11n
167
(K11n
167
)
A knot diagram
1
Linearized knot diagam
5 7 1 10 2 10 3 11 7 4 8
Solving Sequence
1,4 3,8
7 2 11 10 5 6 9
c
3
c
7
c
2
c
11
c
10
c
4
c
5
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−22089881u
18
− 37947869u
17
+ ··· + 242489462b + 98525885,
− 61574971u
18
+ 98525885u
17
+ ··· + 242489462a + 1067204433, u
19
− 8u
17
+ ··· − 5u + 1i
I
u
2
= h1.77398 × 10
18
u
23
+ 2.26651 × 10
18
u
22
+ ··· + 4.24873 × 10
18
b − 7.44747 × 10
18
,
− 1.90928 × 10
19
u
23
− 2.27388 × 10
19
u
22
+ ··· + 2.12437 × 10
19
a + 1.14920 × 10
20
, u
24
+ u
23
+ ··· − 8u + 2i
I
u
3
= h−u
7
+ u
6
+ 2u
5
− u
3
− u
2
+ b − 2u − 1, −u
6
+ u
5
+ u
4
+ a − 2, u
8
− 2u
6
− 2u
5
+ u
3
+ 3u
2
+ 3u + 1i
I
u
4
= h−u
3
− u
2
+ b − 1, u
3
+ 2u
2
+ 2a + u, u
4
+ 2u
3
− u
2
− 2u + 2i
* 4 irreducible components of dim
C
= 0, with total 55 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−2.21 × 10
7
u
18
− 3.79 × 10
7
u
17
+ · · · + 2.42 × 10
8
b + 9.85 × 10
7
, −6.16 ×
10
7
u
18
+9.85×10
7
u
17
+· · · +2.42×10
8
a+1.07×10
9
, u
19
−8u
17
+· · · −5u +1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
0.253928u
18
− 0.406310u
17
+ ··· − 1.98160u − 4.40103
0.0910963u
18
+ 0.156493u
17
+ ··· + 3.28548u − 0.406310
a
7
=
0.253928u
18
− 0.406310u
17
+ ··· − 0.981600u − 4.40103
0.0910963u
18
+ 0.156493u
17
+ ··· + 3.28548u − 0.406310
a
2
=
0.406310u
18
+ 0.0910963u
17
+ ··· + 3.13139u + 1.25393
−0.156493u
18
− 0.188283u
17
+ ··· − 0.0491713u + 0.0910963
a
11
=
−0.610280u
18
− 0.343192u
17
+ ··· − 10.3730u − 2.60824
0.370173u
18
+ 0.142628u
17
+ ··· + 4.39116u − 0.749502
a
10
=
−0.240107u
18
− 0.200564u
17
+ ··· − 5.98180u − 3.35775
0.370173u
18
+ 0.142628u
17
+ ··· + 4.39116u − 0.749502
a
5
=
−0.655534u
18
− 0.0971700u
17
+ ··· − 12.7360u + 2.59475
−0.0593229u
18
− 0.229893u
17
+ ··· + 0.633751u − 0.564438
a
6
=
−1.21860u
18
+ 0.176434u
17
+ ··· − 14.2029u + 4.08632
0.00607376u
18
− 0.198103u
17
+ ··· − 1.60256u − 0.249224
a
9
=
−0.365855u
18
− 0.499533u
17
+ ··· − 17.4546u − 5.30364
0.418084u
18
− 0.0169879u
17
+ ··· + 6.52297u − 1.24903
a
9
=
−0.365855u
18
− 0.499533u
17
+ ··· − 17.4546u − 5.30364
0.418084u
18
− 0.0169879u
17
+ ··· + 6.52297u − 1.24903
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
261922646
121244731
u
18
+
40889015
121244731
u
17
+ ··· +
452208248
121244731
u +
720534416
121244731
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
19
+ 8u
18
+ ··· + 13u + 2
c
2
, c
3
, c
7
u
19
− 8u
17
+ ··· − 5u + 1
c
4
, c
10
u
19
+ 8u
17
+ ··· + 4u + 1
c
6
, c
9
u
