12n
0759
(K12n
0759
)
A knot diagram
1
Linearized knot diagam
4 12 8 1 12 2 11 5 2 8 7 9
Solving Sequence
8,11
7
2,12
3 4 1 6 5 10 9
c
7
c
11
c
2
c
3
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h471524796u
36
− 5108104574u
35
+ ··· + 1495255511b + 27229387303,
12296434297u
36
− 69707922846u
35
+ ··· + 14952555110a − 105681891942,
u
37
− 8u
36
+ ··· + 54u − 10i
I
u
2
= h−u
17
a − u
17
+ ··· + b + a, u
16
a + 2u
17
+ ··· + a + 5, u
18
+ 5u
17
+ ··· + 3u − 1i
I
u
3
= hu
16
+ 5u
15
+ ··· + b + 3, −3u
17
− 17u
16
+ ··· + 2a − 11, u
18
+ 5u
17
+ ··· + 13u + 2i
* 3 irreducible components of dim
C
= 0, with total 91 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
=
h4.72×10
8
u
36
−5.11×10
9
u
35
+· · · +1.50×10
9
b+2.72×10
10
, 1.23×10
10
u
36
−
6.97 × 10
10
u
35
+ · · · + 1.50 × 10
10
a − 1.06 × 10
11
, u
37
− 8u
36
+ · · · + 54u − 10i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
2
=
−0.822363u
36
+ 4.66194u
35
+ ··· − 40.6849u + 7.06781
−0.315347u
36
+ 3.41621u
35
+ ··· + 84.0045u − 18.2105
a
12
=
u
u
3
+ u
a
3
=
1.82105u
36
− 14.2531u
35
+ ··· − 80.8722u + 14.3323
1.02354u
36
− 7.91667u
35
+ ··· − 50.2937u + 11.3771
a
4
=
0.797516u
36
− 6.33640u
35
+ ··· − 30.5786u + 2.95520
1.02354u
36
− 7.91667u
35
+ ··· − 50.2937u + 11.3771
a
1
=
1.17552u
36
− 8.86307u
35
+ ··· − 58.6629u + 12.1412
0.968604u
36
− 9.68456u
35
+ ··· − 102.310u + 21.5655
a
6
=
4.28726u
36
− 34.0282u
35
+ ··· − 123.485u + 23.2929
−2.54465u
36
+ 18.9069u
35
+ ··· + 0.613399u + 3.92450
a
5
=
−0.392450u
36
+ 5.68425u
35
+ ··· + 113.422u − 20.8057
1.18047u
36
− 6.84211u
35
+ ··· + 67.8836u − 17.4261
a
10
=
−u
u
a
9
=
2.92308u
36
− 21.9635u
35
+ ··· − 55.9879u + 8.79131
−2.66058u
36
+ 17.9266u
35
+ ··· + 21.3706u − 3.21429
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
12741675491
1495255511
u
36
+
101934190202
1495255511
u
35
+ ··· +
510036125358
1495255511
u −
91985646542
1495255511
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
37
− 11u
36
+ ··· − 158u + 10
c
2
, c
6
u
37
+ 20u
35
+ ··· + 4u + 1
c
3
, c
9
u
37
− u
36
+ ··· + 286u + 121
c
5
u
37
− 32u
36
+ ··· − 3538944u + 262144
c
7
, c
10
, c
11
u
37
+ 8u
36
+ ··· + 54u + 10
c
8
, c
12
u
37
+ u
36
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
37
+ 23y
36
+ ··· + 1464y −100
c
2
, c
6
y
37
+ 40y
36
+ ··· − 24y −1
c
3
, c
9
y
37
+ 19y
36
+ ··· − 31218y −14641
c
5
y
37
− 6y
36
+ ··· + 51539607552y −68719476736
c
7
, c
10
, c
11
y
37
+ 32y
36
+ ··· + 1176y −100
c
