11a
14
(K11a
14
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 9 3 5 11 6 8 10
Solving Sequence
2,4 5,9
6 10 1 3 7 11 8
c
4
c
5
c
9
c
1
c
2
c
6
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
11
− 2u
10
− u
9
+ 5u
8
− 2u
7
− 5u
6
+ 5u
5
+ 2u
4
− 5u
3
+ u
2
+ b + u,
u
11
− 2u
10
− u
9
+ 5u
8
− 2u
7
− 5u
6
+ 5u
5
+ u
4
− 5u
3
+ 2u
2
+ a + u − 1,
u
12
− 2u
11
− u
10
+ 6u
9
− 3u
8
− 6u
7
+ 8u
6
+ u
5
− 8u
4
+ 4u
3
+ 3u
2
− 3u + 1i
I
u
2
= h−1.93535 × 10
18
u
65
− 2.98312 × 10
18
u
64
+ ··· + 1.31154 × 10
18
b − 9.50336 × 10
18
,
1.46340 × 10
19
u
65
− 7.80076 × 10
19
u
64
+ ··· + 6.55768 × 10
17
a − 1.85522 × 10
19
, u
66
− 6u
65
+ ··· + u + 1i
I
u
3
= h−u
5
+ u
4
− u
2
+ b, −u
3
+ u
2
+ a − 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
4
= h−2a
5
+ 2a
4
− 7a
3
+ 5a
2
+ 3b − 4a + 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 90 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
= hu
11
−2u
10
+· · ·+b +u, u
11
−2u
10
+· · ·+a −1, u
12
−2u
11
+· · ·−3u +1i
(i) Arc colorings
a
2
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−u
11
+ 2u
10
+ u
9
− 5u
8
+ 2u
7
+ 5u
6
− 5u
5
− u
4
+ 5u
3
− 2u
2
− u + 1
−u
11
+ 2u
10
+ u
9
− 5u
8
+ 2u
7
+ 5u
6
− 5u
5
− 2u
4
+ 5u
3
− u
2
− u
a
6
=
−u
9
+ u
8
+ 2u
7
− 3u
6
− u
5
+ 3u
4
− u
3
− 2u
2
+ u + 1
−u
11
+ u
10
+ 2u
9
− 3u
8
− u
7
+ 3u
6
− u
5
− 2u
4
+ 2u
3
+ u
2
− u
a
10
=
−u
11
+ 2u
10
+ u
9
− 5u
8
+ 2u
7
+ 4u
6
− 5u
5
+ 4u
3
− 2u
2
− u
−u
11
+ 2u
10
+ u
9
− 5u
8
+ 2u
7
+ 4u
6
− 5u
5
+ 4u
3
− 2u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
7
=
u
11
− u
10
− 3u
9
+ 4u
8
+ 3u
7
− 7u
6
+ u
5
+ 6u
4
− 5u
3
− 3u
2
+ 3u
−u
11
+ u
10
+ 2u
9
− 4u
8
− u
7
+ 5u
6
− 2u
5
− 4u
4
+ 3u
3
+ u
2
− 2u
a
11
=
−u
10
+ u
9
+ 2u
8
− 3u
7
− u
6
+ 4u
5
− 2u
4
− 2u
3
+ 3u
2
−u
10
+ u
9
+ 2u
8
− 3u
7
− u
6
+ 4u
5
− 2u
4
− 3u
3
+ 3u
2
a
8
=
u
10
− u
9
− 2u
8
+ 3u
7
+ u
6
− 3u
5
+ u
4
+ 2u
3
− 2u
2
− u + 1
u
10
− u
9
− 2u
8
+ 3u
7
+ u
6
− 3u
5
+ u
4
+ 2u
3
− u
2
− u
a
8
=
u
10
− u
9
− 2u
8
+ 3u
7
+ u
6
− 3u
5
+ u
4
+ 2u
3
− 2u
2
− u + 1
u
10
− u
9
− 2u
8
+ 3u
7
+ u
6
− 3u
5
+ u
4
+ 2u
3
− u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
11
− 4u
10
− 4u
9
+ 8u
8
+ 4u
7
− 8u
6
+ 4u
5
+ 12u
4
− 4u
3
− 4u
2
+ 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
10
u
12
− 2u
11
+ ··· − 3u + 1
c
2
, c
11
u
12
+ 6u
11
+ ··· + 3u + 1
c
3
, c
5
, c
6
c
9
u
12
− 3u
10
+ 5u
8
+ 2u
7
− 2u
6
− 5u
5
+ 4u
3
+ u
2
− 3u + 1
c
7
u
12
+ 7u
11
+ ··· + 36u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
y
12
− 6y
11
+ ··· − 3y + 1
c
2
, c
11
y
12
+ 2y
11
+ ··· + 25y + 1
c
3
, c
5
, c
6
c
9
y
12
− 6y
11
+ ··· − 7y + 1
c
7
y
12
− 5y
11
+ ··· − 112y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453738 + 0.929754I
a = 1.66040 − 0.06848I
b = 0.28000 + 1.88655I
8.07063 + 4.68351I 6.05114 − 1.98346I
u = 0.453738 − 0.929754I
