 0.444424I
a = −0.400332 + 0.410197I
b = −0.877603 + 0.143803I
−0.34799 − 3.97887I −12.7101 + 6.2808I
u = −0.086074 + 1.291790I
a = −0.229475 − 0.428589I
b = −0.480662 + 0.342994I
3.27172 + 1.60167I 0
u = −0.086074 − 1.291790I
a = −0.229475 + 0.428589I
b = −0.480662 − 0.342994I
3.27172 − 1.60167I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.196101 + 1.347790I
a = −0.92032 + 1.58873I
b = −0.476991 − 1.161010I
7.50137 − 5.89018I 0
u = 0.196101 − 1.347790I
a = −0.92032 − 1.58873I
b = −0.476991 + 1.161010I
7.50137 + 5.89018I 0
u = −0.494897 + 0.345381I
a = 0.743683 + 0.881715I
b = 0.627955 − 0.059094I
−0.380401 − 0.421487I −13.78617 − 0.50090I
u = −0.494897 − 0.345381I
a = 0.743683 − 0.881715I
b = 0.627955 + 0.059094I
−0.380401 + 0.421487I −13.78617 + 0.50090I
u = −0.218244 + 1.383970I
a = 0.231060 − 0.661790I
b = −0.619071 − 0.079852I
4.97466 + 2.28943I 0
u = −0.218244 − 1.383970I
a = 0.231060 + 0.661790I
b = −0.619071 + 0.079852I
4.97466 − 2.28943I 0
u = −0.18727 + 1.48440I
a = −0.566341 + 0.343477I
b = 1.077180 + 0.055727I
5.94717 + 6.75189I 0
u = −0.18727 − 1.48440I
a = −0.566341 − 0.343477I
b = 1.077180 − 0.055727I
5.94717 − 6.75189I 0
u = 0.08631 + 1.51704I
a = 0.37205 − 1.80580I
b = 0.76083 + 1.29417I
12.88760 − 5.18387I 0
u = 0.08631 − 1.51704I
a = 0.37205 + 1.80580I
b = 0.76083 − 1.29417I
12.88760 + 5.18387I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.196155 + 0.437503I
a = −2.40557 + 1.20349I
b = −0.568477 − 1.145760I
6.24460 − 4.01332I −1.25065 + 4.31997I
u = 0.196155 − 0.437503I
a = −2.40557 − 1.20349I
b = −0.568477 + 1.145760I
6.24460 + 4.01332I −1.25065 − 4.31997I
u = −0.19318 + 1.51184I
a = −0.47092 − 2.41615I
b = −0.165997 + 1.401930I
14.4132 + 7.5144I 0
u = −0.19318 − 1.51184I
a = −0.47092 + 2.41615I
b = −0.165997 − 1.401930I
14.4132 − 7.5144I 0
u = −0.34109 + 1.50383I
a = −1.04827 − 1.63552I
b = −0.193839 + 1.203800I
12.30200 + 4.04048I 0
u = −0.34109 − 1.50383I
a = −1.04827 + 1.63552I
b = −0.193839 − 1.203800I
12.30200 − 4.04048I 0
u = −0.33736 + 1.56810I
a = 0.79574 + 1.76995I
b = 0.62408 − 1.42736I
14.3689 + 19.3341I 0
u = −0.33736 − 1.56810I
a = 0.79574 − 1.76995I
b = 0.62408 + 1.42736I
14.3689 − 19.3341I 0
u = −0.359249
a = 0.959189
b = 0.338732
−0.600677 −16.5800
u = −0.18105 + 1.72191I
a = 0.28126 + 1.52513I
b = −0.18178 − 1.52324I
16.7725 − 3.8927I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18105 − 1.72191I
a = 0.28126 − 1.52513I
b = −0.18178 + 1.52324I
16.7725 + 3.8927I 0
9
II. I
u
2
= h5.18 × 10
49
au
52
− 8.80 × 10
49
u
52
+ · · · + 9.53 × 10
49
a − 3.29 ×
10
50
, −1.62 × 10
46
au
52
− 9.07 × 10
45
u
52
+ · · · − 7.15 × 10
46
a + 1.45 ×
10
46
, u
53
− 3u
52
+ · · · + 6u − 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
a
−0.861283au
52
+ 1.46319u
52
+ ··· − 1.58490a + 5.46434
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
1.93540au
52
− 3.97835u
52
+ ··· + 4.09334a − 10.7382
−0.418054au
52
+ 0.604966u
52
+ ··· − 0.783563a + 1.41655
a
4
=
1.45012au
52
− 4.83707u
52
+ ··· + 3.99061a − 16.1840
0.379491au
52
− 1.47688u
52
+ ··· + 1.28379a − 3.21136
a
2
=
−0.962379au
52
+ 1.24877u
52
+ ··· − 3.12002a + 6.27204
0.435932au
52
− 0.803691u
52
+ ··· + 0.839841a − 4.11386
a
7
=
0.783563au
52
− 1.43416u
52
+ ··· + 1.15238a − 4.29860
−0.606716au
52
