12n
0739
(K12n
0739
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 10 3 11 2 1 6 8 10
Solving Sequence
1,9 5,10
6 4 2 8 3 12 11 7
c
9
c
5
c
4
c
1
c
8
c
3
c
12
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−207u
14
− 5485u
13
+ ··· + 7505b + 493, 207u
14
+ 5485u
13
+ ··· + 7505a + 7012,
u
15
+ u
14
+ 2u
13
− u
12
+ 5u
11
+ u
10
+ 3u
9
− 10u
8
− 3u
7
− 5u
6
+ 2u
5
+ u
4
+ 5u
3
+ 4u
2
+ 2u + 1i
I
u
2
= h−u
8
+ 2u
7
− 5u
6
+ 4u
5
− 6u
4
− 2u
2
+ b − 2u − 1, u
8
− 2u
7
+ 5u
6
− 4u
5
+ 6u
4
+ 2u
2
+ a + 2u + 2,
u
9
− 2u
8
+ 5u
7
− 4u
6
+ 6u
5
+ 2u
3
+ 3u
2
+ u + 1i
I
u
3
= h−2u
13
− 15u
12
+ ··· + 13b − 30, 7u
13
+ 7u
12
+ ··· + 13a + 66,
u
14
− 5u
13
+ 11u
12
− 14u
11
+ 14u
10
− 15u
9
+ 14u
8
− 4u
7
− 10u
6
+ 16u
5
− 9u
4
− u
3
+ 5u
2
− 3u + 1i
I
u
4
= h−76424u
13
− 364211u
12
+ ··· + 631945b − 2212876,
− 4229u
13
+ 600365u
12
+ ··· + 1390279a + 2943530,
u
14
+ 3u
13
+ 7u
12
+ 10u
11
+ 18u
10
+ 23u
9
+ 42u
8
+ 42u
7
+ 66u
6
+ 52u
5
+ 73u
4
+ 49u
3
+ 53u
2
+ 25u + 11i
* 4 irreducible components of dim
C
= 0, with total 52 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−207u
14
− 5485u
13
+ · · · + 7505b + 493, 207u
14
+ 5485u
13
+ · · · +
7505a + 7012, u
15
+ u
14
+ · · · + 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−0.0275816u
14
− 0.730846u
13
+ ··· − 1.43198u − 0.934310
0.0275816u
14
+ 0.730846u
13
+ ··· + 1.43198u − 0.0656895
a
10
=
1
u
2
a
6
=
−0.469420u
14
− 0.646236u
13
+ ··· − 1.43411u − 1.70326
−0.114457u
14
+ 0.107262u
13
+ ··· + 0.820919u − 0.592139
a
4
=
−1
0.0275816u
14
+ 0.730846u
13
+ ··· + 1.43198u − 0.0656895
a
2
=
−u
0.703264u
14
+ 0.233844u
13
+ ··· + 0.879147u − 0.0275816
a
8
=
0.469420u
14
+ 0.646236u
13
+ ··· + 1.43411u + 1.70326
0.526449u
14
+ 0.384410u
13
+ ··· + 0.114724u + 0.441839
a
3
=
0.956163u
14
+ 1.00266u
13
+ ··· + 1.30859u + 1.05610
1.60773u
14
+ 1.71686u
13
+ ··· + 3.41186u + 1.48981
a
12
=
u
u
3
+ u
a
11
=
−0.956163u
14
− 1.00266u
13
+ ··· − 1.30859u − 1.05610
−1.28408u
14
− 1.24717u
13
+ ··· − 2.22212u − 2.05290
a
7
=
−1.29167u
14
− 2.15856u
13
+ ··· − 2.76136u − 2.23771
−2.06236u
14
− 2.95670u
13
+ ··· − 5.58534u − 3.93844
(ii) Obstruction class = −1
(iii) Cusp Shapes =
35
79
u
14
+
171
79
u
13
+
116
79
u
12
+
181
79
u
11
−
11
79
u
10
+
938
79
u
9
−
137
79
u
8
+
16
79
u
7
−
1203
79
u
6
+
527
79
u
5
−
733
79
u
4
−
134
79
u
3
+
108
79
u
2
+
589
79
u +
878
79
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