a = 1.66040 + 0.06848I
b = 0.28000 − 1.88655I
8.07063 − 4.68351I 6.05114 + 1.98346I
u = −0.926778 + 0.513866I
a = −0.968427 − 0.613844I
b = −0.820207 − 0.433144I
−1.88434 + 4.01879I −2.34862 − 5.57352I
u = −0.926778 − 0.513866I
a = −0.968427 + 0.613844I
b = −0.820207 + 0.433144I
−1.88434 − 4.01879I −2.34862 + 5.57352I
u = −1.117600 + 0.115595I
a = −1.48773 − 1.21599I
b = −2.71217 − 0.83584I
−3.84373 + 0.16285I 1.32343 + 10.94047I
u = −1.117600 − 0.115595I
a = −1.48773 + 1.21599I
b = −2.71217 + 0.83584I
−3.84373 − 0.16285I 1.32343 − 10.94047I
u = 1.046970 + 0.439905I
a = −0.128616 + 1.041170I
b = −0.192235 + 0.299420I
−2.42744 − 7.70164I −2.21070 + 10.86632I
u = 1.046970 − 0.439905I
a = −0.128616 − 1.041170I
b = −0.192235 − 0.299420I
−2.42744 + 7.70164I −2.21070 − 10.86632I
u = 1.166620 + 0.659880I
a = −1.38335 − 1.68558I
b = 0.05610 − 2.99601I
3.6549 − 16.4066I 0.26530 + 10.19553I
u = 1.166620 − 0.659880I
a = −1.38335 + 1.68558I
b = 0.05610 + 2.99601I
3.6549 + 16.4066I 0.26530 − 10.19553I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377048 + 0.377232I
a = 0.307725 − 0.384276I
b = −0.611491 − 0.099728I
1.364800 + 0.359490I 6.91945 − 0.04590I
u = 0.377048 − 0.377232I
a = 0.307725 + 0.384276I
b = −0.611491 + 0.099728I
1.364800 − 0.359490I 6.91945 + 0.04590I
6
II.
I
u
2
= h−1.94×10
18
u
65
−2.98×10
18
u
64
+· · ·+1.31×10
18
b−9.50×10
18
, 1.46×
10
19
u
65
−7.80×10
19
u
64
+· · ·+6.56×10
17
a−1.86×10
19
, u
66
−6u
65
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−22.3158u
65
+ 118.956u
64
+ ··· + 46.5353u + 28.2908
1.47564u
65
+ 2.27453u
64
+ ··· + 16.1199u + 7.24598
a
6
=
17.6460u
65
− 85.9310u
64
+ ··· − 5.54679u − 12.6993
−9.07917u
65
+ 44.9975u
64
+ ··· + 7.67709u + 6.14426
a
10
=
−19.4674u
65
+ 106.132u
64
+ ··· + 53.5854u + 28.9858
−6.78423u
65
+ 40.7932u
64
+ ··· + 19.6572u + 11.6136
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
7
=
35.5665u
65
− 177.684u
64
+ ··· − 30.3716u − 28.2580
−0.424705u
65
− 6.71788u
64
+ ··· − 25.7126u − 8.98968
a
11
=
25.6164u
65
− 133.621u
64
+ ··· − 36.9797u − 29.4827
−8.13884u
65
+ 30.6283u
64
+ ··· − 9.28517u − 2.65549
a
8
=
6.14426u
65
− 27.7864u
64
+ ··· + 15.1971u − 1.53283
−19.9447u
65
+ 100.602u
64
+ ··· + 30.3453u + 17.6460
a
8
=
6.14426u
65
− 27.7864u
64
+ ··· + 15.1971u − 1.53283
−19.9447u
65
+ 100.602u
64
+ ··· + 30.3453u + 17.6460
(ii) Obstruction class = −1
(iii) Cusp Shapes =
12086631496832904775
655767731184955984
u
65
−
7581252097116615619
81970966398119498
u
64
+ ··· −
441245495247013113
655767731184955984
u −
4211855983240591645
327883865592477992
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
10
u
66
− 6u
65
+ ··· + u + 1
c
2
, c
11
u
66
+ 30u
65
+ ··· − 25u + 1
c
3
, c
5
, c
6
c
9
u
66
− 2u
65
+ ··· − 64u + 64
c
7
(u
33
− 2u
32
+ ··· + 84u + 49)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
