12a
1176
(K12a
1176
)
A knot diagram
1
Linearized knot diagam
4 10 8 9 11 12 3 1 2 5 6 7
Solving Sequence
5,11
6 12 7
2,10
3 8 9 4 1
c
5
c
11
c
6
c
10
c
2
c
7
c
9
c
4
c
1
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−49u
23
+ 263u
22
+ ··· + 4b + 236, 273u
23
− 1433u
22
+ ··· + 8a − 1244, u
24
− 7u
23
+ ··· − 32u + 8i
I
u
2
= h−1.44275 × 10
19
a
5
u
7
− 5.68398 × 10
19
a
4
u
7
+ ··· − 3.60536 × 10
20
a + 7.51047 × 10
20
,
6u
7
a
4
− 4u
7
a
3
+ ··· − 37a − 45, u
8
+ u
7
− 5u
6
− 4u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u − 1i
I
u
3
= h−u
8
+ 6u
6
− u
5
− 11u
4
+ 3u
3
+ 6u
2
+ b − u,
− u
12
− u
11
+ 10u
10
+ 9u
9
− 37u
8
− 31u
7
+ 61u
6
+ 52u
5
− 41u
4
− 42u
3
+ 5u
2
+ a + 10u + 2,
u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 85 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−49u
23
+ 263u
22
+ · · · + 4b + 236, 273u
23
− 1433u
22
+ · · · + 8a −
1244, u
24
− 7u
23
+ · · · − 32u + 8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−
273
8
u
23
+
1433
8
u
22
+ ··· − 532u +
311
2
49
4
u
23
−
263
4
u
22
+ ··· +
403
2
u − 59
a
10
=
−u
u
a
3
=
303
8
u
23
−
1559
8
u
22
+ ··· + 565u −
325
2
−
239
4
u
23
+
1233
4
u
22
+ ··· −
1791
2
u + 259
a
8
=
26.2500u
23
− 135.750u
22
+ ··· + 395.500u − 113.500
−
79
2
u
23
+ 205u
22
+ ··· −
1201
2
u + 174
a
9
=
−15.2500u
23
+ 81.7500u
22
+ ··· − 251.500u + 73.5000
2u
23
−
25
2
u
22
+ ··· +
93
2
u − 14
a
4
=
51u
23
−
1075
4
u
22
+ ··· +
3227
4
u − 235
−
129
4
u
23
+
685
4
u
22
+ ··· − 518u + 152
a
1
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 81u
23
− 432u
22
+ 8u
21
+ 3419u
20
− 3447u
19
− 11374u
18
+ 17236u
17
+ 18946u
16
−
40556u
15
− 11583u
14
+ 53859u
13
− 14035u
12
− 38970u
11
+ 33571u
10
+ 7682u
9
−
25123u
8
+ 11838u
7
+ 5007u
6
− 9421u
5
+ 3205u
4
+ 124u
3
− 1814u
2
+ 1300u − 374
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 18u
23
+ ··· + 2816u − 256
c
2
, c
3
, c
7
c
9
u
24
− u
23
+ ··· + u − 1
c
4
, c
8
u
24
− 6u
22
+ ··· − 2u + 1
c
5
, c
6
, c
10
c
11
, c
12
u
24
− 7u
23
+ ··· − 32u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 10y
23
+ ··· + 262144y + 65536
c
2
, c
3
, c
7
c
9
y
24
− 13y
23
+ ··· − 3y + 1
c
4
, c
8
y
24
− 12y
23
+ ··· − 30y + 1
c
5
, c
6
, c
10
c
11
, c
12
y
24
− 31y
23
+ ··· − 160y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.907236 + 0.435980I
a = −1.41635 + 0.54146I
b = 0.86042 − 1.37712I
1.84093 − 5.17326I 6.63681 + 8.84471I
u = −0.907236 − 0.435980I
a = −1.41635 − 0.54146I
b = 0.86042 + 1.37712I
1.84093 + 5.17326I 6.63681 − 8.84471I
u = −1.110420 + 0.108192I
a = −0.180104 − 0.437950I
b = 0.385921 − 0.238265I
5.73283 − 1.83988I 11.28356 + 2.30712I
u = −1.110420 − 0.108192I