u
15
− u
14
+ ··· + 2u − 1
c
2
, c
6
, c
7
c
11
u
15
− u
14
+ ··· + 2u − 1
c
3
, c
5
, c
10
u
15
− 19u
13
+ ··· + 17u − 19
c
4
u
15
− 17u
14
+ ··· + 1568u − 192
c
8
u
15
− 4u
13
+ ··· + 19u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
15
+ 3y
14
+ ··· − 4y −1
c
2
, c
6
, c
7
c
11
y
15
− 25y
14
+ ··· − 6y −1
c
3
, c
5
, c
10
y
15
− 38y
14
+ ··· − 1383y −361
c
4
y
15
− 7y
14
+ ··· + 13312y −36864
c
8
y
15
− 8y
14
+ ··· + 429y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024810 + 0.188590I
a = −0.520621 + 0.399007I
b = −0.479379 − 0.399007I
−3.38414 − 1.11532I −1.09725 + 5.91782I
u = 1.024810 − 0.188590I
a = −0.520621 − 0.399007I
b = −0.479379 + 0.399007I
−3.38414 + 1.11532I −1.09725 − 5.91782I
u = −0.616853 + 0.694024I
a = 1.43371 + 1.08009I
b = −2.43371 − 1.08009I
17.2214 + 1.0755I 8.97418 − 5.44707I
u = −0.616853 − 0.694024I
a = 1.43371 − 1.08009I
b = −2.43371 + 1.08009I
17.2214 − 1.0755I 8.97418 + 5.44707I
u = −0.669725 + 0.976114I
a = −0.085207 − 1.287120I
b = −0.91479 + 1.28712I
5.33694 + 6.98165I 12.1571 − 8.1173I
u = −0.669725 − 0.976114I
a = −0.085207 + 1.287120I
b = −0.91479 − 1.28712I
5.33694 − 6.98165I 12.1571 + 8.1173I
u = 0.270838 + 0.767894I
a = 0.37558 + 1.44892I
b = −1.37558 − 1.44892I
3.91615 − 2.51478I 13.05838 + 5.04064I
u = 0.270838 − 0.767894I
a = 0.37558 − 1.44892I
b = −1.37558 + 1.44892I
3.91615 + 2.51478I 13.05838 − 5.04064I
u = −0.110943 + 0.581465I
a = −0.692244 − 0.824852I
b = −0.307756 + 0.824852I
0.987465 − 0.742979I 8.61024 + 4.51729I
u = −0.110943 − 0.581465I
a = −0.692244 + 0.824852I
b = −0.307756 − 0.824852I
0.987465 + 0.742979I 8.61024 − 4.51729I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564042
a = −0.0861991
b = −0.913801
1.42193 5.74330
u = 0.89289 + 1.16102I
a = 0.326675 + 0.764222I
b = −1.32667 − 0.76422I
−2.15203 − 7.07899I 8.39813 − 1.67942I
u = 0.89289 − 1.16102I
a = 0.326675 − 0.764222I
b = −1.32667 + 0.76422I
−2.15203 + 7.07899I 8.39813 + 1.67942I
u = −1.00899 + 1.30137I
a = 0.20521 − 1.66144I
b = −1.20521 + 1.66144I
−19.3469 + 12.7789I 7.52759 − 4.91540I
u = −1.00899 − 1.30137I
a = 0.20521 + 1.66144I
b = −1.20521 − 1.66144I
−19.3469 − 12.7789I 7.52759 + 4.91540I
6
II. I
u
2
= h−u
8
+ 2u
7
+ · · · + b − 1, u
8
− 2u
7
+ 5u
6
− 4u
5
+ 6u
4
+ 2u
2
+ a +
2u + 2, u
9
− 2u
8
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−u
8
+ 2u
7
− 5u
6
+ 4u
5
− 6u
4
− 2u
2