y
66
− 30y
65
+ ··· + 25y + 1
c
2
, c
11
y
66
+ 18y
65
+ ··· + 1453y + 1
c
3
, c
5
, c
6
c
9
y
66
− 36y
65
+ ··· − 36864y + 4096
c
7
(y
33
− 14y
32
+ ··· − 3528y −2401)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904759 + 0.446690I
a = 2.84122 − 1.52553I
b = 1.32232 − 3.04286I
−2.95867 + 1.76219I 0
u = −0.904759 − 0.446690I
a = 2.84122 + 1.52553I
b = 1.32232 + 3.04286I
−2.95867 − 1.76219I 0
u = 0.544139 + 0.827076I
a = 0.172505 − 0.275088I
b = 0.107638 − 0.791057I
3.57176 − 0.40211I 0
u = 0.544139 − 0.827076I
a = 0.172505 + 0.275088I
b = 0.107638 + 0.791057I
3.57176 + 0.40211I 0
u = −0.961832 + 0.210042I
a = 0.756823 − 0.566102I
b = 0.636013 − 0.444310I
−1.74022 + 0.71657I 0
u = −0.961832 − 0.210042I
a = 0.756823 + 0.566102I
b = 0.636013 + 0.444310I
−1.74022 − 0.71657I 0
u = 0.455132 + 0.872435I
a = −0.321275 + 0.229842I
b = −0.339251 + 0.707485I
2.96228 + 4.26802I 0
u = 0.455132 − 0.872435I
a = −0.321275 − 0.229842I
b = −0.339251 − 0.707485I
2.96228 − 4.26802I 0
u = 0.407462 + 0.942447I
a = −1.49558 + 0.17696I
b = −0.33336 − 1.92881I
5.96795 + 10.55640I 0
u = 0.407462 − 0.942447I
a = −1.49558 − 0.17696I
b = −0.33336 + 1.92881I
5.96795 − 10.55640I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.914238 + 0.471505I
a = 0.274153 − 0.838704I
b = 1.65746 + 0.36585I
−2.80746 − 3.11554I 0
u = 0.914238 − 0.471505I
a = 0.274153 + 0.838704I
b = 1.65746 − 0.36585I
−2.80746 + 3.11554I 0
u = 0.862360 + 0.437489I
a = 0.51258 + 1.50106I
b = −0.216752 + 0.388716I
−2.55962 − 0.56819I 0
u = 0.862360 − 0.437489I
a = 0.51258 − 1.50106I
b = −0.216752 − 0.388716I
−2.55962 + 0.56819I 0
u = 0.480350 + 0.829100I
a = −2.22215 + 0.10328I
b = −0.03293 − 1.98412I
1.71328 + 1.77212I 0
u = 0.480350 − 0.829100I
a = −2.22215 − 0.10328I
b = −0.03293 + 1.98412I
1.71328 − 1.77212I 0
u = −0.732260 + 0.589717I
a = −2.12270 + 0.89719I
b = −0.87763 + 2.26509I
3.57176 + 0.40211I 3.54240 + 0.I
u = −0.732260 − 0.589717I
a = −2.12270 − 0.89719I
b = −0.87763 − 2.26509I
3.57176 − 0.40211I 3.54240 + 0.I
u = 0.603634 + 0.892529I
a = 1.83672 + 0.40288I
b = 0.14265 + 1.57592I
9.06216 0
u = 0.603634 − 0.892529I
a = 1.83672 − 0.40288I
b = 0.14265 − 1.57592I
9.06216 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.929321 + 0.583508I
a = −2.15255 + 1.50339I
b = −0.74412 + 2.72281I
2.96228 + 4.26802I 0
u = −0.929321 − 0.583508I
a = −2.15255 − 1.50339I
b = −0.74412 − 2.72281I
2.96228 − 4.26802I 0
u = 0.665888 + 0.873727I
a = −1.77794 − 0.54323I
b = −0.133969 − 1.404830I
7.69426 − 5.94756I 0
u = 0.665888 − 0.873727I
a = −1.77794 + 0.54323I
b = −0.133969 + 1.404830I
7.69426 + 5.94756I 0
u = 0.957231 + 0.541430I
a = −0.526732 − 0.892898I
b = 0.065036 − 0.385894I
0.32108 − 4.39805I 0
u = 0.957231 − 0.541430I
a = −0.526732 + 0.892898I
b = 0.065036 + 0.385894I
0.32108 + 4.39805I 0
u = 0.853729 + 0.285494I