8
, c
12
y
37
+ 21y
36
+ ··· + y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139810 + 0.947636I
a = 1.72762 − 0.66054I
b = −1.14617 − 0.94052I
2.14502 − 0.46485I −1.94282 − 0.92392I
u = −0.139810 − 0.947636I
a = 1.72762 + 0.66054I
b = −1.14617 + 0.94052I
2.14502 + 0.46485I −1.94282 + 0.92392I
u = 1.039010 + 0.115439I
a = −0.192987 + 0.037881I
b = −0.62037 + 1.63193I
10.1014 + 11.1664I 0. − 6.23795I
u = 1.039010 − 0.115439I
a = −0.192987 − 0.037881I
b = −0.62037 − 1.63193I
10.1014 − 11.1664I 0. + 6.23795I
u = 0.916293 + 0.067951I
a = 0.097764 + 0.172517I
b = 0.46237 − 1.48507I
5.40488 + 5.68156I −1.59495 − 5.13236I
u = 0.916293 − 0.067951I
a = 0.097764 − 0.172517I
b = 0.46237 + 1.48507I
5.40488 − 5.68156I −1.59495 + 5.13236I
u = 0.885871 + 0.114565I
a = 0.281357 + 0.113956I
b = −0.25335 − 1.47096I
9.31086 + 0.52432I 3.94650 − 0.50356I
u = 0.885871 − 0.114565I
a = 0.281357 − 0.113956I
b = −0.25335 + 1.47096I
9.31086 − 0.52432I 3.94650 + 0.50356I
u = 0.056118 + 1.111250I
a = −1.50526 + 0.77231I
b = 1.324570 + 0.077249I
0.897651 + 0.070840I −4.00000 + 0.I
u = 0.056118 − 1.111250I
a = −1.50526 − 0.77231I
b = 1.324570 − 0.077249I
0.897651 − 0.070840I −4.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.609754 + 0.620108I
a = 0.782999 + 0.288087I
b = 0.627363 − 0.626705I
2.48681 − 2.57040I −2.36259 + 3.28826I
u = −0.609754 − 0.620108I
a = 0.782999 − 0.288087I
b = 0.627363 + 0.626705I
2.48681 + 2.57040I −2.36259 − 3.28826I
u = 0.086875 + 1.167150I
a = 1.63975 + 0.44424I
b = −1.11741 − 0.88125I
−4.39474 + 1.30377I −15.9395 + 0.I
u = 0.086875 − 1.167150I
a = 1.63975 − 0.44424I
b = −1.11741 + 0.88125I
−4.39474 − 1.30377I −15.9395 + 0.I
u = −0.245173 + 1.209770I
a = −0.978004 − 0.158481I
b = 0.640982 + 1.102120I
−0.79010 − 3.56350I 0
u = −0.245173 − 1.209770I
a = −0.978004 + 0.158481I
b = 0.640982 − 1.102120I
−0.79010 + 3.56350I 0
u = 0.443655 + 1.201050I
a = −1.79320 + 0.50024I
b = 0.819804 − 0.963504I
5.97221 + 4.23436I 0
u = 0.443655 − 1.201050I
a = −1.79320 − 0.50024I
b = 0.819804 + 0.963504I
5.97221 − 4.23436I 0
u = 0.435560 + 1.215640I
a = −1.06951 + 0.99559I
b = 0.263581 − 1.008440I
1.85513 − 0.84698I 0
u = 0.435560 − 1.215640I
a = −1.06951 − 0.99559I
b = 0.263581 + 1.008440I
1.85513 + 0.84698I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.295335 + 0.570556I
a = −0.576122 + 0.317004I
b = 0.130785 + 0.394729I
−0.109537 − 1.239830I −1.37448 + 5.92241I
u = −0.295335 − 0.570556I
a = −0.576122 − 0.317004I