− 2u − 2
u
8
− 2u
7
+ 5u
6
− 4u
5
+ 6u
4
+ 2u
2
+ 2u + 1
a
10
=
1
u
2
a
6
=
−u
3
+ u
2
− u − 1
u
8
− 2u
7
+ 5u
6
− 5u
5
+ 7u
4
− 2u
3
+ 2u
2
+ u + 1
a
4
=
−1
u
8
− 2u
7
+ 5u
6
− 4u
5
+ 6u
4
+ 2u
2
+ 2u + 1
a
2
=
−u
−u
2
+ u − 1
a
8
=
u
3
− u
2
+ u + 1
u
4
− 2u
3
+ 3u
2
− 2u + 1
a
3
=
−u
8
+ 2u
7
− 4u
6
+ 2u
5
− 2u
4
− 2u
3
− 2u − 1
u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 4u − 2
a
12
=
u
u
3
+ u
a
11
=
u
8
− 2u
7
+ 4u
6
− 2u
5
+ 2u
4
+ 2u
3
+ 2u + 1
−2u
8
+ 5u
7
− 12u
6
+ 13u
5
− 17u
4
+ 9u
3
− 8u
2
− 2
a
7
=
0
−3u
8
+ 8u
7
− 21u
6
+ 26u
5
− 36u
4
+ 22u
3
− 21u
2
+ 2u − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
8
+ 3u
7
− 9u
6
− 2u
5
− 5u
4
− 9u
3
− 2u
2
− 3u + 8
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
9
− 2u
8
+ 5u
7
− 4u
6
+ 6u
5
+ 2u
3
+ 3u
2
+ u + 1
c
2
, c
7
u
9
− 2u
8
− 3u
7
+ u
6
+ 4u
5
+ u
4
− 3u
3
+ u − 1
c
3
, c
5
u
9
+ u
8
− 7u
7
+ 4u
6
− 3u
5
+ 10u
4
− 4u
3
− 2u + 1
c
4
u
9
− u
8
− 3u
7
+ 5u
6
− 2u
5
+ 8u
4
− 15u
3
+ 9u
2
− 2u + 1
c
6
, c
11
u
9
+ 2u
8
− 3u
7
− u
6
+ 4u
5
− u
4
− 3u
3
+ u + 1
c
8
u
9
+ u
8
+ 4u
6
+ u
5
+ u
4
+ 4u
2
− 4u + 1
c
10
u
9
− u
8
− 7u
7
− 4u
6
− 3u
5
− 10u
4
− 4u
3
− 2u − 1
c
12
u
9
+ 2u
8
+ 5u
7
+ 4u
6
+ 6u
5
+ 2u
3
− 3u
2
+ u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
9
+ 6y
8
+ 21y
7
+ 48y
6
+ 70y
5
+ 62y
4
+ 24y
3
− 5y
2
− 5y −1
c
2
, c
6
, c
7
c
11
y
9
− 10y
8
+ 21y
7
− 27y
6
+ 34y
5
− 35y
4
+ 19y
3
− 4y
2
+ y −1
c
3
, c
5
, c
10
y
9
− 15y
8
+ 35y
7
− 2y
6
− 19y
5
− 50y
4
+ 20y
3
− 4y
2
+ 4y −1
c
4
y
9
− 7y
8
+ 15y
7
− 27y
6
+ 28y
5
− 80y
4
+ 79y
3
− 37y
2
− 14y −1
c
8
y
9
− y
8
− 6y
7
− 18y
6
− 23y
5
− 35y
4
− 24y
3
− 18y
2
+ 8y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.004662 + 1.194450I
a = −0.992070 + 0.357253I
b = −0.007930 − 0.357253I
8.02017 + 1.95166I 14.1693 − 3.5989I
u = 0.004662 − 1.194450I
a = −0.992070 − 0.357253I
b = −0.007930 + 0.357253I
8.02017 − 1.95166I 14.1693 + 3.5989I
u = 0.550956 + 1.082030I
a = −0.075345 + 0.348116I
b = −0.924655 − 0.348116I
0.27958 − 4.93472I 9.47602 + 5.23959I
u = 0.550956 − 1.082030I
a = −0.075345 − 0.348116I
b = −0.924655 + 0.348116I
0.27958 + 4.93472I 9.47602 − 5.23959I
u = −0.625063
a = −3.22490
b = 2.22490
17.5031 10.0010
u = −0.157854 + 0.553845I
a = −1.63380 − 1.11606I
b = 0.633803 + 1.116060I
3.35250 − 1.52704I 7.69508 − 0.35030I
u = −0.157854 − 0.553845I
a = −1.63380 + 1.11606I
b = 0.633803 − 1.116060I