a = −0.543347 − 0.659944I
b = 1.020820 − 0.059850I
−1.19449 + 4.90633I 1.49511 + 0.I
u = 0.853729 − 0.285494I
a = −0.543347 + 0.659944I
b = 1.020820 + 0.059850I
−1.19449 − 4.90633I 1.49511 + 0.I
u = −0.770621 + 0.443457I
a = 1.182830 + 0.436102I
b = 0.913903 + 0.253008I
−1.31058 −6 − 1.00000 + 0.10I
u = −0.770621 − 0.443457I
a = 1.182830 − 0.436102I
b = 0.913903 − 0.253008I
−1.31058 −6 − 1.00000 + 0.10I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636940 + 0.614253I
a = 1.97230 − 0.67580I
b = 0.75955 − 2.09262I
1.98821 − 5.14475I 1.15894 + 2.87802I
u = −0.636940 − 0.614253I
a = 1.97230 + 0.67580I
b = 0.75955 + 2.09262I
1.98821 + 5.14475I 1.15894 − 2.87802I
u = −0.982708 + 0.588767I
a = 2.05598 − 1.64453I
b = 0.60719 − 2.77532I
0.94779 + 9.91324I 0
u = −0.982708 − 0.588767I
a = 2.05598 + 1.64453I
b = 0.60719 + 2.77532I
0.94779 − 9.91324I 0
u = 0.726072 + 0.397331I
a = 0.228530 + 0.275068I
b = −0.921432 − 0.266276I
1.240670 + 0.272253I 4.90559 + 1.40386I
u = 0.726072 − 0.397331I
a = 0.228530 − 0.275068I
b = −0.921432 + 0.266276I
1.240670 − 0.272253I 4.90559 − 1.40386I
u = −1.115560 + 0.407709I
a = −0.525366 − 0.866763I
b = −0.470438 − 0.713792I
−2.55962 − 0.56819I 0
u = −1.115560 − 0.407709I
a = −0.525366 + 0.866763I
b = −0.470438 + 0.713792I
−2.55962 + 0.56819I 0
u = −1.228300 + 0.089688I
a = 0.00030 + 1.42724I
b = 0.001942 + 1.245290I
−2.95867 − 1.76219I 0
u = −1.228300 − 0.089688I
a = 0.00030 − 1.42724I
b = 0.001942 − 1.245290I
−2.95867 + 1.76219I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.195920 + 0.308871I
a = 0.280220 + 1.105220I
b = 0.260029 + 0.942647I
−2.80746 + 3.11554I 0
u = −1.195920 − 0.308871I
a = 0.280220 − 1.105220I
b = 0.260029 − 0.942647I
−2.80746 − 3.11554I 0
u = 1.117620 + 0.541451I
a = 0.455569 − 0.426873I
b = 0.251455 − 0.081822I
−1.19449 − 4.90633I 0
u = 1.117620 − 0.541451I
a = 0.455569 + 0.426873I
b = 0.251455 + 0.081822I
−1.19449 + 4.90633I 0
u = 1.002330 + 0.741441I
a = −0.967924 − 0.751179I
b = −0.66959 − 2.18374I
6.67035 0
u = 1.002330 − 0.741441I
a = −0.967924 + 0.751179I
b = −0.66959 + 2.18374I
6.67035 0
u = 1.067510 + 0.658022I
a = −0.869685 − 0.189017I
b = −0.302076 − 0.305752I
1.98821 − 5.14475I 0
u = 1.067510 − 0.658022I
a = −0.869685 + 0.189017I
b = −0.302076 + 0.305752I
1.98821 + 5.14475I 0
u = 1.100320 + 0.643486I
a = −1.82351 − 1.35338I
b = −0.53477 − 3.38382I
−0.15117 − 7.27375I 0
u = 1.100320 − 0.643486I
a = −1.82351 + 1.35338I
b = −0.53477 + 3.38382I
−0.15117 + 7.27375I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.053810 + 0.724277I
a = 1.17869 + 0.95847I
b = 0.61114 + 2.49765I
7.69426 − 5.94756I 0
u = 1.053810 − 0.724277I
a = 1.17869 − 0.95847I
b = 0.61114 − 2.49765I
7.69426 + 5.94756I 0
u = 1.122900 + 0.653215I
a = 0.911720 − 0.036398I
b = 0.401683 + 0.200042I
0.94779 − 9.91324I 0