b = 0.130785 − 0.394729I
−0.109537 + 1.239830I −1.37448 − 5.92241I
u = 0.614437 + 1.236310I
a = 0.902398 − 0.941361I
b = 0.392590 + 1.064250I
6.68893 − 5.37975I 0
u = 0.614437 − 1.236310I
a = 0.902398 + 0.941361I
b = 0.392590 − 1.064250I
6.68893 + 5.37975I 0
u = 0.434151 + 1.339220I
a = 1.76152 − 0.74711I
b = −1.14193 + 1.58433I
1.00539 + 10.52360I 0
u = 0.434151 − 1.339220I
a = 1.76152 + 0.74711I
b = −1.14193 − 1.58433I
1.00539 − 10.52360I 0
u = 0.38979 + 1.37969I
a = 0.93958 − 1.24376I
b = −0.37436 + 1.70929I
4.58667 + 5.11314I 0
u = 0.38979 − 1.37969I
a = 0.93958 + 1.24376I
b = −0.37436 − 1.70929I
4.58667 − 5.11314I 0
u = 0.48491 + 1.39397I
a = −1.66833 + 0.76934I
b = 1.01582 − 1.92652I
5.3737 + 16.5878I 0
u = 0.48491 − 1.39397I
a = −1.66833 − 0.76934I
b = 1.01582 + 1.92652I
5.3737 − 16.5878I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456996 + 0.144661I
a = −0.60975 − 1.37109I
b = −0.583726 − 0.575126I
3.13815 − 0.83302I −1.02036 + 3.40722I
u = −0.456996 − 0.144661I
a = −0.60975 + 1.37109I
b = −0.583726 + 0.575126I
3.13815 + 0.83302I −1.02036 − 3.40722I
u = −0.05084 + 1.54951I
a = 0.027721 + 0.450422I
b = 0.223004 − 0.781521I
−7.37098 − 2.21708I 0
u = −0.05084 − 1.54951I
a = 0.027721 − 0.450422I
b = 0.223004 + 0.781521I
−7.37098 + 2.21708I 0
u = −0.12383 + 1.62650I
a = 0.376630 − 0.307169I
b = −0.973816 + 0.280615I
−5.40481 − 5.27286I 0
u = −0.12383 − 1.62650I
a = 0.376630 + 0.307169I
b = −0.973816 − 0.280615I
−5.40481 + 5.27286I 0
u = 0.270127
a = −2.08837
b = 0.620523
−1.19161 −2.79840
8
II.
I
u
2
= h−u
17
a−u
17
+· · ·+b+a, u
16
a+2u
17
+· · ·+a+5, u
18
+5u
17
+· · ·+3u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
2
=
a
u
17
a + u
17
+ ··· − a + 2u
a
12
=
u
u
3
+ u
a
3
=
−u
17
a − 4u
16
a + ··· + 2a − u
−u
17
a − 4u
16
a + ··· + a + 1
a
4
=
u
16
+ 4u
15
+ ··· + a − 1
−u
17
a − 4u
16
a + ··· + a + 1
a
1
=
−u
16
− 4u
15
+ ··· + a + 2
u
17
a + 4u
16
a + ··· − a − 1
a
6
=
u
15
a − u
16
+ ··· − a + 3
u
17
a + 4u
16
a + ··· − a − 1
a
5
=
u
15
a − u
16
+ ··· − a + 3
u
17
a + 4u
16
a + ··· − a − 1
a
10
=
−u
u
a
9
=
−u
16
− 6u
15
+ ··· − a − 2
u
17
a + 4u
16
a + ··· − a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
16
+ 20u
15
+ 72u
14
+ 180u
13
+ 356u
12
+ 572u
11
+ 744u
10
+
808u
9
+ 692u
8
+ 460u
7
+ 204u
6
+ 12u
5
− 36u
4
− 32u
3
+ 8u
2
+ 20u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
18
+ 5u
17
+ ··· + 3u − 1)
2
c
2
, c
6
u
36
− 5u
35
+ ··· − 8364u + 2329
c
3
, c
9
u
36
− u
35