19
+ 2u
18
+ ··· + 11u + 2
c
8
, c
11
u
19
+ 7u
18
+ ··· + 47u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
19
− 4y
18
+ ··· − 27y −4
c
2
, c
3
, c
7
y
19
− 16y
18
+ ··· + 19y −1
c
4
, c
10
y
19
+ 16y
18
+ ··· − 12y −1
c
6
, c
9
y
19
− 16y
18
+ ··· + 81y −4
c
8
, c
11
y
19
+ 7y
18
+ ··· + 1025y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.953283 + 0.590186I
a = 0.497813 − 0.825854I
b = −0.30300 + 1.61317I
−3.36214 + 0.48881I −6.63793 − 2.65665I
u = −0.953283 − 0.590186I
a = 0.497813 + 0.825854I
b = −0.30300 − 1.61317I
−3.36214 − 0.48881I −6.63793 + 2.65665I
u = 0.978082 + 0.672701I
a = 1.070170 − 0.278653I
b = 0.071909 − 0.595075I
5.37613 − 7.26815I −2.70960 + 5.48443I
u = 0.978082 − 0.672701I
a = 1.070170 + 0.278653I
b = 0.071909 + 0.595075I
5.37613 + 7.26815I −2.70960 − 5.48443I
u = −1.124820 + 0.396400I
a = 0.225058 − 0.730978I
b = −0.72235 + 1.40708I
−3.09782 + 0.05780I −6.02643 + 0.15389I
u = −1.124820 − 0.396400I
a = 0.225058 + 0.730978I
b = −0.72235 − 1.40708I
−3.09782 − 0.05780I −6.02643 − 0.15389I
u = −1.054220 + 0.617800I
a = −1.066300 + 0.064508I
b = −0.360174 − 0.818216I
4.51703 − 0.89042I −2.37683 + 0.17113I
u = −1.054220 − 0.617800I
a = −1.066300 − 0.064508I
b = −0.360174 + 0.818216I
4.51703 + 0.89042I −2.37683 − 0.17113I
u = 0.741245 + 0.208527I
a = −0.51834 − 1.73606I
b = 0.466823 + 1.247140I
−2.65661 + 3.10000I −6.27419 − 4.22218I
u = 0.741245 − 0.208527I
a = −0.51834 + 1.73606I
b = 0.466823 − 1.247140I
−2.65661 − 3.10000I −6.27419 + 4.22218I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46886 + 0.25961I
a = 0.273323 − 0.690530I
b = 0.37094 + 1.49448I
−8.71916 − 2.37470I −12.53850 − 4.28279I
u = 1.46886 − 0.25961I
a = 0.273323 + 0.690530I
b = 0.37094 − 1.49448I
−8.71916 + 2.37470I −12.53850 + 4.28279I
u = −0.477001
a = −0.253883
b = −0.419235
−0.803589 −12.4280
u = −1.39506 + 0.83246I
a = −0.053021 − 0.851335I
b = 0.64874 + 1.77620I
3.02325 + 5.91409I −2.64836 − 3.66933I
u = −1.39506 − 0.83246I
a = −0.053021 + 0.851335I
b = 0.64874 − 1.77620I
3.02325 − 5.91409I −2.64836 + 3.66933I
u = 1.38951 + 0.89919I
a = −0.052745 − 0.891369I
b = −0.77871 + 2.03128I
2.6009 − 14.2087I −4.30199 + 7.64083I
u = 1.38951 − 0.89919I
a = −0.052745 + 0.891369I
b = −0.77871 − 2.03128I
2.6009 + 14.2087I −4.30199 − 7.64083I
u = 0.188175 + 0.151731I
a = −4.24902 + 1.30686I
b = 0.315435 + 0.378179I
1.89777 + 1.11232I 4.22795 − 4.88598I
u = 0.188175 − 0.151731I
a = −4.24902 − 1.30686I
b = 0.315435 − 0.378179I
1.89777 − 1.11232I 4.22795 + 4.88598I
6
II.