a = −0.180104 + 0.437950I
b = 0.385921 + 0.238265I
5.73283 + 1.83988I 11.28356 − 2.30712I
u = 0.590338 + 0.652762I
a = −1.171600 − 0.599827I
b = −0.006346 + 1.289090I
−4.24228 − 4.48435I −0.15247 + 3.55403I
u = 0.590338 − 0.652762I
a = −1.171600 + 0.599827I
b = −0.006346 − 1.289090I
−4.24228 + 4.48435I −0.15247 − 3.55403I
u = −1.048400 + 0.428308I
a = 1.79332 − 0.68716I
b = −0.92291 + 1.62751I
−1.26907 − 12.76890I 2.91843 + 8.75350I
u = −1.048400 − 0.428308I
a = 1.79332 + 0.68716I
b = −0.92291 − 1.62751I
−1.26907 + 12.76890I 2.91843 − 8.75350I
u = 0.242387 + 0.711300I
a = 0.388011 − 0.226722I
b = −0.46013 − 1.55775I
−5.25345 + 8.92776I −1.31883 − 7.64206I
u = 0.242387 − 0.711300I
a = 0.388011 + 0.226722I
b = −0.46013 + 1.55775I
−5.25345 − 8.92776I −1.31883 + 7.64206I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33594
a = 1.98547
b = −1.43379
2.74446 −2.28800
u = −0.016484 + 0.578692I
a = 0.554305 + 0.154675I
b = 0.093232 + 1.039400I
−0.87333 + 1.64838I 3.09303 − 4.00385I
u = −0.016484 − 0.578692I
a = 0.554305 − 0.154675I
b = 0.093232 − 1.039400I
−0.87333 − 1.64838I 3.09303 + 4.00385I
u = −1.43642 + 0.29668I
a = −1.124190 + 0.697341I
b = 0.437158 − 0.696629I
2.30586 + 0.99863I 1.91156 − 3.99663I
u = −1.43642 − 0.29668I
a = −1.124190 − 0.697341I
b = 0.437158 + 0.696629I
2.30586 − 0.99863I 1.91156 + 3.99663I
u = 0.417711 + 0.252673I
a = 0.709564 + 0.673149I
b = 0.223162 − 0.102887I
0.898603 + 0.583790I 8.28194 − 3.24260I
u = 0.417711 − 0.252673I
a = 0.709564 − 0.673149I
b = 0.223162 + 0.102887I
0.898603 − 0.583790I 8.28194 + 3.24260I
u = 1.69916 + 0.12248I
a = −1.96502 − 1.07970I
b = 1.40767 + 1.48523I
10.97660 + 7.39354I 6.46638 − 6.79577I
u = 1.69916 − 0.12248I
a = −1.96502 + 1.07970I
b = 1.40767 − 1.48523I
10.97660 − 7.39354I 6.46638 + 6.79577I
u = 1.73198 + 0.11712I
a = 2.05259 + 1.20136I
b = −1.29425 − 1.66429I
8.5296 + 15.0189I 0. − 7.46096I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73198 − 0.11712I
a = 2.05259 − 1.20136I
b = −1.29425 + 1.66429I
8.5296 − 15.0189I 0. + 7.46096I
u = 1.74907 + 0.02053I
a = −0.329253 − 0.013460I
b = 0.383663 + 0.561786I
16.0549 + 2.3419I 10.98491 + 0.I
u = 1.74907 − 0.02053I
a = −0.329253 + 0.013460I
b = 0.383663 − 0.561786I
16.0549 − 2.3419I 10.98491 + 0.I
u = 1.84069
a = −0.608035
b = 0.218649
15.0349 0
7
II. I
u
2
= h−1.44 × 10
19
a
5
u
7
− 5.68 × 10
19
a
4
u
7
+ · · · − 3.61 × 10
20
a + 7.51 ×
10
20
, 6u
7
a
4
− 4u
7
a
3
+ · · · − 37a − 45, u
8
+ u
7
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
a
0.0404307a
5
u
7
+ 0.159284a
4
u
7
+ ··· + 1.01034a − 2.10469
a
10
=
−u
u
a
3
=
−0.148451a
5
u
7
+ 0.103349a
4
u
7
+ ··· + 0.884112a + 0.377445
