12n
0529
(K12n
0529
)
A knot diagram
1
Linearized knot diagam
3 6 10 1 8 2 11 5 11 4 8 9
Solving Sequence
3,10
4
6,11
2 7 8 1 5 9 12
c
3
c
10
c
2
c
6
c
7
c
1
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.62257 × 10
140
u
80
− 6.47276 × 10
140
u
79
+ ··· + 2.66122 × 10
142
b − 8.68171 × 10
142
,
3.03432 × 10
143
u
80
− 2.26585 × 10
143
u
79
+ ··· + 6.25386 × 10
144
a − 4.22144 × 10
145
, u
81
− u
80
+ ··· + 13u + 47i
I
u
2
= h−5u
23
+ u
22
+ ··· + b − 1, 16u
23
− 14u
22
+ ··· + a + 33, u
24
− 7u
22
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
= h8.62 × 10
140
u
80
− 6.47 × 10
140
u
79
+ · · · + 2.66 × 10
142
b − 8.68 ×
10
142
, 3.03 × 10
143
u
80
− 2.27 × 10
143
u
79
+ · · · + 6.25 × 10
144
a − 4.22 ×
10
145
, u
81
− u
80
+ · · · + 13u + 47i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−0.0485191u
80
+ 0.0362312u
79
+ ··· + 15.1878u + 6.75014
−0.0324008u
80
+ 0.0243225u
79
+ ··· + 6.35687u + 3.26231
a
11
=
−u
−u
3
+ u
a
2
=
0.145918u
80
− 0.00189727u
79
+ ··· − 15.4510u − 12.1681
−0.0187396u
80
− 0.0319668u
79
+ ··· − 1.63055u + 2.79062
a
7
=
0.0764253u
80
− 0.0146344u
79
+ ··· − 6.83981u − 7.33819
0.0574398u
80
− 0.0642603u
79
+ ··· − 8.20882u − 3.09289
a
8
=
0.169348u
80
− 0.0360227u
79
+ ··· − 13.2694u − 11.0124
0.0617316u
80
− 0.0482530u
79
+ ··· − 7.07660u − 2.78079
a
1
=
0.127178u
80
− 0.0338641u
79
+ ··· − 17.0815u − 9.37752
−0.0187396u
80
− 0.0319668u
79
+ ··· − 1.63055u + 2.79062
a
5
=
0.0973705u
80
+ 0.0318201u
79
+ ··· − 1.32449u − 4.48371
0.0209631u
80
+ 0.0149658u
79
+ ··· + 2.54446u − 2.31091
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
0.0533183u
80
− 0.0156877u
79
+ ··· − 12.0825u − 6.28809
−0.0819438u
80
− 0.00309381u
79
+ ··· + 5.06453u + 6.74036
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.574685u
80
− 0.0343111u
79
+ ··· − 42.1791u − 39.7887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 47u
80
+ ··· − 12u − 1
c
2
, c
6
u
81
− u
80
+ ··· + 6u
2
+ 1
c
3
, c
10
u
81
− u
80
+ ··· + 13u + 47
c
4
u
81
− 3u
80
+ ··· + 1837u + 347
c
5
, c
8
u
81
− 3u
80
+ ··· − 35u − 49
c
7
, c
11
u
81
+ 5u
80
+ ··· − 11394u + 9307
c
9
u
81
+ 43u
80
+ ··· + 30249u + 2209
c
12
u
81
− u
80
+ ··· − 251686u + 41753
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
− 9y
80
+ ··· − 28y −1
c
2
, c
6
y
81
+ 47y
80
+ ··· − 12y −1
c
3
, c
10
y
81
− 43y
80
+ ··· + 30249y −2209
c
4
y
81
+ 37y
80
+ ··· − 3637607y −120409
c
5
, c
8
y
81
+ 27y
80
+ ··· − 50323y −2401
c
7
, c
11
y
81
+ 63y
80
+ ··· + 678266132y −86620249
c
9
y
81
+ 5y
80
+ ··· − 223295699y −4879681
c
12
y
81
− 37y
80
+ ··· + 94686312444y −1743313009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159420 + 0.995305I
a = 0.935421 + 0.685407I
b = −0.578486 − 1.135720I
−2.78412 + 4.09191I 0
u = 0.159420 − 0.995305I
a = 0.935421 − 0.685407I
b = −0.578486 + 1.135720I
−2.78412 − 4.09191I 0
u = 0.376854 + 0.905642I
a = −0.252327 + 0.170325I
b = 0.413913 − 0.717629I
4.18971 − 1.89813I 6.48835 + 0.I
u = 0.376854 − 0.905642I
a = −0.252327 − 0.170325I