3.35250 + 1.52704I 7.69508 + 0.35030I
u = 0.91477 + 1.20682I
a = 0.313669 + 0.680564I
b = −1.31367 − 0.68056I
−2.30953 − 7.37195I −3.8408 + 19.6853I
u = 0.91477 − 1.20682I
a = 0.313669 − 0.680564I
b = −1.31367 + 0.68056I
−2.30953 + 7.37195I −3.8408 − 19.6853I
10
III. I
u
3
= h−2u
13
− 15u
12
+ · · · + 13b − 30, 7u
13
+ 7u
12
+ · · · + 13a +
66, u
14
− 5u
13
+ · · · − 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−0.538462u
13
− 0.538462u
12
+ ··· + 9.38462u − 5.07692
0.153846u
13
+ 1.15385u
12
+ ··· − 3.53846u + 2.30769
a
10
=
1
u
2
a
6
=
2u
13
− 11u
12
+ ··· + 15u − 6
1.53846u
13
− 5.46154u
12
+ ··· + 0.615385u + 0.0769231
a
4
=
−0.384615u
13
+ 0.615385u
12
+ ··· + 5.84615u − 2.76923
0.153846u
13
+ 1.15385u
12
+ ··· − 3.53846u + 2.30769
a
2
=
1.53846u
13
− 10.4615u
12
+ ··· + 16.6154u − 5.92308
−2.30769u
13
+ 9.69231u
12
+ ··· − 4.92308u + 2.38462
a
8
=
1.84615u
13
− 10.1538u
12
+ ··· + 8.53846u − 1.30769
−3.84615u
13
+ 15.1538u
12
+ ··· − 7.53846u + 2.30769
a
3
=
−0.538462u
13
− 3.53846u
12
+ ··· + 18.3846u − 11.0769
−3.92308u
13
+ 15.0769u
12
+ ··· − 7.76923u + 3.15385
a
12
=
u
u
3
+ u
a
11
=
−2.38462u
13
+ 12.6154u
12
+ ··· − 16.1538u + 8.23077
−1.92308u
13
+ 9.07692u
12
+ ··· − 4.76923u + 2.15385
a
7
=
8.15385u
13
− 39.8462u
12
+ ··· + 32.4615u − 5.69231
−5.30769u
13
+ 20.6923u
12
+ ··· − 10.9231u + 2.38462
(ii) Obstruction class = 1
(iii) Cusp Shapes =
14
13
u
13
+
53
13
u
12
−
269
13
u
11
+
439
13
u
10
−
368
13
u
9
+ 31u
8
−
493
13
u
7
+
366
13
u
6
+
223
13
u
5
−
557
13
u
4
+
432
13
u
3
+
69
13
u
2
−
179
13
u +
223
13
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
14
− 5u
13
+ ··· − 3u + 1
c
2
, c
7
u
14
+ 2u
13
+ ··· + 5u + 1
c
3
, c
5
u
14
+ 4u
13
+ ··· + 11u
2
+ 1
c
4
(u
7
+ 4u
6
+ 8u
5
+ 8u
4
+ 3u
3
− 2u
2
− 2u − 1)
2
c
6
, c
11
u
14
− 2u
13
+ ··· − 5u + 1
c
8
u
14
− 4u
13
+ ··· + 2u + 1
c
10
u
14
− 4u
13
+ ··· + 11u
2
+ 1
c
12
u
14
+ 5u
13
+ ··· + 3u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
14
− 3y
13
+ ··· + y + 1
c
2
, c
6
, c
7
c
11
y
14
− 12y
12
+ ··· + 9y + 1
c
3
, c
5
, c
10
y
14
− 2y
13
+ ··· + 22y + 1
c
4
(y
7
+ 6y
5
− 4y
4
+ 17y
3
− 1)
2
c
8
y
14
− 6y
13
+ ··· − 4y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.824621 + 0.598672I
a = 0.235195 − 0.772341I
b = 0.88008 + 1.25705I
4.69297 − 5.82963I 8.36406 + 2.54601I
u = 0.824621 − 0.598672I
a = 0.235195 + 0.772341I
b = 0.88008 − 1.25705I