+ 1.43629u
52
+ ··· − 1.51735a + 3.57261
a
12
=
−0.861283au
52
+ 1.46319u
52
+ ··· − 0.584905a + 5.46434
−0.861283au
52
+ 1.46319u
52
+ ··· − 1.58490a + 5.46434
a
3
=
1.58490au
52
− 4.09334u
52
+ ··· + 4.18730a − 11.7934
0.439415au
52
− 0.733148u
52
+ ··· + 0.861283a + 1.17925
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.38328u
52
− 7.96262u
51
+ ··· − 15.2149u − 8.35008
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
106
− 11u
105
+ ··· − 292365u + 34945
c
2
, c
6
, c
8
c
12
u
106
− 3u
105
+ ··· − 2223u + 1483
c
3
(u
53
− 10u
52
+ ··· + 1907u − 181)
2
c
4
, c
7
u
106
+ 5u
105
+ ··· − 10087462u + 1845977
c
5
, c
9
, c
10
(u
53
− 3u
52
+ ··· + 6u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
106
+ 21y
105
+ ··· + 39625037985y + 1221153025
c
2
, c
6
, c
8
c
12
y
106
+ 63y
105
+ ··· + 84050135y + 2199289
c
3
(y
53
+ 14y
52
+ ··· − 619023y −32761)
2
c
4
, c
7
y
106
+ 23y
105
+ ··· + 310954538449436y + 3407631084529
c
5
, c
9
, c
10
(y
53
+ 57y
52
+ ··· − 12y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165800 + 1.012010I
a = −1.094450 − 0.095380I
b = −0.101040 − 1.202420I
6.54117 + 4.06649I 0
u = 0.165800 + 1.012010I
a = 0.433857 − 1.284040I
b = −0.506296 + 1.189990I
6.54117 + 4.06649I 0
u = 0.165800 − 1.012010I
a = −1.094450 + 0.095380I
b = −0.101040 + 1.202420I
6.54117 − 4.06649I 0
u = 0.165800 − 1.012010I
a = 0.433857 + 1.284040I
b = −0.506296 − 1.189990I
6.54117 − 4.06649I 0
u = −0.320431 + 0.885853I
a = 0.628969 + 0.703759I
b = 0.394636 − 1.088800I
1.29625 + 4.76203I −12.00000 − 7.37621I
u = −0.320431 + 0.885853I
a = −0.32366 − 1.55316I
b = −0.485105 + 0.237839I
1.29625 + 4.76203I −12.00000 − 7.37621I
u = −0.320431 − 0.885853I
a = 0.628969 − 0.703759I
b = 0.394636 + 1.088800I
1.29625 − 4.76203I −12.00000 + 7.37621I
u = −0.320431 − 0.885853I
a = −0.32366 + 1.55316I
b = −0.485105 − 0.237839I
1.29625 − 4.76203I −12.00000 + 7.37621I
u = 0.710053 + 0.578175I
a = −0.779976 + 0.261249I
b = −1.092580 − 0.045489I
3.02300 − 8.93280I −12.0000 + 8.9248I
u = 0.710053 + 0.578175I
a = −1.13394 + 1.05639I
b = −0.485181 − 1.231800I
3.02300 − 8.93280I −12.0000 + 8.9248I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.710053 − 0.578175I
a = −0.779976 − 0.261249I
b = −1.092580 + 0.045489I
3.02300 + 8.93280I −12.0000 − 8.9248I
u = 0.710053 − 0.578175I
a = −1.13394 − 1.05639I
b = −0.485181 + 1.231800I
3.02300 + 8.93280I −12.0000 − 8.9248I
u = 0.745217 + 0.349897I
a = 1.38397 − 0.60955I
b = 0.463875 + 1.229330I
2.91474 − 3.67297I −10.77436 + 2.95919I
u = 0.745217 + 0.349897I
a = −0.165723 − 0.424108I
b = −0.035039 + 0.341204I
2.91474 − 3.67297I −10.77436 + 2.95919I
u = 0.745217 − 0.349897I
a = 1.38397 + 0.60955I
b = 0.463875 − 1.229330I
2.91474 + 3.67297I −10.77436 − 2.95919I
u = 0.745217 − 0.349897I
a = −0.165723 + 0.424108I
b = −0.035039 − 0.341204I
2.91474 + 3.67297I −10.77436 − 2.95919I
u = 0.760227 + 0.235180I
a = 1.40140 − 0.75993I
b = 0.790773 − 0.648400I
2.33845 + 4.28571I −11.32554 − 7.01776I
u = 0.760227 + 0.235180I
a = −0.235745 + 0.321056I
b = 0.373530 − 1.039210I
2.33845 + 4.28571I −11.32554 − 7.01776I
u = 0.760227 − 0.235180I
a = 1.40140 + 0.75993I
b = 0.790773 + 0.648400I
2.33845 − 4.28571I −11.32554 + 7.01776I
u = 0.760227 − 0.235180I
a = −0.235745 − 0.321056I
b = 0.373530 + 1.039210I