+ ··· + 8146u + 1229
c
5
(u + 1)
36
c
7
, c
10
, c
11
(u
18
− 5u
17
+ ··· − 3u − 1)
2
c
8
, c
12
u
36
+ 5u
35
+ ··· + 4u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
(y
18
+ 13y
17
+ ··· − 11y + 1)
2
c
2
, c
6
y
36
+ 15y
35
+ ··· + 24442532y + 5424241
c
3
, c
9
y
36
+ 23y
35
+ ··· − 9149824y + 1510441
c
5
(y −1)
36
c
8
, c
12
y
36
− 5y
35
+ ··· + 20y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.912787
a = −0.316703 + 0.131353I
b = −0.415001 − 1.265310I
4.47245 −3.52670
u = −0.912787
a = −0.316703 − 0.131353I
b = −0.415001 + 1.265310I
4.47245 −3.52670
u = 0.193687 + 1.098120I
a = 0.25197 − 1.40720I
b = −0.00135 + 2.27636I
0.62200 + 7.06147I −4.14650 − 10.25752I
u = 0.193687 + 1.098120I
a = −2.64599 − 0.58963I
b = 1.112400 − 0.674637I
0.62200 + 7.06147I −4.14650 − 10.25752I
u = 0.193687 − 1.098120I
a = 0.25197 + 1.40720I
b = −0.00135 − 2.27636I
0.62200 − 7.06147I −4.14650 + 10.25752I
u = 0.193687 − 1.098120I
a = −2.64599 + 0.58963I
b = 1.112400 + 0.674637I
0.62200 − 7.06147I −4.14650 + 10.25752I
u = −1.098040 + 0.205475I
a = 0.433613 + 0.557861I
b = 0.95722 + 2.11469I
7.71440 − 1.25989I 8.84485 + 4.81225I
u = −1.098040 + 0.205475I
a = −0.067996 + 0.235470I
b = 0.055833 − 0.954772I
7.71440 − 1.25989I 8.84485 + 4.81225I
u = −1.098040 − 0.205475I
a = 0.433613 − 0.557861I
b = 0.95722 − 2.11469I
7.71440 + 1.25989I 8.84485 − 4.81225I
u = −1.098040 − 0.205475I
a = −0.067996 − 0.235470I
b = 0.055833 + 0.954772I
7.71440 + 1.25989I 8.84485 − 4.81225I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.074623 + 1.166690I
a = 0.948927 + 0.761406I
b = −0.68925 − 1.45078I
−4.42453 + 1.25989I −12.84485 − 4.81225I
u = 0.074623 + 1.166690I
a = 2.01169 + 0.29861I
b = −1.225920 − 0.410668I
−4.42453 + 1.25989I −12.84485 − 4.81225I
u = 0.074623 − 1.166690I
a = 0.948927 − 0.761406I
b = −0.68925 + 1.45078I
−4.42453 − 1.25989I −12.84485 + 4.81225I
u = 0.074623 − 1.166690I
a = 2.01169 − 0.29861I
b = −1.225920 + 0.410668I
−4.42453 − 1.25989I −12.84485 + 4.81225I
u = −0.618147 + 1.082030I
a = 1.224620 − 0.051654I
b = −0.763703 − 0.555491I
5.04831 − 4.71254I 4.73930 + 5.43197I
u = −0.618147 + 1.082030I
a = −1.21202 − 1.10387I
b = −1.114730 + 0.784301I
5.04831 − 4.71254I 4.73930 + 5.43197I
u = −0.618147 − 1.082030I
a = 1.224620 + 0.051654I
b = −0.763703 + 0.555491I
5.04831 + 4.71254I 4.73930 − 5.43197I
u = −0.618147 − 1.082030I
a = −1.21202 + 1.10387I
b = −1.114730 − 0.784301I
5.04831 + 4.71254I 4.73930 − 5.43197I
u = −0.088119 + 1.247720I