4.69297 + 5.82963I 8.36406 − 2.54601I
u = 0.339968 + 0.854890I
a = −0.69195 − 1.38631I
b = 1.134240 + 0.687214I
2.76370 − 1.55495I 7.48608 + 1.41640I
u = 0.339968 − 0.854890I
a = −0.69195 + 1.38631I
b = 1.134240 − 0.687214I
2.76370 + 1.55495I 7.48608 − 1.41640I
u = −0.748013 + 0.140438I
a = −0.487954 − 0.334328I
b = 1.134240 − 0.687214I
2.76370 + 1.55495I 7.48608 − 1.41640I
u = −0.748013 − 0.140438I
a = −0.487954 + 0.334328I
b = 1.134240 + 0.687214I
2.76370 − 1.55495I 7.48608 + 1.41640I
u = −0.629497 + 1.067390I
a = −0.12590 + 1.58483I
b = 0.88008 − 1.25705I
4.69297 + 5.82963I 8.36406 − 2.54601I
u = −0.629497 − 1.067390I
a = −0.12590 − 1.58483I
b = 0.88008 + 1.25705I
4.69297 − 5.82963I 8.36406 + 2.54601I
u = 1.120970 + 0.609039I
a = 0.083330 + 0.838972I
b = −0.627505
−4.08865 −8.17020 + 0.I
u = 1.120970 − 0.609039I
a = 0.083330 − 0.838972I
b = −0.627505
−4.08865 −8.17020 + 0.I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.251668 + 0.533254I
a = −0.22477 + 3.09190I
b = 0.299431 − 0.543268I
−2.12248 + 0.90211I 8.73496 − 3.41851I
u = 0.251668 − 0.533254I
a = −0.22477 − 3.09190I
b = 0.299431 + 0.543268I
−2.12248 − 0.90211I 8.73496 + 3.41851I
u = 1.34028 + 0.68122I
a = −0.287947 − 0.151238I
b = 0.299431 + 0.543268I
−2.12248 − 0.90211I 8.73496 + 3.41851I
u = 1.34028 − 0.68122I
a = −0.287947 + 0.151238I
b = 0.299431 − 0.543268I
−2.12248 + 0.90211I 8.73496 − 3.41851I
15
IV.
I
u
4
= h−7.64×10
4
u
13
−3.64×10
5
u
12
+· · ·+6.32×10
5
b−2.21×10
6
, −4229u
13
+
6.00 × 10
5
u
12
+ · · · + 1.39 × 10
6
a + 2.94 × 10
6
, u
14
+ 3u
13
+ · · · + 25u + 11i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.00304184u
13
− 0.431831u
12
+ ··· − 4.05446u − 2.11722
0.120935u
13
+ 0.576333u
12
+ ··· + 4.32192u + 3.50169
a
10
=
1
u
2
a
6
=
−0.490357u
13
− 1.61139u
12
+ ··· − 10.7230u − 3.46605
0.548984u
13
+ 0.861747u
12
+ ··· + 2.23327u + 0.194632
a
4
=
0.123976u
13
+ 0.144503u
12
+ ··· + 0.267462u + 1.38447
0.120935u
13
+ 0.576333u
12
+ ··· + 4.32192u + 3.50169
a
2
=
0.178417u
13
+ 0.968921u
12
+ ··· + 5.51717u + 5.22971
−0.624988u
13
− 1.57000u
12
+ ··· − 10.0894u − 3.40664
a
8
=
0.971701u
13
+ 2.51608u
12
+ ··· + 13.2352u + 3.59349
−0.430484u
13
+ 0.0465183u
12
+ ··· + 7.00827u + 5.54079
a
3
=
2.52636u
13
+ 6.53620u
12
+ ··· + 37.0653u + 15.1615
−1.33212u
13
− 0.597770u
12
+ ··· + 9.52228u + 12.5691
a
12
=
u
u
3
+ u
a
11
=
2.71551u
13
+ 6.94732u
12
+ ··· + 41.5292u + 15.0912