2.33845 − 4.28571I −11.32554 + 7.01776I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142560 + 1.262400I
a = −1.050780 − 0.255874I
b = −0.120285 + 0.863933I
3.57551 + 1.17561I 0
u = −0.142560 + 1.262400I
a = 0.281677 − 0.588104I
b = −0.955485 + 0.189872I
3.57551 + 1.17561I 0
u = −0.142560 − 1.262400I
a = −1.050780 + 0.255874I
b = −0.120285 − 0.863933I
3.57551 − 1.17561I 0
u = −0.142560 − 1.262400I
a = 0.281677 + 0.588104I
b = −0.955485 − 0.189872I
3.57551 − 1.17561I 0
u = −1.183730 + 0.574246I
a = 0.878938 + 0.256019I
b = 0.57796 − 1.65346I
4.87494 + 4.47737I 0
u = −1.183730 + 0.574246I
a = −0.428863 − 0.749061I
b = −0.073896 + 1.102200I
4.87494 + 4.47737I 0
u = −1.183730 − 0.574246I
a = 0.878938 − 0.256019I
b = 0.57796 + 1.65346I
4.87494 − 4.47737I 0
u = −1.183730 − 0.574246I
a = −0.428863 + 0.749061I
b = −0.073896 − 1.102200I
4.87494 − 4.47737I 0
u = 0.383615 + 0.550853I
a = 0.296284 − 1.012710I
b = −0.305092 + 1.164560I
4.00302 − 0.21246I −6.41251 + 2.33360I
u = 0.383615 + 0.550853I
a = 0.435115 − 0.395260I
b = −0.461808 − 0.062250I
4.00302 − 0.21246I −6.41251 + 2.33360I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383615 − 0.550853I
a = 0.296284 + 1.012710I
b = −0.305092 − 1.164560I
4.00302 + 0.21246I −6.41251 − 2.33360I
u = 0.383615 − 0.550853I
a = 0.435115 + 0.395260I
b = −0.461808 + 0.062250I
4.00302 + 0.21246I −6.41251 − 2.33360I
u = −0.732211 + 1.139200I
a = −0.379690 − 1.037050I
b = −0.176094 + 1.080830I
6.83164 + 2.79575I 0
u = −0.732211 + 1.139200I
a = 0.234424 + 0.022259I
b = −0.76627 − 1.47031I
6.83164 + 2.79575I 0
u = −0.732211 − 1.139200I
a = −0.379690 + 1.037050I
b = −0.176094 − 1.080830I
6.83164 − 2.79575I 0
u = −0.732211 − 1.139200I
a = 0.234424 − 0.022259I
b = −0.76627 + 1.47031I
6.83164 − 2.79575I 0
u = 0.078360 + 1.381480I
a = 0.031873 + 1.046050I
b = −0.837965 − 1.021720I
6.12362 − 5.69143I 0
u = 0.078360 + 1.381480I
a = −0.99155 + 3.19832I
b = −0.136056 − 1.049730I
6.12362 − 5.69143I 0
u = 0.078360 − 1.381480I
a = 0.031873 − 1.046050I
b = −0.837965 + 1.021720I
6.12362 + 5.69143I 0
u = 0.078360 − 1.381480I
a = −0.99155 − 3.19832I
b = −0.136056 + 1.049730I
6.12362 + 5.69143I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.058991 + 1.396780I
a = 1.062550 − 0.008805I
b = 0.475274 − 0.740829I
3.44261 + 2.00436I 0
u = −0.058991 + 1.396780I
a = 1.193410 − 0.396669I
b = −1.45822 + 0.09321I
3.44261 + 2.00436I 0
u = −0.058991 − 1.396780I
a = 1.062550 + 0.008805I
b = 0.475274 + 0.740829I
3.44261 − 2.00436I 0
u = −0.058991 − 1.396780I
a = 1.193410 + 0.396669I
b = −1.45822 − 0.09321I
3.44261 − 2.00436I 0
u = −0.570795 + 0.179775I
a = 0.945476 − 0.124446I
b = 0.923520 + 0.127555I
−0.70537 − 1.38192I −15.6108 + 3.1019I
u = −0.570795 + 0.179775I
a = 0.836409 − 0.890935I
b = −0.189018 − 0.915447I
−0.70537 − 1.38192I −15.6108 + 3.1019I
u = −0.570795 − 0.179775I
a = 0.945476 + 0.124446I
b = 0.923520 − 0.127555I
−0.70537 + 1.38192I −15.6108 − 3.1019I
u = −0.570795 − 0.179775I
a = 0.836409 + 0.890935I
b = −0.189018 + 0.915447I
−0.70537 + 1.38192I −15.6108 − 3.1019I
u = 0.16387 + 1.41729I
a = 1.302090 − 0.402861I
b = 0.404933 + 0.947181I
9.30783 − 8.99341I 0
u = 0.16387 + 1.41729I
a = −0.49011 + 2.50301I
b = −0.51699 − 1.57230I
9.30783 − 8.99341I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16387 − 1.41729I