u = 1.122900 − 0.653215I
a = 0.911720 + 0.036398I
b = 0.401683 − 0.200042I
0.94779 + 9.91324I 0
u = −1.307610 + 0.078191I
a = 0.047475 + 0.477579I
b = 1.39323 + 0.46432I
1.71328 − 1.77212I 0
u = −1.307610 − 0.078191I
a = 0.047475 − 0.477579I
b = 1.39323 − 0.46432I
1.71328 + 1.77212I 0
u = 0.209151 + 0.653417I
a = −0.350286 − 0.352621I
b = −0.604455 + 0.140178I
1.240670 + 0.272253I 4.90559 + 1.40386I
u = 0.209151 − 0.653417I
a = −0.350286 + 0.352621I
b = −0.604455 − 0.140178I
1.240670 − 0.272253I 4.90559 − 1.40386I
u = 1.144110 + 0.674165I
a = 1.41189 + 1.53805I
b = 0.13026 + 2.98702I
5.96795 − 10.55640I 0
u = 1.144110 − 0.674165I
a = 1.41189 − 1.53805I
b = 0.13026 − 2.98702I
5.96795 + 10.55640I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.322010 + 0.130704I
a = 0.130195 − 0.748866I
b = −1.24973 − 0.75426I
−0.15117 − 7.27375I 0
u = −1.322010 − 0.130704I
a = 0.130195 + 0.748866I
b = −1.24973 + 0.75426I
−0.15117 + 7.27375I 0
u = −0.114209 + 0.585210I
a = 0.862900 + 0.756442I
b = 0.850025 + 0.016896I
0.32108 + 4.39805I 1.68085 − 6.72354I
u = −0.114209 − 0.585210I
a = 0.862900 − 0.756442I
b = 0.850025 − 0.016896I
0.32108 − 4.39805I 1.68085 + 6.72354I
u = −0.085935 + 0.142884I
a = 4.58644 + 1.21264I
b = 0.298158 − 0.682511I
−1.74022 + 0.71657I −3.97070 − 0.74474I
u = −0.085935 − 0.142884I
a = 4.58644 − 1.21264I
b = 0.298158 + 0.682511I
−1.74022 − 0.71657I −3.97070 + 0.74474I
16
III. I
u
3
= h−u
5
+ u
4
− u
2
+ b, −u
3
+ u
2
+ a − 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
u
3
− u
2
+ 1
u
5
− u
4
+ u
2
a
6
=
1
u
2
a
10
=
u
3
− u
2
+ 1
u
5
− u
4
+ u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
7
=
−u
3
−u
5
+ u
3
− u
a
11
=
u
3
− u
2
+ u + 1
u
5
− u
4
+ u
2
+ u
a
8
=
−u
−u
a
8
=
−u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
+ 2u
3
− 3u
2
+ 2u − 1
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
9
u
6
c
7
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
(u − 1)
6
c
10
, c
11
(u + 1)
6
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
7
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
5
, c
9
y
6
c
8
, c
10
, c
11
(y − 1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.66103 + 1.45708I
b = 0.25695 + 1.72779I
−3.53554 + 0.92430I −5.77331 + 0.83820I
u = −1.002190 − 0.295542I
a = −0.66103 − 1.45708I
b = 0.25695 − 1.72779I
−3.53554 − 0.92430I −5.77331 − 0.83820I
u = 0.428243 + 0.664531I
a = 0.769407 − 0.497010I
b = 0.084211 + 0.566250I
0.245672 + 0.924305I −1.11831 − 1.11590I
u = 0.428243 − 0.664531I
a = 0.769407 + 0.497010I
b = 0.084211 − 0.566250I
0.245672 − 0.924305I −1.11831 + 1.11590I
u = 1.073950 + 0.558752I
a = 0.391622 + 0.558752I
b = −0.341164 + 0.940004I
−1.64493 − 5.69302I −3.10838 + 7.09196I
u = 1.073950 − 0.558752I
a = 0.391622 − 0.558752I
b = −0.341164 − 0.940004I
−1.64493 + 5.69302I −3.10838 − 7.09196I
20
IV.