−1.26225u
13
+ 0.181940u
12
+ ··· + 15.6077u + 14.8873
a
7
=
−7.25391u
13
− 14.2592u
12
+ ··· − 59.7943u − 8.30265
−0.388020u
13
− 9.21642u
12
+ ··· − 91.6224u − 59.4716
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
228962
631945
u
13
−
1046983
631945
u
12
+ ··· −
12407333
631945
u −
707243
631945
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
u
14
− 3u
13
+ ··· − 25u + 11
c
2
, c
6
, c
7
c
11
u
14
− 16u
12
+ ··· + 129u + 67
c
3
, c
5
, c
10
u
14
+ 6u
13
+ ··· + 1292u + 361
c
4
(u
7
− 2u
6
+ 2u
5
+ u
3
− 2u
2
+ 2u − 1)
2
c
8
u
14
+ 3u
12
+ ··· + 1198u + 617
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
y
14
+ 5y
13
+ ··· + 541y + 121
c
2
, c
6
, c
7
c
11
y
14
− 32y
13
+ ··· + 2253y + 4489
c
3
, c
5
, c
10
y
14
− 38y
13
+ ··· + 94582y + 130321
c
4
(y
7
+ 6y
5
+ 5y
3
− 1)
2
c
8
y
14
+ 6y
13
+ ··· − 369028y + 380689
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000054 + 1.125940I
a = 1.39090 − 1.23779I
b = −0.336624 + 0.691909I
5.81224 + 1.32363I 9.85670 − 0.78636I
u = −0.000054 − 1.125940I
a = 1.39090 + 1.23779I
b = −0.336624 − 0.691909I
5.81224 − 1.32363I 9.85670 + 0.78636I
u = 0.630623 + 0.982226I
a = −0.226353 − 0.728957I
b = 0.756475 + 0.682867I
0.20654 − 2.41511I 5.45272 + 4.26386I
u = 0.630623 − 0.982226I
a = −0.226353 + 0.728957I
b = 0.756475 − 0.682867I
0.20654 + 2.41511I 5.45272 − 4.26386I
u = −0.615301 + 1.127030I
a = 1.19053 − 2.45478I
b = −1.05621 + 1.05857I
18.6867 + 3.8928I 7.94167 − 2.18375I
u = −0.615301 − 1.127030I
a = 1.19053 + 2.45478I
b = −1.05621 − 1.05857I
18.6867 − 3.8928I 7.94167 + 2.18375I
u = 0.969804 + 0.887001I
a = 0.638279 + 0.996031I
b = −0.727290
−3.35276 6.49781 + 0.I
u = 0.969804 − 0.887001I
a = 0.638279 − 0.996031I
b = −0.727290
−3.35276 6.49781 + 0.I
u = −0.614572 + 1.187090I
a = 1.084610 + 0.304620I
b = −0.336624 − 0.691909I
5.81224 − 1.32363I 9.85670 + 0.78636I
u = −0.614572 − 1.187090I
a = 1.084610 − 0.304620I
b = −0.336624 + 0.691909I
5.81224 + 1.32363I 9.85670 − 0.78636I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379578 + 0.491634I
a = 1.115730 + 0.520094I
b = 0.756475 − 0.682867I
0.20654 + 2.41511I 5.45272 − 4.26386I
u = −0.379578 − 0.491634I
a = 1.115730 − 0.520094I
b = 0.756475 + 0.682867I
0.20654 − 2.41511I 5.45272 + 4.26386I
u = −1.49092 + 1.01048I
a = 1.124480 + 0.348913I
b = −1.05621 − 1.05857I
18.6867 − 3.8928I 7.94167 + 2.18375I
u = −1.49092 − 1.01048I
a = 1.124480 − 0.348913I