a = 1.302090 + 0.402861I
b = 0.404933 − 0.947181I
9.30783 + 8.99341I 0
u = 0.16387 − 1.41729I
a = −0.49011 − 2.50301I
b = −0.51699 + 1.57230I
9.30783 + 8.99341I 0
u = 0.22320 + 1.41867I
a = −0.495162 − 0.151068I
b = −0.114424 + 0.462619I
9.63534 − 2.43945I 0
u = 0.22320 + 1.41867I
a = −1.00514 + 2.10235I
b = 0.036584 − 1.212710I
9.63534 − 2.43945I 0
u = 0.22320 − 1.41867I
a = −0.495162 + 0.151068I
b = −0.114424 − 0.462619I
9.63534 + 2.43945I 0
u = 0.22320 − 1.41867I
a = −1.00514 − 2.10235I
b = 0.036584 + 1.212710I
9.63534 + 2.43945I 0
u = 0.501775 + 0.192333I
a = 1.42985 − 0.74793I
b = 0.50145 + 1.37772I
4.05191 − 6.64531I −9.1791 + 10.7763I
u = 0.501775 + 0.192333I
a = −1.69790 − 2.24036I
b = −0.238689 − 1.071730I
4.05191 − 6.64531I −9.1791 + 10.7763I
u = 0.501775 − 0.192333I
a = 1.42985 + 0.74793I
b = 0.50145 − 1.37772I
4.05191 + 6.64531I −9.1791 − 10.7763I
u = 0.501775 − 0.192333I
a = −1.69790 + 2.24036I
b = −0.238689 + 1.071730I
4.05191 + 6.64531I −9.1791 − 10.7763I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01462 + 1.46728I
a = 0.200669 + 0.640544I
b = −1.132310 − 0.660021I
4.83886 − 1.12887I 0
u = 0.01462 + 1.46728I
a = −0.26712 − 2.68797I
b = 0.043516 + 1.100890I
4.83886 − 1.12887I 0
u = 0.01462 − 1.46728I
a = 0.200669 − 0.640544I
b = −1.132310 + 0.660021I
4.83886 + 1.12887I 0
u = 0.01462 − 1.46728I
a = −0.26712 + 2.68797I
b = 0.043516 − 1.100890I
4.83886 + 1.12887I 0
u = 0.191180 + 0.495191I
a = 1.073640 + 0.709225I
b = 0.785121 − 0.050099I
−1.46223 − 0.91843I −13.3729 + 7.7566I
u = 0.191180 + 0.495191I
a = 0.34506 + 2.46564I
b = −0.239112 − 0.649465I
−1.46223 − 0.91843I −13.3729 + 7.7566I
u = 0.191180 − 0.495191I
a = 1.073640 − 0.709225I
b = 0.785121 + 0.050099I
−1.46223 + 0.91843I −13.3729 − 7.7566I
u = 0.191180 − 0.495191I
a = 0.34506 − 2.46564I
b = −0.239112 + 0.649465I
−1.46223 + 0.91843I −13.3729 − 7.7566I
u = −0.04064 + 1.48820I
a = 0.601502 − 0.231951I
b = 0.643761 + 0.618196I
8.39307 + 4.86079I 0
u = −0.04064 + 1.48820I
a = 0.05006 − 2.19788I
b = −0.51719 + 1.47742I
8.39307 + 4.86079I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04064 − 1.48820I
a = 0.601502 + 0.231951I
b = 0.643761 − 0.618196I
8.39307 − 4.86079I 0
u = −0.04064 − 1.48820I
a = 0.05006 + 2.19788I
b = −0.51719 − 1.47742I
8.39307 − 4.86079I 0
u = 0.04043 + 1.49038I
a = −0.441164 − 0.164774I
b = 0.957149 + 0.434176I
10.47290 − 1.35301I 0
u = 0.04043 + 1.49038I
a = −0.07772 + 2.12151I
b = 0.48833 − 1.34727I
10.47290 − 1.35301I 0
u = 0.04043 − 1.49038I
a = −0.441164 + 0.164774I
b = 0.957149 − 0.434176I
10.47290 + 1.35301I 0
u = 0.04043 − 1.49038I
a = −0.07772 − 2.12151I
b = 0.48833 + 1.34727I
10.47290 + 1.35301I 0
u = 0.26409 + 1.47574I
a = 0.009353 + 0.281949I
b = 0.352757 − 0.172771I
8.89216 − 7.33924I 0
u = 0.26409 + 1.47574I
a = −0.86508 + 2.04217I
b = −0.51365 − 1.36756I
8.89216 − 7.33924I 0
u = 0.26409 − 1.47574I
a = 0.009353 − 0.281949I
b = 0.352757 + 0.172771I
8.89216 + 7.33924I 0
u = 0.26409 − 1.47574I
a = −0.86508 − 2.04217I
b = −0.51365 + 1.36756I
8.89216 + 7.33924I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24922 + 1.55201I
a = −0.469789 − 0.422188I
b = 1.350200 − 0.068557I
10.0179 − 12.5057I 0
u = 0.24922 + 1.55201I
a = 0.69070 − 2.00160I