I
u
2
= h1.77×10
18
u
23
+2.27×10
18
u
22
+· · ·+4.25×10
18
b−7.45×10
18
, −1.91×
10
19
u
23
−2.27×10
19
u
22
+· · ·+2.12×10
19
a+1.15×10
20
, u
24
+u
23
+· · ·−8u+2i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
0.898752u
23
+ 1.07038u
22
+ ··· + 12.0912u − 5.40961
−0.417531u
23
− 0.533456u
22
+ ··· − 3.66675u + 1.75287
a
7
=
1
2
u
23
+
1
2
u
22
+ ··· + 8u − 4
−0.398752u
23
− 0.570379u
22
+ ··· − 3.09123u + 1.40961
a
2
=
−0.704807u
23
− 1.10356u
22
+ ··· − 6.67794u + 2.54722
−0.244696u
23
− 0.273474u
22
+ ··· − 2.26972u + 0.601506
a
11
=
1.24995u
23
+ 1.72388u
22
+ ··· + 14.2509u − 5.98658
−0.507773u
23
− 0.801281u
22
+ ··· − 2.45122u + 1.52483
a
10
=
0.742173u
23
+ 0.922597u
22
+ ··· + 11.7997u − 4.46175
−0.507773u
23
− 0.801281u
22
+ ··· − 2.45122u + 1.52483
a
5
=
0.239284u
23
+ 0.478472u
22
+ ··· + 2.29165u − 1.06026
−0.596088u
23
− 0.741810u
22
+ ··· − 5.97824u + 2.40135
a
6
=
0.359990u
23
+ 0.826922u
22
+ ··· + 1.48988u − 0.206011
−0.282468u
23
− 0.307556u
22
+ ··· − 2.91950u + 1.66220
a
9
=
2.18922u
23
+ 3.04082u
22
+ ··· + 25.5796u − 11.0724
−0.844038u
23
− 1.26644u
22
+ ··· − 5.33860u + 3.13224
a
9
=
2.18922u
23
+ 3.04082u
22
+ ··· + 25.5796u − 11.0724
−0.844038u
23
− 1.26644u
22
+ ··· − 5.33860u + 3.13224
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4484056006391387816
2124366145116320153
u
23
+
6874045510728739710
2124366145116320153
u
22
+ ··· +
19962270314208126262
2124366145116320153
u −
11397374893510619150
2124366145116320153
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
12
− 3u
11
+ ··· − 3u + 1)
2
c
2
, c
3
, c
7
u
24
+ u
23
+ ··· − 8u + 2
c
4
, c
10
u
24
+ u
23
+ ··· − 60u + 10
c
6
, c
9
u
24
+ 3u
23
+ ··· + 192u + 17
c
8
, c
11
(u
12
− 3u
11
+ ··· − 5u + 3)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
12
− y
11
+ ··· + 3y + 1)
2
c
2
, c
3
, c
7
y
24
− 3y
23
+ ··· − 36y
2
+ 4
c
4
, c
10
y
24
+ 21y
23
+ ··· + 3560y + 100
c
6
, c
9
y
24
− 21y
23
+ ··· − 16090y + 289
c
8
, c
11
(y
12
+ 7y
11
+ ··· + 35y + 9)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787408 + 0.597220I
a = 0.219391 − 0.993794I
b = 1.46372 + 2.07332I
5.39798 + 5.66008I −4.22997 − 6.14268I
u = −0.787408 − 0.597220I
a = 0.219391 + 0.993794I
b = 1.46372 − 2.07332I
5.39798 − 5.66008I −4.22997 + 6.14268I