a = −0.055705 + 0.760873I
b = −0.129650 + 0.365843I
−1.75844 − 4.71254I −8.73930 + 5.43197I
u = −0.088119 + 1.247720I
a = −2.17705 − 0.69599I
b = 2.28573 + 1.08019I
−1.75844 − 4.71254I −8.73930 + 5.43197I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088119 − 1.247720I
a = −0.055705 − 0.760873I
b = −0.129650 − 0.365843I
−1.75844 + 4.71254I −8.73930 − 5.43197I
u = −0.088119 − 1.247720I
a = −2.17705 + 0.69599I
b = 2.28573 − 1.08019I
−1.75844 + 4.71254I −8.73930 − 5.43197I
u = −0.438063 + 1.312710I
a = 0.981041 + 0.771931I
b = −0.266538 − 0.848544I
0.37326 − 4.83126I −7.11010 + 2.24363I
u = −0.438063 + 1.312710I
a = −1.55067 − 0.56043I
b = 1.10173 + 1.50831I
0.37326 − 4.83126I −7.11010 + 2.24363I
u = −0.438063 − 1.312710I
a = 0.981041 − 0.771931I
b = −0.266538 + 0.848544I
0.37326 + 4.83126I −7.11010 − 2.24363I
u = −0.438063 − 1.312710I
a = −1.55067 + 0.56043I
b = 1.10173 − 1.50831I
0.37326 + 4.83126I −7.11010 − 2.24363I
u = −0.52615 + 1.42545I
a = −0.966701 − 0.471265I
b = 0.693432 + 0.999976I
2.66787 − 7.06147I 0.14650 + 10.25752I
u = −0.52615 + 1.42545I
a = 1.51704 + 0.90563I
b = −0.50804 − 2.48535I
2.66787 − 7.06147I 0.14650 + 10.25752I
u = −0.52615 − 1.42545I
a = −0.966701 + 0.471265I
b = 0.693432 − 0.999976I
2.66787 + 7.06147I 0.14650 − 10.25752I
u = −0.52615 − 1.42545I
a = 1.51704 − 0.90563I
b = −0.50804 + 2.48535I
2.66787 + 7.06147I 0.14650 − 10.25752I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316467 + 0.267299I
a = −1.22025 − 1.72230I
b = −1.118440 − 0.785603I
2.91661 − 4.83126I 3.11010 + 2.24363I
u = 0.316467 + 0.267299I
a = 2.99288 − 0.82848I
b = −0.141618 + 0.818664I
2.91661 − 4.83126I 3.11010 + 2.24363I
u = 0.316467 − 0.267299I
a = −1.22025 + 1.72230I
b = −1.118440 + 0.785603I
2.91661 + 4.83126I 3.11010 − 2.24363I
u = 0.316467 − 0.267299I
a = 2.99288 + 0.82848I
b = −0.141618 − 0.818664I
2.91661 + 4.83126I 3.11010 − 2.24363I
u = 0.280251
a = −2.14871 + 0.64223I
b = 0.667889 + 0.191026I
−1.18258 −0.473290
u = 0.280251
a = −2.14871 − 0.64223I
b = 0.667889 − 0.191026I
−1.18258 −0.473290
15
III. I
u
3
=
hu
16
+5u
15
+· · ·+b+3, −3u
17
−17u
16
+· · ·+2a−11, u
18
+5u
17
+· · ·+13u+2i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
2
=
3
2
u
17
+
17
2
u
16
+ ··· + 31u +
11
2
−u
16
− 5u
15
+ ··· − 16u − 3
a
12
=
u
u
3
+ u
a
3
=
3
2
u
17
+
15
2
u
16
+ ··· + 17u +
7
2
−u
16
− 5u
15
+ ··· − 17u − 3
a
4
=
3
2
u
17
+
17
2
u
16
+ ··· + 34u +
13
2
−u
16
− 5u
15
+ ··· − 17u − 3
a
1
=
1
2
u