b = 0.54050 + 1.34699I
10.0179 − 12.5057I 0
u = 0.24922 − 1.55201I
a = −0.469789 + 0.422188I
b = 1.350200 + 0.068557I
10.0179 + 12.5057I 0
u = 0.24922 − 1.55201I
a = 0.69070 + 2.00160I
b = 0.54050 − 1.34699I
10.0179 + 12.5057I 0
u = 0.374085
a = 2.88440 + 0.51386I
b = −0.252055 − 0.829039I
4.56201 −5.65850
u = 0.374085
a = 2.88440 − 0.51386I
b = −0.252055 + 0.829039I
4.56201 −5.65850
u = −0.13724 + 1.62204I
a = −0.34113 − 1.66416I
b = 0.40688 + 1.71494I
15.9830 + 5.4339I 0
u = −0.13724 + 1.62204I
a = 0.25543 + 2.03224I
b = 0.335139 − 1.353430I
15.9830 + 5.4339I 0
u = −0.13724 − 1.62204I
a = −0.34113 + 1.66416I
b = 0.40688 − 1.71494I
15.9830 − 5.4339I 0
u = −0.13724 − 1.62204I
a = 0.25543 − 2.03224I
b = 0.335139 + 1.353430I
15.9830 − 5.4339I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.137843 + 0.321165I
a = −0.79809 + 1.36947I
b = 0.568829 − 1.166050I
2.04905 + 4.64753I −16.1218 − 0.9894I
u = 0.137843 + 0.321165I
a = −1.04701 − 5.62813I
b = −0.016950 − 0.512489I
2.04905 + 4.64753I −16.1218 − 0.9894I
u = 0.137843 − 0.321165I
a = −0.79809 − 1.36947I
b = 0.568829 + 1.166050I
2.04905 − 4.64753I −16.1218 + 0.9894I
u = 0.137843 − 0.321165I
a = −1.04701 + 5.62813I
b = −0.016950 + 0.512489I
2.04905 − 4.64753I −16.1218 + 0.9894I
u = −0.35704 + 1.62467I
a = −0.66966 − 1.53369I
b = −0.72403 + 1.51116I
12.1307 + 9.9759I 0
u = −0.35704 + 1.62467I
a = 0.59759 + 1.62302I
b = 0.260021 − 1.206480I
12.1307 + 9.9759I 0
u = −0.35704 − 1.62467I
a = −0.66966 + 1.53369I
b = −0.72403 − 1.51116I
12.1307 − 9.9759I 0
u = −0.35704 − 1.62467I
a = 0.59759 − 1.62302I
b = 0.260021 + 1.206480I
12.1307 − 9.9759I 0
u = 0.37616 + 1.73030I
a = 0.34715 − 1.44958I
b = 0.019349 + 1.149640I
8.25412 − 1.33361I 0
u = 0.37616 + 1.73030I
a = 0.373776 + 0.123190I
b = −1.72623 + 0.70422I
8.25412 − 1.33361I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37616 − 1.73030I
a = 0.34715 + 1.44958I
b = 0.019349 − 1.149640I
8.25412 + 1.33361I 0
u = 0.37616 − 1.73030I
a = 0.373776 − 0.123190I
b = −1.72623 − 0.70422I
8.25412 + 1.33361I 0
u = −0.149074 + 0.152659I
a = 2.39079 − 0.28224I
b = 1.231550 + 0.225810I
−1.06121 − 1.24134I −33.2596 + 9.1380I
u = −0.149074 + 0.152659I
a = 8.15308 + 0.11625I
b = −0.248584 − 0.841284I
−1.06121 − 1.24134I −33.2596 + 9.1380I
u = −0.149074 − 0.152659I
a = 2.39079 + 0.28224I
b = 1.231550 − 0.225810I
−1.06121 + 1.24134I −33.2596 − 9.1380I
u = −0.149074 − 0.152659I
a = 8.15308 − 0.11625I
b = −0.248584 + 0.841284I
−1.06121 + 1.24134I −33.2596 − 9.1380I
23
III. I
u
3
= h286u
15
a + 870u
15
+ · · · + 412a − 1440, u
15
a − 5u
15
+ · · · − 2a +
3, u
16
− 2u
15
+ · · · + 11u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
a
−0.311887au
15
− 0.948746u
15
+ ··· − 0.449291a + 1.57034
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−1.94875au
15
+ 0.393675u
15
+ ··· + 0.570338a + 1.21047
0.189749au
15
− 1.47874u
15
+ ··· − 1.31407a − 2.24209
a
4
=
0.824427au
15
− 3.11450u
15
+ ··· − 1.84733a + 3.53435
1.50382au
15
− 0.236641u
15
+ ··· − 1.35115a − 1.22901
a
2
=
−0.849509au
15
− 0.758997u
15
+ ··· − 1.55943a + 4.25627
0.418757au
15
+ 2.32279u
15
+ ··· + 0.617230a + 0.0174482
a
7
=
−1.31407au
15
− 0.242094u
15
+ ··· + 0.0370774a − 1.01309
0.958561au
15
− 1.57361u
15
+ ··· − 1.75900a − 3.08506
a
12
=
−0.311887au
15
− 0.948746u