u = −0.600013 + 0.769421I
a = −0.539028 + 1.257780I
b = −0.117110 − 0.655487I
−0.77344 + 4.75233I −0.57550 − 5.65227I
u = −0.600013 − 0.769421I
a = −0.539028 − 1.257780I
b = −0.117110 + 0.655487I
−0.77344 − 4.75233I −0.57550 + 5.65227I
u = 0.920865 + 0.478649I
a = 0.235557 + 1.372650I
b = −0.02624 − 1.98543I
−3.09418 − 6.13442I −10.3699 + 10.2596I
u = 0.920865 − 0.478649I
a = 0.235557 − 1.372650I
b = −0.02624 + 1.98543I
−3.09418 + 6.13442I −10.3699 − 10.2596I
u = 0.839992 + 0.703903I
a = −0.124749 − 0.804667I
b = −1.49997 + 1.70732I
5.86114 + 1.98712I −2.94340 + 1.27592I
u = 0.839992 − 0.703903I
a = −0.124749 + 0.804667I
b = −1.49997 − 1.70732I
5.86114 − 1.98712I −2.94340 − 1.27592I
u = 1.169280 + 0.449583I
a = −0.145064 + 1.055900I
b = 0.67915 − 1.84712I
−0.77344 − 4.75233I −0.57550 + 5.65227I
u = 1.169280 − 0.449583I
a = −0.145064 − 1.055900I
b = 0.67915 + 1.84712I
−0.77344 + 4.75233I −0.57550 − 5.65227I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.418416 + 0.516472I
a = 0.80019 + 1.21965I
b = −1.146740 − 0.284708I
−4.41600 − 1.23001I −6.02056 + 5.25591I
u = 0.418416 − 0.516472I
a = 0.80019 − 1.21965I
b = −1.146740 + 0.284708I
−4.41600 + 1.23001I −6.02056 − 5.25591I
u = −1.09051 + 0.92826I
a = −0.389136 + 0.931266I
b = −0.83707 − 1.57150I
−3.09418 + 6.13442I −10.3699 − 10.2596I
u = −1.09051 − 0.92826I
a = −0.389136 − 0.931266I
b = −0.83707 + 1.57150I
−3.09418 − 6.13442I −10.3699 + 10.2596I
u = 0.488121 + 0.138133I
a = −1.77306 + 0.99449I
b = 0.399018 − 0.436599I
1.95930 − 1.10762I 2.13937 + 5.92060I
u = 0.488121 − 0.138133I
a = −1.77306 − 0.99449I
b = 0.399018 + 0.436599I
1.95930 + 1.10762I 2.13937 − 5.92060I
u = −0.57462 + 1.39073I
a = −0.586220 − 0.089711I
b = 0.043111 − 0.376940I
5.86114 + 1.98712I −2.94340 + 1.27592I
u = −0.57462 − 1.39073I
a = −0.586220 + 0.089711I
b = 0.043111 + 0.376940I
5.86114 − 1.98712I −2.94340 − 1.27592I
u = −0.123712 + 0.457725I
a = 0.06216 + 2.17412I
b = 0.253968 + 0.291137I
1.95930 + 1.10762I 2.13937 − 5.92060I
u = −0.123712 − 0.457725I
a = 0.06216 − 2.17412I
b = 0.253968 − 0.291137I
1.95930 − 1.10762I 2.13937 + 5.92060I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.58682 + 1.60527I
a = 0.586529 − 0.047705I
b = 0.432171 − 0.614303I
5.39798 + 5.66008I −4.22997 − 6.14268I
u = 0.58682 − 1.60527I