0.188881a
5
u
7
+ 0.0559350a
4
u
7
+ ··· + 1.12623a − 2.48213
a
8
=
0.0237472a
5
u
7
− 0.301682a
4
u
7
+ ··· − 1.09617a + 1.05392
0.246102a
5
u
7
− 0.461154a
4
u
7
+ ··· + 0.187318a + 1.13432
a
9
=
−0.0788423a
5
u
7
+ 0.0602619a
4
u
7
+ ··· − 0.128977a − 1.90494
0.0146164a
5
u
7
+ 0.197157a
4
u
7
+ ··· + 1.71940a − 1.98699
a
4
=
0.352334a
5
u
7
− 0.681823a
4
u
7
+ ··· + 0.871371a + 0.687129
0.233033a
5
u
7
− 0.00868867a
4
u
7
+ ··· + 0.931401a − 2.76607
a
1
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
20156225182067388064
50977871582846282497
u
7
a
5
+
29676483013256697332
50977871582846282497
u
7
a
4
+ ··· +
21731100052659838880
50977871582846282497
a +
182955131839228302618
50977871582846282497
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
16
c
2
, c
3
, c
7
c
9
u
48
+ u
47
+ ··· + 628u + 199
c
4
, c
8
u
48
+ 3u
47
+ ··· − 34u − 1
c
5
, c
6
, c
10
c
11
, c
12
(u
8
+ u
7
− 5u
6
− 4u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
16
c
2
, c
3
, c
7
c
9
y
48
− 33y
47
+ ··· − 434980y + 39601
c
4
, c
8
y
48
+ 11y
47
+ ··· − 668y + 1
c
5
, c
6
, c
10
c
11
, c
12
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008780 + 0.254919I
a = −0.166634 − 0.860931I
b = −0.251079 − 0.246323I
2.43453 + 6.46095I 5.93215 − 7.49747I
u = 1.008780 + 0.254919I
a = 0.980017 + 0.579991I
b = −0.240136 − 0.202961I
2.43453 + 0.80471I 5.93215 − 1.53858I
u = 1.008780 + 0.254919I
a = 1.271630 + 0.216056I
b = −0.266125 − 1.193000I
−1.70306 + 3.63283I −0.59711 − 4.51802I
u = 1.008780 + 0.254919I
a = −0.68837 − 1.35983I
b = −0.25696 + 1.69313I
−1.70306 + 3.63283I −0.59711 − 4.51802I
u = 1.008780 + 0.254919I
a = 1.86379 + 0.32622I
b = −1.104540 − 0.808153I
2.43453 + 0.80471I 5.93215 − 1.53858I
u = 1.008780 + 0.254919I
a = −2.23689 − 0.90869I
b = 1.20089 + 1.63498I
2.43453 + 6.46095I 5.93215 − 7.49747I
u = 1.008780 − 0.254919I
a = −0.166634 + 0.860931I
b = −0.251079 + 0.246323I
2.43453 − 6.46095I 5.93215 + 7.49747I
u = 1.008780 − 0.254919I
a = 0.980017 − 0.579991I
b = −0.240136 + 0.202961I
2.43453 − 0.80471I 5.93215 + 1.53858I
u = 1.008780 − 0.254919I
a = 1.271630 − 0.216056I
b = −0.266125 + 1.193000I
−1.70306 − 3.63283I −0.59711 + 4.51802I
u = 1.008780 − 0.254919I
a = −0.68837 + 1.35983I
b = −0.25696 − 1.69313I
−1.70306 − 3.63283I −0.59711 + 4.51802I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008780 − 0.254919I
a = 1.86379 − 0.32622I
b = −1.104540 + 0.808153I
2.43453 − 0.80471I 5.93215 + 1.53858I
u = 1.008780 − 0.254919I
a = −2.23689 + 0.90869I
b = 1.20089 − 1.63498I
2.43453 − 6.46095I 5.93215 + 7.49747I
u = −0.772257
a = −1.364720 + 0.339718I
b = 0.223038 − 1.310810I
−0.55639 − 2.82812I 2.51294 + 2.97945I