15
+ ··· + 0.550709a + 1.57034
−0.311887au
15
− 0.948746u
15
+ ··· − 0.449291a + 1.57034
a
3
=
−0.449291au
15
+ 0.570338u
15
+ ··· + 0.191930a + 3.81461
1.23010au
15
+ 3.44820u
15
+ ··· − 0.311887a − 0.948746
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
15
− 6u
14
+ 50u
13
− 37u
12
+ 155u
11
− 89u
10
+ 210u
9
− 92u
8
+
73u
7
+ 13u
6
− 90u
5
+ 132u
4
− 63u
3
+ 120u
2
− 3u + 27
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
32
− 4u
31
+ ··· − 3u + 1
c
2
, c
8
u
32
+ 4u
31
+ ··· + 16u + 8
c
3
(u
16
− 5u
15
+ ··· − 4u + 1)
2
c
4
, c
7
u
32
+ 2u
31
+ ··· + 108u + 11
c
5
(u
16
+ 2u
15
+ ··· + 11u
2
+ 1)
2
c
6
, c
12
u
32
− 4u
31
+ ··· − 16u + 8
c
9
, c
10
(u
16
− 2u
15
+ ··· + 11u
2
+ 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
32
+ 12y
31
+ ··· + 19y + 1
c
2
, c
6
, c
8
c
12
y
32
+ 12y
31
+ ··· + 1344y + 64
c
3
(y
16
+ y
15
+ ··· − 4y + 1)
2
c
4
, c
7
y
32
+ 6y
31
+ ··· − 708y + 121
c
5
, c
9
, c
10
(y
16
+ 18y
15
+ ··· + 22y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885109 + 0.349966I
a = 1.218280 − 0.222557I
b = 0.63010 + 1.40168I
3.72418 − 4.45667I −6.48074 + 7.95119I
u = 0.885109 + 0.349966I
a = −0.467582 + 0.173710I
b = −0.170510 − 0.913317I
3.72418 − 4.45667I −6.48074 + 7.95119I
u = 0.885109 − 0.349966I
a = 1.218280 + 0.222557I
b = 0.63010 − 1.40168I
3.72418 + 4.45667I −6.48074 − 7.95119I
u = 0.885109 − 0.349966I
a = −0.467582 − 0.173710I
b = −0.170510 + 0.913317I
3.72418 + 4.45667I −6.48074 − 7.95119I
u = −0.028300 + 1.244790I
a = 0.403771 − 1.292850I
b = −0.749213 + 1.070340I
4.97809 + 4.94738I −10.20424 − 5.44012I
u = −0.028300 + 1.244790I
a = −1.31270 − 1.41867I
b = −0.002845 − 0.642593I
4.97809 + 4.94738I −10.20424 − 5.44012I
u = −0.028300 − 1.244790I
a = 0.403771 + 1.292850I
b = −0.749213 − 1.070340I
4.97809 − 4.94738I −10.20424 + 5.44012I
u = −0.028300 − 1.244790I
a = −1.31270 + 1.41867I
b = −0.002845 + 0.642593I
4.97809 − 4.94738I −10.20424 + 5.44012I
u = −0.350680 + 1.261700I
a = −0.105470 + 0.969664I
b = 0.167778 − 0.811319I
6.41137 + 2.01073I −3.72582 + 1.88569I
u = −0.350680 + 1.261700I
a = 0.044675 − 0.456439I
b = −0.795291 − 0.798520I
6.41137 + 2.01073I −3.72582 + 1.88569I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350680 − 1.261700I
a = −0.105470 − 0.969664I
b = 0.167778 + 0.811319I
6.41137 − 2.01073I −3.72582 − 1.88569I
u = −0.350680 − 1.261700I
a = 0.044675 + 0.456439I
b = −0.795291 + 0.798520I
6.41137 − 2.01073I −3.72582 − 1.88569I
u = −0.040347 + 1.317260I
a = 0.880036 − 0.606283I
b = −1.244970 + 0.297003I
2.67693 + 1.72947I −15.1210 − 2.2121I
u = −0.040347 + 1.317260I
a = −1.261780 + 0.312098I
b = −0.352705 + 0.765126I
2.67693 + 1.72947I −15.1210 − 2.2121I
u = −0.040347 − 1.317260I
a = 0.880036 + 0.606283I
b = −1.244970 − 0.297003I
2.67693 − 1.72947I −15.1210 + 2.2121I
u = −0.040347 − 1.317260I
a = −1.261780 − 0.312098I
b = −0.352705 − 0.765126I
2.67693 − 1.72947I −15.1210 + 2.2121I
u = 0.041332 + 0.605390I
a = 0.654840 − 0.834249I
b = 0.579131 + 1.181470I
2.51143 − 4.84190I −0.95877 + 6.52369I
u = 0.041332 + 0.605390I
a = −2.02957 + 3.61356I
b = −0.023092 − 0.730181I
2.51143 − 4.84190I −0.95877 + 6.52369I
u = 0.041332 − 0.605390I
a = 0.654840 + 0.834249I
b = 0.579131 − 1.181470I
2.51143 + 4.84190I −0.95877 − 6.52369I
u = 0.041332 − 0.605390I