a = 0.586529 + 0.047705I
b = 0.432171 + 0.614303I
5.39798 − 5.66008I −4.22997 + 6.14268I
u = −1.74722 + 0.05067I
a = 0.153439 + 0.533057I
b = −0.14400 − 2.11524I
−4.41600 + 1.23001I −6.02056 − 5.25591I
u = −1.74722 − 0.05067I
a = 0.153439 − 0.533057I
b = −0.14400 + 2.11524I
−4.41600 − 1.23001I −6.02056 + 5.25591I
12
III. I
u
3
= h−u
7
+ u
6
+ 2u
5
− u
3
− u
2
+ b − 2u − 1, −u
6
+ u
5
+ u
4
+ a −
2, u
8
− 2u
6
− 2u
5
+ u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
u
6
− u
5
− u
4
+ 2
u
7
− u
6
− 2u
5
+ u
3
+ u
2
+ 2u + 1
a
7
=
u
6
− u
5
− u
4
− u + 2
u
7
− u
6
− 2u
5
+ 2u
3
+ u
2
+ 2u + 1
a
2
=
u
7
− u
6
− u
5
− u
2
+ 2u + 1
−u
7
+ 2u
5
+ 2u
4
− 2u
2
− 2u − 1
a
11
=
−u
7
+ 2u
6
− u
3
− 2u + 1
u
7
− u
6
− u
5
− u
4
+ u
2
+ 3u + 1
a
10
=
u
6
− u
5
− u
4
− u
3
+ u
2
+ u + 2
u
7
− u
6
− u
5
− u
4
+ u
2
+ 3u + 1
a
5
=
2u
7
− u
6
− 4u
5
− 2u
4
+ 2u
3
+ 2u
2
+ 5u + 3
u
2
− u − 1
a
6
=
2u
7
− u
6
− 4u
5
− u
4
+ 2u
3
+ 3u + 3
−u
6
+ 2u
4
+ 2u
3
− 2u − 1
a
9
=
−2u
7
+ 3u
6
+ u
5
+ u
4
− 2u
3
− 5u + 1
2u
7
− 2u
6
− 3u
5
− u
4
+ 2u
3
+ u
2
+ 4u + 2
a
9
=
−2u
7
+ 3u
6
+ u
5
+ u
4
− 2u
3
− 5u + 1
2u
7
− 2u
6
− 3u
5
− u
4
+ 2u
3
+ u
2
+ 4u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
7
+ u
6
+ 12u
5
+ 9u
4
− 4u
3
− 6u
2
− 18u − 18
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 5u
7
+ 10u
6
+ 10u
5
+ 5u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
2
u
8
− 2u
6
+ 2u
5
− u
3
+ 3u
2
− 3u + 1
c
3
, c
7
u
8
− 2u
6
− 2u
5
+ u
3
+ 3u
2
+ 3u + 1
c
4
u
8
+ 2u
6
− u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 2u + 1
c
5
u
8
− 5u
7
+ 10u
6
− 10u
5
+ 5u
4
− 3u
3
+ 4u
2
− 2u + 1
c
6
u
8
+ 2u
7
− 2u
6
− 6u
5
+ 5u
3
+ u
2
− u + 1
c
8
u
8
+ 4u
7
+ 9u
6
+ 12u
5
+ 9u
4
+ 2u
3
− 2u
2
− u + 1
c
9
u
8
− 2u
7
− 2u
6
+ 6u
5
− 5u
3
+ u
2
+ u + 1
c
10
u
8
+ 2u
6
+ u
5
+ 2u
4
− 2u
3
+ 4u
2
− 2u + 1
c
11
u
8
− 4u
7
+ 9u
6
− 12u
5
+ 9u
4
− 2u
3
− 2u
2
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
− 5y
7
+ 10y
6
− 22y
5
+ 27y
4
+ 11y
3
+ 14y
2
+ 4y + 1
c
2
, c
3
, c
7
y
8
− 4y
7
+ 4y
6
+ 2y
5
− 6y
4
+ 7y
3
+ 3y
2
− 3y + 1
c
4
, c
10
y
8
+ 4y
7
+ 8y
6
+ 15y
5
+ 26y
4
+ 20y
3
+ 12y
2
+ 4y + 1
c
6
, c
9
y
8
− 8y
7
+ 28y
6
− 54y
5
+ 62y
4
− 41y
3
+ 11y
2
+ y + 1
c
8
, c
11
y
8
+ 2y
7
+ 3y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 26y