17
+
5
2
u
16
+ ··· + 16u +
3
2
−u
9
− 3u
8
− 9u
7
− 16u
6
− 24u
5
− 27u
4
− 22u
3
− 15u
2
− 5u − 1
a
6
=
1
2
u
17
+
7
2
u
16
+ ··· + 26u +
13
2
−u
16
− 4u
15
+ ··· − 3u − 1
a
5
=
1
2
u
17
+
5
2
u
16
+ ··· + 14u +
9
2
−u
3
− u
2
− 2u − 1
a
10
=
−u
u
a
9
=
−
1
2
u
17
−
5
2
u
16
+ ··· − 22u −
7
2
u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 6u
2
+ 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
17
+ 3u
16
+ 15u
15
+ 12u
14
+ 26u
13
− 13u
12
− 41u
11
− 106u
10
−
145u
9
− 101u
8
− 54u
7
+ 89u
6
+ 142u
5
+ 163u
4
+ 144u
3
+ 55u
2
+ 40u
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 8u
17
+ ··· − 73u + 12
c
2
, c
6
u
18
− 3u
14
+ ··· − 6u
2
+ 1
c
3
, c
9
u
18
− u
17
+ ··· − u
2
+ 1
c
4
u
18
+ 8u
17
+ ··· + 73u + 12
c
5
u
18
+ 5u
17
+ ··· − 3u + 7
c
7
u
18
+ 5u
17
+ ··· + 13u + 2
c
8
, c
12
u
18
− u
17
+ ··· + u + 1
c
10
, c
11
u
18
− 5u
17
+ ··· − 13u + 2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
18
+ 10y
17
+ ··· + 623y + 144
c
2
, c
6
y
18
− 6y
16
+ ··· − 12y + 1
c
3
, c
9
y
18
+ 11y
17
+ ··· − 2y + 1
c
5
y
18
− 5y
17
+ ··· − 597y + 49
c
7
, c
10
, c
11
y
18
+ 19y
17
+ ··· + 39y + 4
c
8
, c
12
y
18
− 3y
17
+ ··· + 3y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.005820 + 0.143618I
a = −0.191143 − 0.040717I
b = −0.163157 − 1.366040I
6.70136 − 0.69923I −0.082570 + 0.255758I
u = −1.005820 − 0.143618I
a = −0.191143 + 0.040717I
b = −0.163157 + 1.366040I
6.70136 + 0.69923I −0.082570 − 0.255758I
u = −0.108804 + 1.151700I
a = −1.76688 + 0.65260I
b = 1.10749 − 0.99631I
−4.02138 − 1.16907I 3.75736 − 3.23683I
u = −0.108804 − 1.151700I
a = −1.76688 − 0.65260I
b = 1.10749 + 0.99631I
−4.02138 + 1.16907I 3.75736 + 3.23683I
u = 0.079474 + 1.171950I
a = 1.53601 − 0.65895I
b = −0.79013 + 1.51732I
−0.20326 + 5.79607I −5.72434 − 5.34843I
u = 0.079474 − 1.171950I
a = 1.53601 + 0.65895I
b = −0.79013 − 1.51732I
−0.20326 − 5.79607I −5.72434 + 5.34843I
u = −0.566647 + 1.152440I
a = 1.188160 + 0.386784I
b = −0.136894 − 0.761815I
3.59865 − 4.81934I −2.65309 + 4.91066I
u = −0.566647 − 1.152440I
a = 1.188160 − 0.386784I
b = −0.136894 + 0.761815I
3.59865 + 4.81934I −2.65309 − 4.91066I
u = 0.043618 + 0.529613I
a = 1.40097 − 1.49588I
b = 0.590722 + 0.667130I
1.95706 − 5.18785I −6.23632 + 5.50637I
u = 0.043618 − 0.529613I
a = 1.40097 + 1.49588I
b = 0.590722 − 0.667130I
1.95706 + 5.18785I −6.23632 − 5.50637I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47475 + 1.39812I
a = −1.179570 − 0.770752I