a = −2.02957 − 3.61356I
b = −0.023092 + 0.730181I
2.51143 + 4.84190I −0.95877 − 6.52369I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22711 + 1.45555I
a = 0.743816 − 0.475853I
b = 0.287983 + 0.711932I
9.68939 − 7.99529I −1.24986 + 5.38298I
u = 0.22711 + 1.45555I
a = −0.75447 + 2.17487I
b = −0.56213 − 1.45146I
9.68939 − 7.99529I −1.24986 + 5.38298I
u = 0.22711 − 1.45555I
a = 0.743816 + 0.475853I
b = 0.287983 − 0.711932I
9.68939 + 7.99529I −1.24986 − 5.38298I
u = 0.22711 − 1.45555I
a = −0.75447 − 2.17487I
b = −0.56213 + 1.45146I
9.68939 + 7.99529I −1.24986 − 5.38298I
u = 0.38691 + 1.59563I
a = −0.53938 + 1.51502I
b = −0.008035 − 1.140650I
7.93298 − 1.46735I −8.76314 + 4.88302I
u = 0.38691 + 1.59563I
a = 0.266507 + 0.100955I
b = −1.30677 + 0.74563I
7.93298 − 1.46735I −8.76314 + 4.88302I
u = 0.38691 − 1.59563I
a = −0.53938 − 1.51502I
b = −0.008035 + 1.140650I
7.93298 + 1.46735I −8.76314 − 4.88302I
u = 0.38691 − 1.59563I
a = 0.266507 − 0.100955I
b = −1.30677 − 0.74563I
7.93298 + 1.46735I −8.76314 − 4.88302I
u = −0.121140 + 0.310338I
a = 1.249810 + 0.520105I
b = 1.303160 + 0.228621I
−0.91335 − 1.19226I 16.0035 − 7.2037I
u = −0.121140 + 0.310338I
a = −4.99079 − 2.40986I
b = 0.247408 + 0.863493I
−0.91335 − 1.19226I 16.0035 − 7.2037I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121140 − 0.310338I
a = 1.249810 − 0.520105I
b = 1.303160 − 0.228621I
−0.91335 + 1.19226I 16.0035 + 7.2037I
u = −0.121140 − 0.310338I
a = −4.99079 + 2.40986I
b = 0.247408 − 0.863493I
−0.91335 + 1.19226I 16.0035 + 7.2037I
30
IV.
I
u
4
= h−u
12
−3u
11
+· · ·+b+u, u
12
+2u
11
+· · ·+a−3u, u
13
+3u
12
+· · ·+4u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
−u
12
− 2u
11
+ ··· + 6u
2
+ 3u
u
12
+ 3u
11
+ ··· + 2u
2
− u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
10
+ 2u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 3u
5
− 8u
3
− 5u
2
− 5u
−u
10
− 3u
9
− 9u
8
− 16u
7
− 25u
6
− 27u
5
− 26u
4
− 15u
3
− 8u
2
− u
a
4
=
−u
11
− 3u
10
+ ··· − 9u − 3
−u
12
− 3u
11
+ ··· − 12u
2
− 2u
a
2
=
−u
12
− 2u
11
+ ··· − 3u
2
+ 4u
u
12
+ 3u
11
+ ··· + 5u + 1
a
7
=
−u
9
− 3u
8
− 9u
7
− 16u
6
− 25u
5
− 27u
4
− 26u
3
− 15u
2
− 8u − 1
−u
10
− 3u
9
− 9u
8
− 16u
7
− 24u
6
− 26u
5
− 23u
4
− 13u
3
− 6u
2
a
12
=
u
11
+ 3u
10
+ ··· + 8u
2
+ 2u
u
12
+ 3u
11
+ ··· + 2u
2
− u
a
3
=
u
11
+ 3u
10
+ ··· + 2u − 1
u
12
+ 3u
11
+ ··· + 8u
3
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
12
−3u
11
−21u
10
−31u
9
−84u
8
−100u
7
−157u
6
−130u
5
−153u
4
−70u
3
−77u
2
−16u−18
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
13
+ u
12
+ ··· + 3u
2
− 1
c
2
, c
8
u
13
+ u
12
+ ··· − u
2
− 1
c
3
u
13
+ 7u
12
+ ··· + 30u + 11
c
4
, c
7
u
13
− u
12
− u
11
+ 2u
10
− 6u
8
− 4u
7
+ u
6
+ 10u
5
+ 9u
4
+ 2u
3
− 4u
2
− 1
c
5
u
13
− 3u
12
+ ··· + 4u − 1
c
6
, c
12
u
13
− u
12
+ ··· + u
2
+ 1
c
9
, c
10
u
13
+ 3u
12
+ ··· + 4u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
13
− 7y
12
+ ··· + 6y −1
c
2
, c
6
, c
8
c
12
y
13
+ 13y
12
+ ··· − 2y −1
c
3
y
13
+ 5y
12
+ ··· + 20y −121
c
4
, c
7
y
13
− 3y
12
+ ··· − 8y −1
c
5
, c
9
, c
10
y
13
+ 13y
12
+ ··· − 2y −1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343544 + 0.921866I
a = 0.62202 − 1.56996I
b = 0.150421 + 0.585473I
−0.81818 + 1.45542I 6.61897 − 3.82327I
u = −0.343544 − 0.921866I