u = −0.772257
a = −1.364720 − 0.339718I
b = 0.223038 + 1.310810I
−0.55639 + 2.82812I 2.51294 − 2.97945I
u = −0.772257
a = 1.70574 + 1.73282I
b = −0.72520 − 1.74104I
−0.55639 − 2.82812I 2.51294 + 2.97945I
u = −0.772257
a = 1.70574 − 1.73282I
b = −0.72520 + 1.74104I
−0.55639 + 2.82812I 2.51294 − 2.97945I
u = −0.772257
a = −2.61907
b = 0.283127
−4.69397 −4.01630
u = −0.772257
a = 3.52258
b = −1.61356
−4.69397 −4.01630
u = −0.240178 + 0.426557I
a = −0.900832 − 0.716113I
b = 0.49484 − 1.58079I
−1.41940 − 4.10344I 0.69028 + 8.06462I
u = −0.240178 + 0.426557I
a = −0.757692 − 0.900356I
b = −0.585477 − 1.229040I
−5.55698 − 1.27532I −5.83898 + 5.08518I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.240178 + 0.426557I
a = 0.540126 − 0.065165I
b = −0.772436 + 0.638956I
−1.41940 + 1.55280I 0.69028 + 2.10573I
u = −0.240178 + 0.426557I
a = 1.70370 + 0.18215I
b = −0.068775 + 1.092420I
−1.41940 + 1.55280I 0.69028 + 2.10573I
u = −0.240178 + 0.426557I
a = −1.26218 + 1.32424I
b = −0.252731 − 0.328836I
−1.41940 − 4.10344I 0.69028 + 8.06462I
u = −0.240178 + 0.426557I
a = 0.86475 + 1.86092I
b = −0.208159 + 0.992906I
−5.55698 − 1.27532I −5.83898 + 5.08518I
u = −0.240178 − 0.426557I
a = −0.900832 + 0.716113I
b = 0.49484 + 1.58079I
−1.41940 + 4.10344I 0.69028 − 8.06462I
u = −0.240178 − 0.426557I
a = −0.757692 + 0.900356I
b = −0.585477 + 1.229040I
−5.55698 + 1.27532I −5.83898 − 5.08518I
u = −0.240178 − 0.426557I
a = 0.540126 + 0.065165I
b = −0.772436 − 0.638956I
−1.41940 − 1.55280I 0.69028 − 2.10573I
u = −0.240178 − 0.426557I
a = 1.70370 − 0.18215I
b = −0.068775 − 1.092420I
−1.41940 − 1.55280I 0.69028 − 2.10573I
u = −0.240178 − 0.426557I
a = −1.26218 − 1.32424I
b = −0.252731 + 0.328836I
−1.41940 + 4.10344I 0.69028 − 8.06462I
u = −0.240178 − 0.426557I
a = 0.86475 − 1.86092I
b = −0.208159 − 0.992906I
−5.55698 + 1.27532I −5.83898 − 5.08518I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67992
a = −1.22399 + 0.97102I
b = 0.58572 − 1.53466I
8.26521 − 2.82812I 3.33185 + 2.97945I
u = 1.67992
a = −1.22399 − 0.97102I
b = 0.58572 + 1.53466I
8.26521 + 2.82812I 3.33185 − 2.97945I
u = 1.67992
a = −2.06031
b = 0.835472
4.12763 −3.19740
u = 1.67992
a = 1.71698 + 2.02515I
b = −1.19582 − 2.17322I
8.26521 − 2.82812I 3.33185 + 2.97945I
u = 1.67992
a = 1.71698 − 2.02515I
b = −1.19582 + 2.17322I
8.26521 + 2.82812I 3.33185 − 2.97945I
u = 1.67992
a = 3.36647
b = −2.45190
4.12763 −3.19740
u = −1.72243 + 0.06628I
a = 1.108900 − 0.735799I
b = −0.423485 + 1.321650I
8.02419 − 4.93524I −0.03508 + 2.99422I
u = −1.72243 + 0.06628I
a = 0.564850 − 0.069165I
b = −0.193774 − 0.376350I
12.16180 − 2.10712I 6.49419 + 0.01478I
u = −1.72243 + 0.06628I