b = 0.59799 + 1.57020I
1.87518 − 5.99210I −3.66371 + 3.71889I
u = −0.47475 − 1.39812I
a = −1.179570 + 0.770752I
b = 0.59799 − 1.57020I
1.87518 + 5.99210I −3.66371 − 3.71889I
u = −0.08311 + 1.51235I
a = −0.379469 + 0.480793I
b = 0.485462 − 0.844585I
−7.63748 − 1.81605I −11.92101 − 4.04816I
u = −0.08311 − 1.51235I
a = −0.379469 − 0.480793I
b = 0.485462 + 0.844585I
−7.63748 + 1.81605I −11.92101 + 4.04816I
u = −0.315334 + 0.278447I
a = 1.04390 + 1.08403I
b = −0.603695 + 0.097936I
−1.45757 − 0.47837I −8.82227 + 8.75123I
u = −0.315334 − 0.278447I
a = 1.04390 − 1.08403I
b = −0.603695 − 0.097936I
−1.45757 + 0.47837I −8.82227 − 8.75123I
u = −0.06863 + 1.59394I
a = 0.598023 + 0.023436I
b = −1.087790 + 0.106451I
−5.74737 − 5.68174I −10.6541 + 9.4506I
u = −0.06863 − 1.59394I
a = 0.598023 − 0.023436I
b = −1.087790 − 0.106451I
−5.74737 + 5.68174I −10.6541 − 9.4506I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 8u
17
+ ··· − 73u + 12)(u
18
+ 5u
17
+ ··· + 3u − 1)
2
· (u
37
− 11u
36
+ ··· − 158u + 10)
c
2
, c
6
(u
18
− 3u
14
+ ··· − 6u
2
+ 1)(u
36
− 5u
35
+ ··· − 8364u + 2329)
· (u
37
+ 20u
35
+ ··· + 4u + 1)
c
3
, c
9
(u
18
− u
17
+ ··· − u
2
+ 1)(u
36
− u
35
+ ··· + 8146u + 1229)
· (u
37
− u
36
+ ··· + 286u + 121)
c
4
((u
18
+ 5u
17
+ ··· + 3u − 1)
2
)(u
18
+ 8u
17
+ ··· + 73u + 12)
· (u
37
− 11u
36
+ ··· − 158u + 10)
c
5
((u + 1)
36
)(u
18
+ 5u
17
+ ··· − 3u + 7)
· (u
37
− 32u
36
+ ··· − 3538944u + 262144)
c
7
((u
18
− 5u
17
+ ··· − 3u − 1)
2
)(u
18
+ 5u
17
+ ··· + 13u + 2)
· (u
37
+ 8u
36
+ ··· + 54u + 10)
c
8
, c
12
(u
18
− u
17
+ ··· + u + 1)(u
36
+ 5u
35
+ ··· + 4u + 1)
· (u
37
+ u
36
+ ··· + 5u + 1)
c
10
, c
11
((u
18
− 5u
17
+ ··· − 3u − 1)
2
)(u
18
− 5u
17
+ ··· − 13u + 2)
· (u
37
+ 8u
36
+ ··· + 54u + 10)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
18
+ 10y
17
+ ··· + 623y + 144)(y
18
+ 13y
17
+ ··· − 11y + 1)
2
· (y
37
+ 23y
36
+ ··· + 1464y −100)
c
2
, c
6
(y
18
− 6y
16
+ ··· − 12y + 1)
· (y
36
+ 15y
35
+ ··· + 24442532y + 5424241)
· (y
37
+ 40y
36
+ ··· − 24y −1)
c
3
, c
9
(y
18
+ 11y
17
+ ··· − 2y + 1)
· (y
36
+ 23y
35
+ ··· − 9149824y + 1510441)
· (y
37
+ 19y
36
+ ··· − 31218y −14641)
c
5
((y −1)
36
)(y
18
− 5y
17
+ ··· − 597y + 49)
· (y
37
− 6y
36
+ ··· + 51539607552y −68719476736)
c
7
, c
10
, c
11
((y
18
+ 13y
17
+ ··· − 11y + 1)
2
)(y
18
+ 19y
17
+ ··· + 39y + 4)
· (y
37
+ 32y
36
+ ··· + 1176y −100)
c
8
, c
12
(y
18
− 3y
17
+ ··· + 3y + 1)(y
36
− 5y
35
+ ··· + 20y + 1)
· (y
37
+ 21y
36
+ ··· + y −1)
22