I
u
4
= h−2a
5
+ 2a
4
− 7a
3
+ 5a
2
+ 3b − 4a + 4, a
6
+ 4a
4
+ a
3
+ 4a
2
+ 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
4
=
1
0
a
5
=
1
1
a
9
=
a
2
3
a
5
−
2
3
a
4
+ ··· +
4
3
a −
4
3
a
6
=
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
0
a
10
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
2
3
a
5
−
2
3
a
4
+ ··· +
4
3
a −
4
3
a
1
=
−1
−1
a
3
=
1
0
a
7
=
2
3
a
5
+
1
3
a
4
+ ··· +
4
3
a +
5
3
0
a
11
=
1
3
a
5
−
1
3
a
4
+ ··· −
1
3
a −
2
3
−
2
3
a
5
−
1
3
a
4
+ ··· −
4
3
a −
5
3
a
8
=
0
−
2
3
a
5
−
1
3
a
4
+ ··· −
4
3
a −
5
3
a
8
=
0
−
2
3
a
5
−
1
3
a
4
+ ··· −
4
3
a −
5
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
5
− a
4
− 12a
3
− 8a
2
− 4a − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
6
u
6
c
5
, c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
, c
9
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
6
y
6
c
5
, c
8
, c
9
c
10
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
7
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.341164 + 0.940004I
b = 0.732786 + 0.381252I
−1.64493 − 5.69302I −3.10838 + 7.09196I
u = −1.00000
a = −0.341164 − 0.940004I
b = 0.732786 − 0.381252I
−1.64493 + 5.69302I −3.10838 − 7.09196I
u = −1.00000
a = 0.084211 + 0.566250I
b = −0.917982 + 0.270708I
0.245672 + 0.924305I −1.11831 − 1.11590I
u = −1.00000
a = 0.084211 − 0.566250I
b = −0.917982 − 0.270708I
0.245672 − 0.924305I −1.11831 + 1.11590I
u = −1.00000
a = 0.25695 + 1.72779I
b = 0.685196 + 1.063260I
−3.53554 + 0.92430I −5.77331 + 0.83820I
u = −1.00000
a = 0.25695 − 1.72779I
b = 0.685196 − 1.063260I
−3.53554 − 0.92430I −5.77331 − 0.83820I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
((u − 1)
6
)(u
6
+ u
5
+ ··· + u + 1)(u
12
− 2u
11
+ ··· − 3u + 1)
· (u
66
− 6u
65
+ ··· + u + 1)
c
2
, c
11
((u + 1)
6
)(u
6
+ 3u
5
+ ··· + u + 1)(u
12
+ 6u
11
+ ··· + 3u + 1)
· (u
66
+ 30u
65
+ ··· − 25u + 1)
c
3
, c
5
u
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
· (u
12
− 3u
10
+ 5u
8
+ 2u
7
− 2u
6
− 5u
5
+ 4u
3
+ u
2
− 3u + 1)
· (u
66
− 2u
65
+ ··· − 64u + 64)
c
4
, c
10
((u + 1)
6
)(u
6
− u
5
+ ··· − u + 1)(u
12
− 2u
11
+ ··· − 3u + 1)
· (u
66
− 6u
65
+ ··· + u + 1)
c
6
, c
9
u
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
· (u
12
− 3u
10
+ 5u
8
+ 2u
7
− 2u
6
− 5u
5
+ 4u
3
+ u
2
− 3u + 1)
· (u
66
− 2u
65
+ ··· − 64u + 64)
c
7
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
12
+ 7u
11
+ ··· + 36u + 8)
· (u
33
− 2u
32
+ ··· + 84u + 49)
2
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
((y − 1)
6
)(y
6
− 3y
5
+ ··· − y + 1)(y
12
− 6y
11
+ ··· − 3y + 1)
· (y
66
− 30y
65
+ ··· + 25y + 1)
c
2
, c
11
((y − 1)
6
)(y
6
+ y
5
+ ··· + 3y + 1)(y
12
+ 2y
11
+ ··· + 25y + 1)
· (y
66
+ 18y
65
+ ··· + 1453y + 1)
c
3
, c
5
, c
6
c
9
y
6
(y
6
− 3y
5
+ ··· − y + 1)(y
12
− 6y
11
+ ··· − 7y + 1)
· (y
66
− 36y
65
+ ··· − 36864y + 4096)
c
7
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
12
− 5y
11
+ ··· − 112y + 64)
· (y
33
− 14y
32
+ ··· − 3528y − 2401)
2
26