b = −1.05621 + 1.05857I
18.6867 + 3.8928I 7.94167 − 2.18375I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
9
− 2u
8
+ 5u
7
− 4u
6
+ 6u
5
+ 2u
3
+ 3u
2
+ u + 1)
· (u
14
− 5u
13
+ ··· − 3u + 1)(u
14
− 3u
13
+ ··· − 25u + 11)
· (u
15
− u
14
+ ··· + 2u − 1)
c
2
, c
7
(u
9
− 2u
8
− 3u
7
+ u
6
+ 4u
5
+ u
4
− 3u
3
+ u − 1)
· (u
14
− 16u
12
+ ··· + 129u + 67)(u
14
+ 2u
13
+ ··· + 5u + 1)
· (u
15
− u
14
+ ··· + 2u − 1)
c
3
, c
5
(u
9
+ u
8
− 7u
7
+ 4u
6
− 3u
5
+ 10u
4
− 4u
3
− 2u + 1)
· (u
14
+ 4u
13
+ ··· + 11u
2
+ 1)(u
14
+ 6u
13
+ ··· + 1292u + 361)
· (u
15
− 19u
13
+ ··· + 17u − 19)
c
4
(u
7
− 2u
6
+ 2u
5
+ u
3
− 2u
2
+ 2u − 1)
2
· (u
7
+ 4u
6
+ 8u
5
+ 8u
4
+ 3u
3
− 2u
2
− 2u − 1)
2
· (u
9
− u
8
− 3u
7
+ 5u
6
− 2u
5
+ 8u
4
− 15u
3
+ 9u
2
− 2u + 1)
· (u
15
− 17u
14
+ ··· + 1568u − 192)
c
6
, c
11
(u
9
+ 2u
8
− 3u
7
− u
6
+ 4u
5
− u
4
− 3u
3
+ u + 1)
· (u
14
− 16u
12
+ ··· + 129u + 67)(u
14
− 2u
13
+ ··· − 5u + 1)
· (u
15
− u
14
+ ··· + 2u − 1)
c
8
(u
9
+ u
8
+ 4u
6
+ u
5
+ u
4
+ 4u
2
− 4u + 1)
· (u
14
+ 3u
12
+ ··· + 1198u + 617)(u
14
− 4u
13
+ ··· + 2u + 1)
· (u
15
− 4u
13
+ ··· + 19u − 1)
c
10
(u
9
− u
8
− 7u
7
− 4u
6
− 3u
5
− 10u
4
− 4u
3
− 2u − 1)
· (u
14
− 4u
13
+ ··· + 11u
2
+ 1)(u
14
+ 6u
13
+ ··· + 1292u + 361)
· (u
15
− 19u
13
+ ··· + 17u − 19)
c
12
(u
9
+ 2u
8
+ 5u
7
+ 4u
6
+ 6u
5
+ 2u
3
− 3u
2
+ u − 1)
· (u
14
− 3u
13
+ ··· − 25u + 11)(u
14
+ 5u
13
+ ··· + 3u + 1)
· (u
15
− u
14
+ ··· + 2u − 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
(y
9
+ 6y
8
+ 21y
7
+ 48y
6
+ 70y
5
+ 62y
4
+ 24y
3
− 5y
2
− 5y −1)
· (y
14
− 3y
13
+ ··· + y + 1)(y
14
+ 5y
13
+ ··· + 541y + 121)
· (y
15
+ 3y
14
+ ··· − 4y −1)
c
2
, c
6
, c
7
c
11
(y
9
− 10y
8
+ 21y
7
− 27y
6
+ 34y
5
− 35y
4
+ 19y
3
− 4y
2
+ y −1)
· (y
14
− 12y
12
+ ··· + 9y + 1)(y
14
− 32y
13
+ ··· + 2253y + 4489)
· (y
15
− 25y
14
+ ··· − 6y −1)
c
3
, c
5
, c
10
(y
9
− 15y
8
+ 35y
7
− 2y
6
− 19y
5
− 50y
4
+ 20y
3
− 4y
2
+ 4y −1)
· (y
14
− 38y
13
+ ··· + 94582y + 130321)(y
14
− 2y
13
+ ··· + 22y + 1)
· (y
15
− 38y
14
+ ··· − 1383y −361)
c
4
(y
7
+ 6y
5
+ 5y
3
− 1)
2
(y
7
+ 6y
5
− 4y
4
+ 17y
3
− 1)
2
· (y
9
− 7y
8
+ 15y
7
− 27y
6
+ 28y
5
− 80y
4
+ 79y
3
− 37y
2
− 14y −1)
· (y
15
− 7y
14
+ ··· + 13312y −36864)
c
8
(y
9
− y
8
− 6y
7
− 18y
6
− 23y
5
− 35y
4
− 24y
3
− 18y
2
+ 8y −1)
· (y
14
− 6y
13
+ ··· − 4y + 1)(y
14
+ 6y
13
+ ··· − 369028y + 380689)
· (y
15
− 8y
14
+ ··· + 429y −1)
22