2
− 5y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047355 + 0.955386I
a = 0.250346 − 0.387349I
b = 0.145540 − 1.330730I
5.86099 + 3.83824I −2.61527 − 2.77290I
u = 0.047355 − 0.955386I
a = 0.250346 + 0.387349I
b = 0.145540 + 1.330730I
5.86099 − 3.83824I −2.61527 + 2.77290I
u = −0.923072 + 0.606984I
a = −0.288078 + 1.324400I
b = −0.42170 − 1.57032I
−2.20821 + 5.58533I −2.91572 − 6.03344I
u = −0.923072 − 0.606984I
a = −0.288078 − 1.324400I
b = −0.42170 + 1.57032I
−2.20821 − 5.58533I −2.91572 + 6.03344I
u = −0.595163 + 0.229046I
a = 1.91573 + 0.00857I
b = 0.014742 + 0.290671I
1.46644 − 0.78325I −8.36606 − 3.84221I
u = −0.595163 − 0.229046I
a = 1.91573 − 0.00857I
b = 0.014742 − 0.290671I
1.46644 + 0.78325I −8.36606 + 3.84221I
u = 1.47088 + 0.19586I
a = −0.377996 + 0.744591I
b = −0.23859 − 1.56042I
−8.40909 − 2.81417I −3.60294 + 7.34570I
u = 1.47088 − 0.19586I
a = −0.377996 − 0.744591I
b = −0.23859 + 1.56042I
−8.40909 + 2.81417I −3.60294 − 7.34570I
16
IV. I
u
4
= h−u
3
− u
2
+ b − 1, u
3
+ 2u
2
+ 2a + u, u
4
+ 2u
3
− u
2
− 2u + 2i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
−
1
2
u
3
− u
2
−
1
2
u
u
3
+ u
2
+ 1
a
7
=
−
1
2
u
3
− u
2
+
1
2
u + 1
1
a
2
=
1
2
u
3
+ u
2
−
1
2
u − 1
−u
2
− u − 1
a
11
=
−
1
2
u
3
− u
2
+
1
2
u + 1
u
3
+ 2u
2
− 1
a
10
=
1
2
u
3
+ u
2
+
1
2
u
u
3
+ 2u
2
− 1
a
5
=
1
2
u
3
+ u
2
−
1
2
u − 1
−u
2
− 2u − 1
a
6
=
0
−u
a
9
=
0
u
3
+ u
2
− u
a
9
=
0
u
3
+ u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
u
4
− 2u
3
− u
2
+ 2u + 2
c
3
, c
7
u
4
+ 2u
3
− u
2
− 2u + 2
c
4
u
4
+ 3u
2
− 2u + 2
c
5
(u + 1)
4
c
6
, c
8
, c
9
c
11
(u
2
+ 1)
2
c
10
u
4
+ 3u
2
+ 2u + 2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
c
2
, c
3
, c
7
y
4
− 6y
3
+ 13y
2
− 8y + 4
c
4
, c
10
y
4
+ 6y
3
+ 13y
2
+ 8y + 4
c
6
, c
8
, c
9
c
11
(y + 1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693897 + 0.418797I
a = −0.637550 − 1.056350I
b = 1.27510 + 1.11269I
−4.93480 −12.0000
u = 0.693897 − 0.418797I
a = −0.637550 + 1.056350I
b = 1.27510 − 1.11269I
−4.93480 −12.0000
u = −1.69390 + 0.41880I
a = 0.137550 − 0.556347I
b = −0.27510 + 2.11269I
−4.93480 −12.0000
u = −1.69390 − 0.41880I
a = 0.137550 + 0.556347I
b = −0.27510 − 2.11269I
−4.93480 −12.0000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