a = 0.62202 + 1.56996I
b = 0.150421 − 0.585473I
−0.81818 − 1.45542I 6.61897 + 3.82327I
u = −0.947385 + 0.780952I
a = 0.506075 + 0.646149I
b = 0.058701 − 1.324110I
5.42036 + 3.32162I −2.61851 − 4.59404I
u = −0.947385 − 0.780952I
a = 0.506075 − 0.646149I
b = 0.058701 + 1.324110I
5.42036 − 3.32162I −2.61851 + 4.59404I
u = 0.095927 + 1.286340I
a = −1.20827 + 1.74531I
b = −0.422793 − 1.243340I
8.20996 − 6.82298I −2.15916 + 7.91462I
u = 0.095927 − 1.286340I
a = −1.20827 − 1.74531I
b = −0.422793 + 1.243340I
8.20996 + 6.82298I −2.15916 − 7.91462I
u = −0.085790 + 1.341900I
a = 0.0993100 − 0.0234426I
b = −0.660490 + 0.270566I
2.26746 + 1.44605I −14.1870 − 1.9161I
u = −0.085790 − 1.341900I
a = 0.0993100 + 0.0234426I
b = −0.660490 − 0.270566I
2.26746 − 1.44605I −14.1870 + 1.9161I
u = 0.140856 + 0.497451I
a = −1.73165 + 0.18003I
b = 0.301110 − 1.268970I
5.28281 + 5.83734I −4.39076 − 6.29666I
u = 0.140856 − 0.497451I
a = −1.73165 − 0.18003I
b = 0.301110 + 1.268970I
5.28281 − 5.83734I −4.39076 + 6.29666I
34
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19091 + 1.57579I
a = −0.35933 − 2.03612I
b = −0.17604 + 1.43575I
13.5564 + 7.0066I −4.60599 − 3.77657I
u = −0.19091 − 1.57579I
a = −0.35933 + 2.03612I
b = −0.17604 − 1.43575I
13.5564 − 7.0066I −4.60599 + 3.77657I
u = −0.338303
a = −0.856316
b = 0.498180
−2.04028 −20.3150
35
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
13
+ u
12
+ ··· + 3u
2
− 1)(u
32
− 4u
31
+ ··· − 3u + 1)
· (u
41
− u
40
+ ··· + 7u + 1)(u
106
− 11u
105
+ ··· − 292365u + 34945)
c
2
, c
8
(u
13
+ u
12
+ ··· − u
2
− 1)(u
32
+ 4u
31
+ ··· + 16u + 8)
· (u
41
+ u
40
+ ··· + 16u + 8)(u
106
− 3u
105
+ ··· − 2223u + 1483)
c
3
(u
13
+ 7u
12
+ ··· + 30u + 11)(u
16
− 5u
15
+ ··· − 4u + 1)
2
· (u
41
+ 24u
40
+ ··· + 23118u + 1748)
· (u
53
− 10u
52
+ ··· + 1907u − 181)
2
c
4
, c
7
(u
13
− u
12
− u
11
+ 2u
10
− 6u
8
− 4u
7
+ u
6
+ 10u
5
+ 9u
4
+ 2u
3
− 4u
2
− 1)
· (u
32
+ 2u
31
+ ··· + 108u + 11)(u
41
+ u
40
+ ··· − 11u + 1)
· (u
106
+ 5u
105
+ ··· − 10087462u + 1845977)
c
5
(u
13
− 3u
12
+ ··· + 4u − 1)(u
16
+ 2u
15
+ ··· + 11u
2
+ 1)
2
· (u
41
+ 8u
40
+ ··· + 194u + 20)(u
53
− 3u
52
+ ··· + 6u − 1)
2
c
6
, c
12
(u
13
− u
12
+ ··· + u
2
+ 1)(u
32
− 4u
31
+ ··· − 16u + 8)
· (u
41
+ u
40
+ ··· + 16u + 8)(u
106
− 3u
105
+ ··· − 2223u + 1483)
c
9
, c
10
(u
13
+ 3u
12
+ ··· + 4u + 1)(u
16
− 2u
15
+ ··· + 11u
2
+ 1)
2
· (u
41
+ 8u
40
+ ··· + 194u + 20)(u
53
− 3u
52
+ ··· + 6u − 1)
2
36
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
13
− 7y
12
+ ··· + 6y −1)(y
32
+ 12y
31
+ ··· + 19y + 1)
· (y
41
+ 21y
40
+ ··· − 3y −1)
· (y
106
+ 21y
105
+ ··· + 39625037985y + 1221153025)
c
2
, c
6
, c
8
c
12
(y
13
+ 13y
12
+ ··· − 2y −1)(y
32
+ 12y
31
+ ··· + 1344y + 64)
· (y
41
+ 35y
40
+ ··· + 384y −64)
· (y
106
+ 63y
105
+ ··· + 84050135y + 2199289)
c
3
(y
13
+ 5y
12
+ ··· + 20y −121)(y
16
+ y
15
+ ··· − 4y + 1)
2
· (y
41
+ 4y
40
+ ··· + 11912284y −3055504)
· (y
53
+ 14y
52
+ ··· − 619023y −32761)
2
c
4
, c
7
(y
13
− 3y
12
+ ··· − 8y −1)(y
32
+ 6y
31
+ ··· − 708y + 121)
· (y
41
+ 37y
40
+ ··· + 29y −1)
· (y
106
+ 23y
105
+ ··· + 310954538449436y + 3407631084529)
c
5
, c
9
, c
10
(y
13
+ 13y
12
+ ··· − 2y −1)(y
16
+ 18y
15
+ ··· + 22y + 1)
2
· (y
41
+ 40y
40
+ ··· − 484y −400)(y
53
+ 57y
52
+ ··· − 12y −1)
2
37