a = 0.091340 + 0.181993I
b = −0.257409 + 0.636530I
12.1618 − 7.7634I 6.49419 + 5.97367I
u = −1.72243 + 0.06628I
a = −0.62469 + 1.84935I
b = 0.07951 − 2.00864I
8.02419 − 4.93524I −0.03508 + 2.99422I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.72243 + 0.06628I
a = 2.17225 − 0.62127I
b = −1.51193 + 0.90608I
12.16180 − 2.10712I 6.49419 + 0.01478I
u = −1.72243 + 0.06628I
a = −2.46292 + 1.34903I
b = 1.70346 − 1.68486I
12.1618 − 7.7634I 6.49419 + 5.97367I
u = −1.72243 − 0.06628I
a = 1.108900 + 0.735799I
b = −0.423485 − 1.321650I
8.02419 + 4.93524I −0.03508 − 2.99422I
u = −1.72243 − 0.06628I
a = 0.564850 + 0.069165I
b = −0.193774 + 0.376350I
12.16180 + 2.10712I 6.49419 − 0.01478I
u = −1.72243 − 0.06628I
a = 0.091340 − 0.181993I
b = −0.257409 − 0.636530I
12.1618 + 7.7634I 6.49419 − 5.97367I
u = −1.72243 − 0.06628I
a = −0.62469 − 1.84935I
b = 0.07951 + 2.00864I
8.02419 + 4.93524I −0.03508 − 2.99422I
u = −1.72243 − 0.06628I
a = 2.17225 + 0.62127I
b = −1.51193 − 0.90608I
12.16180 + 2.10712I 6.49419 − 0.01478I
u = −1.72243 − 0.06628I
a = −2.46292 − 1.34903I
b = 1.70346 + 1.68486I
12.1618 + 7.7634I 6.49419 − 5.97367I
15
III. I
u
3
= h−u
8
+ 6u
6
− u
5
− 11u
4
+ 3u
3
+ 6u
2
+ b − u, −u
12
− u
11
+ · · · +
a + 2, u
13
− 10u
11
+ · · · − 6u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
u
12
+ u
11
+ ··· − 10u − 2
u
8
− 6u
6
+ u
5
+ 11u
4
− 3u
3
− 6u
2
+ u
a
10
=
−u
u
a
3
=
u
12
− 10u
10
+ ··· − 9u − 1
u
11
− 8u
9
+ u
8
+ 23u
7
− 5u
6
− 28u
5
+ 7u
4
+ 12u
3
− 2u
2
− 1
a
8
=
u
10
+ u
9
− 8u
8
− 7u
7
+ 23u
6
+ 18u
5
− 27u
4
− 21u
3
+ 8u
2
+ 10u + 3
−u
12
+ 9u
10
− u
9
− 30u
8
+ 5u
7
+ 45u
6
− 6u
5
− 29u
4
− u
3
+ 6u
2
+ 2u
a
9
=
u
10
− 8u
8
− u
7
+ 23u
6
+ 7u
5
− 28u
4
− 15u
3
+ 11u
2
+ 10u + 2
−u
12
+ 9u
10
− 30u
8
− u
7
+ 45u
6
+ 5u
5
− 29u
4
− 7u
3
+ 6u
2
+ 2u
a
4
=
−u
12
− u
11
+ ··· + 7u + 5
−u
3
+ 2u
a
1
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
12
− 38u
10
+ 131u
8
+ 3u
7
− 193u
6
− 21u
5
+ 101u
4
+ 40u
3
+ 8u
2
− 13u − 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 5u
12
+ ··· + 4u
2
− 1
c
2
, c
7
u
13
+ u
12
+ ··· + u + 1
c
3
, c
9
u
13
− u
12
+ ··· + u − 1
c
4
, c
8
u
13
+ u
10
− 4u
9
+ u
8
− u
7
+ 3u
5
− 2u
4
+ u
3
− 2u
2
+ 1
c
5
, c
6
u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1
c
10
, c
11
, c
12
u
13
− 10u
11
+ 38u
9
− u
8
− 68u
7
+ 6u
6
+ 57u
5
− 11u
4
− 18u
3
+ 6u
2
− 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 9y
12
+ ··· + 8y −1
c
2
, c
3
, c
7
c
9
y
13
− 13y
12
+ ··· + 13y −1
c
4
, c
8
y
13
− 8y
11
− 3y
10
+ 20y
9
+ 9y
8
− 19y
7
− 6y
6
+ 9y
5
− 7y
3
+ 4y −1
c
5
, c
6
, c
10
c
11
, c
12
y
13
− 20y
12
+ ··· + 12y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900642 + 0.211290I