8
+ 5u
7
+ 10u
6
+ 10u
5
+ 5u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
· ((u
12
− 3u
11
+ ··· − 3u + 1)
2
)(u
19
+ 8u
18
+ ··· + 13u + 2)
c
2
(u
4
− 2u
3
− u
2
+ 2u + 2)(u
8
− 2u
6
+ 2u
5
− u
3
+ 3u
2
− 3u + 1)
· (u
19
− 8u
17
+ ··· − 5u + 1)(u
24
+ u
23
+ ··· − 8u + 2)
c
3
, c
7
(u
4
+ 2u
3
− u
2
− 2u + 2)(u
8
− 2u
6
− 2u
5
+ u
3
+ 3u
2
+ 3u + 1)
· (u
19
− 8u
17
+ ··· − 5u + 1)(u
24
+ u
23
+ ··· − 8u + 2)
c
4
(u
4
+ 3u
2
− 2u + 2)(u
8
+ 2u
6
− u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 2u + 1)
· (u
19
+ 8u
17
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· − 60u + 10)
c
5
(u + 1)
4
(u
8
− 5u
7
+ 10u
6
− 10u
5
+ 5u
4
− 3u
3
+ 4u
2
− 2u + 1)
· ((u
12
− 3u
11
+ ··· − 3u + 1)
2
)(u
19
+ 8u
18
+ ··· + 13u + 2)
c
6
(u
2
+ 1)
2
(u
8
+ 2u
7
− 2u
6
− 6u
5
+ 5u
3
+ u
2
− u + 1)
· (u
19
+ 2u
18
+ ··· + 11u + 2)(u
24
+ 3u
23
+ ··· + 192u + 17)
c
8
(u
2
+ 1)
2
(u
8
+ 4u
7
+ 9u
6
+ 12u
5
+ 9u
4
+ 2u
3
− 2u
2
− u + 1)
· ((u
12
− 3u
11
+ ··· − 5u + 3)
2
)(u
19
+ 7u
18
+ ··· + 47u + 4)
c
9
(u
2
+ 1)
2
(u
8
− 2u
7
− 2u
6
+ 6u
5
− 5u
3
+ u
2
+ u + 1)
· (u
19
+ 2u
18
+ ··· + 11u + 2)(u
24
+ 3u
23
+ ··· + 192u + 17)
c
10
(u
4
+ 3u
2
+ 2u + 2)(u
8
+ 2u
6
+ u
5
+ 2u
4
− 2u
3
+ 4u
2
− 2u + 1)
· (u
19
+ 8u
17
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· − 60u + 10)
c
11
(u
2
+ 1)
2
(u
8
− 4u
7
+ 9u
6
− 12u
5
+ 9u
4
− 2u
3
− 2u
2
+ u + 1)
· ((u
12
− 3u
11
+ ··· − 5u + 3)
2
)(u
19
+ 7u
18
+ ··· + 47u + 4)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
(y
8
− 5y
7
+ 10y
6
− 22y
5
+ 27y
4
+ 11y
3
+ 14y
2
+ 4y + 1)
· ((y
12
− y
11
+ ··· + 3y + 1)
2
)(y
19
− 4y
18
+ ··· − 27y −4)
c
2
, c
3
, c
7
(y
4
− 6y
3
+ 13y
2
− 8y + 4)
· (y
8
− 4y
7
+ 4y
6
+ 2y
5
− 6y
4
+ 7y
3
+ 3y
2
− 3y + 1)
· (y
19
− 16y
18
+ ··· + 19y −1)(y
24
− 3y
23
+ ··· − 36y
2
+ 4)
c
4
, c
10
(y
4
+ 6y
3
+ 13y
2
+ 8y + 4)
· (y
8
+ 4y
7
+ 8y
6
+ 15y
5
+ 26y
4
+ 20y
3
+ 12y
2
+ 4y + 1)
· (y
19
+ 16y
18
+ ··· − 12y −1)(y
24
+ 21y
23
+ ··· + 3560y + 100)
c
6
, c
9
(y + 1)
4
(y
8
− 8y
7
+ 28y
6
− 54y
5
+ 62y
4
− 41y
3
+ 11y
2
+ y + 1)
· (y
19
− 16y
18
+ ··· + 81y −4)(y
24
− 21y
23
+ ··· − 16090y + 289)
c
8
, c
11
(y + 1)
4
(y
8
+ 2y
7
+ 3y
6
− 2y
5
+ 7y
4
+ 2y
3
+ 26y
2
− 5y + 1)
· ((y
12
+ 7y
11
+ ··· + 35y + 9)
2
)(y
19
+ 7y
18
+ ··· + 1025y −16)
22