a = −0.806576 + 0.876637I
b = 0.07621 − 1.64069I
0.15794 − 4.22361I 4.67376 + 7.74732I
u = −0.900642 − 0.211290I
a = −0.806576 − 0.876637I
b = 0.07621 + 1.64069I
0.15794 + 4.22361I 4.67376 − 7.74732I
u = 0.835287
a = 3.11335
b = −1.13883
−4.06419 11.1840
u = 1.349780 + 0.188354I
a = 1.53326 + 0.73818I
b = −1.030280 − 0.706563I
3.33191 − 0.41146I 8.75330 + 4.03305I
u = 1.349780 − 0.188354I
a = 1.53326 − 0.73818I
b = −1.030280 + 0.706563I
3.33191 + 0.41146I 8.75330 − 4.03305I
u = −1.48165
a = −1.60389
b = 0.723464
0.435715 −0.725220
u = −0.246497 + 0.330591I
a = 2.16431 − 0.42060I
b = −0.44057 + 1.37835I
−2.02748 + 2.39614I −5.69138 − 3.50014I
u = −0.246497 − 0.330591I
a = 2.16431 + 0.42060I
b = −0.44057 − 1.37835I
−2.02748 − 2.39614I −5.69138 + 3.50014I
u = 0.333287
a = −4.10575
b = −0.312491
−5.76311 −9.04720
u = −1.68760
a = 2.68033
b = −1.63543
4.96623 8.76410
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70777 + 0.05845I
a = −0.84719 − 1.38187I
b = 0.35559 + 1.80257I
9.50181 + 5.30924I 6.33383 − 5.02700I
u = 1.70777 − 0.05845I
a = −0.84719 + 1.38187I
b = 0.35559 − 1.80257I
9.50181 − 5.30924I 6.33383 + 5.02700I
u = −1.82016
a = 0.828351
b = −0.558619
15.3957 16.6850
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
16
)(u
13
− 5u
12
+ ··· + 4u
2
− 1)
· (u
24
− 18u
23
+ ··· + 2816u − 256)
c
2
, c
7
(u
13
+ u
12
+ ··· + u + 1)(u
24
− u
23
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· + 628u + 199)
c
3
, c
9
(u
13
− u
12
+ ··· + u − 1)(u
24
− u
23
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· + 628u + 199)
c
4
, c
8
(u
13
+ u
10
− 4u
9
+ u
8
− u
7
+ 3u
5
− 2u
4
+ u
3
− 2u
2
+ 1)
· (u
24
− 6u
22
+ ··· − 2u + 1)(u
48
+ 3u
47
+ ··· − 34u − 1)
c
5
, c
6
(u
8
+ u
7
− 5u
6
− 4u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u − 1)
6
· (u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1)
· (u
24
− 7u
23
+ ··· − 32u + 8)
c
10
, c
11
, c
12
(u
8
+ u
7
− 5u
6
− 4u
5
+ 7u
4
+ 4u
3
− 2u
2
− 2u − 1)
6
· (u
13
− 10u
11
+ 38u
9
− u
8
− 68u
7
+ 6u
6
+ 57u
5
− 11u
4
− 18u
3
+ 6u
2
− 1)
· (u
24
− 7u
23
+ ··· − 32u + 8)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
16
)(y
13
− 9y
12
+ ··· + 8y −1)
· (y
24
− 10y
23
+ ··· + 262144y + 65536)
c
2
, c
3
, c
7
c
9
(y
13
− 13y
12
+ ··· + 13y −1)(y
24
− 13y
23
+ ··· − 3y + 1)
· (y
48
− 33y
47
+ ··· − 434980y + 39601)
c
4
, c
8
(y
13
− 8y
11
− 3y
10
+ 20y
9
+ 9y
8
− 19y
7
− 6y
6
+ 9y
5
− 7y
3
+ 4y −1)
· (y
24
− 12y
23
+ ··· − 30y + 1)(y
48
+ 11y
47
+ ··· − 668y + 1)
c
5
, c
6
, c
10
c
11
, c
12
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
6
· (y
13
− 20y
12
+ ··· + 12y −1)(y
24
− 31y
23
+ ··· − 160y + 64)
22