b = 0.413913 + 0.717629I
4.18971 + 1.89813I 6.48835 + 0.I
u = −0.661263 + 0.704542I
a = 0.839577 − 0.272761I
b = −0.476366 + 1.005480I
1.42827 − 2.25830I −4.00000 + 5.30334I
u = −0.661263 − 0.704542I
a = 0.839577 + 0.272761I
b = −0.476366 − 1.005480I
1.42827 + 2.25830I −4.00000 − 5.30334I
u = −1.000680 + 0.339594I
a = −0.64504 + 1.66330I
b = 0.332392 + 1.158070I
0.71275 + 3.59108I 0
u = −1.000680 − 0.339594I
a = −0.64504 − 1.66330I
b = 0.332392 − 1.158070I
0.71275 − 3.59108I 0
u = −0.571724 + 0.894004I
a = −0.351532 + 0.151292I
b = 0.436363 − 0.928482I
1.58675 + 1.13569I 0
u = −0.571724 − 0.894004I
a = −0.351532 − 0.151292I
b = 0.436363 + 0.928482I
1.58675 − 1.13569I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.934622
a = −0.202474
b = 0.471310
−1.70013 −4.55780
u = 0.883279 + 0.595878I
a = 0.630805 − 0.530733I
b = −0.525868 + 0.421987I
3.21313 − 3.83074I 0
u = 0.883279 − 0.595878I
a = 0.630805 + 0.530733I
b = −0.525868 − 0.421987I
3.21313 + 3.83074I 0
u = −0.408368 + 0.839079I
a = −1.46418 + 0.42247I
b = 0.924562 + 0.331227I
0.85878 − 5.06052I 0. + 2.81038I
u = −0.408368 − 0.839079I
a = −1.46418 − 0.42247I
b = 0.924562 − 0.331227I
0.85878 + 5.06052I 0. − 2.81038I
u = −0.979097 + 0.487895I
a = 0.105613 − 0.719977I
b = −0.931801 + 0.774121I
3.71023 + 0.03758I 0
u = −0.979097 − 0.487895I
a = 0.105613 + 0.719977I
b = −0.931801 − 0.774121I
3.71023 − 0.03758I 0
u = 0.322513 + 1.061320I
a = −0.810462 − 0.694013I
b = 0.599928 + 1.189190I
−1.78824 + 10.62680I 0
u = 0.322513 − 1.061320I
a = −0.810462 + 0.694013I
b = 0.599928 − 1.189190I
−1.78824 − 10.62680I 0
u = 0.823612 + 0.751253I
a = 0.811016 − 0.029992I
b = −0.409599 + 0.082280I
3.40007 − 1.49524I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823612 − 0.751253I
a = 0.811016 + 0.029992I
b = −0.409599 − 0.082280I
3.40007 + 1.49524I 0
u = 0.864023 + 0.185989I
a = 1.90280 + 2.54662I
b = −0.066643 + 0.845765I
−2.91161 + 2.49317I −8.76964 − 0.67821I
u = 0.864023 − 0.185989I
a = 1.90280 − 2.54662I
b = −0.066643 − 0.845765I
−2.91161 − 2.49317I −8.76964 + 0.67821I
u = 1.100390 + 0.201043I
a = 1.00477 + 1.01305I
b = −0.740363 − 0.292523I
−4.23067 + 2.70934I 0
u = 1.100390 − 0.201043I
a = 1.00477 − 1.01305I
b = −0.740363 + 0.292523I
−4.23067 − 2.70934I 0
u = 0.871403 + 0.717699I
a = 0.976706 − 0.631023I
b = −0.042020 + 0.535241I
3.36043 − 1.33032I 0
u = 0.871403 − 0.717699I
a = 0.976706 + 0.631023I
b = −0.042020 − 0.535241I
3.36043 + 1.33032I 0
u = 1.122290 + 0.197548I
a = −1.04175 − 1.25015I
b = 0.313035 − 0.963622I
−4.22930 − 2.75874I 0
u = 1.122290 − 0.197548I
a = −1.04175 + 1.25015I
b = 0.313035 + 0.963622I
−4.22930 + 2.75874I 0
u = 1.081310 + 0.429427I
a = −0.239516 − 0.185534I
b = −0.32431 − 1.54232I
−7.39105 − 5.07513I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.081310 − 0.429427I
a = −0.239516 + 0.185534I
b = −0.32431 + 1.54232I
−7.39105 + 5.07513I 0
u = −0.353227 + 0.757360I
a = 1.13050 − 1.44697I
b = −0.309577 + 1.131200I
−4.70079 − 3.78323I −5.54818 + 3.30856I
u = −0.353227 − 0.757360I
a = 1.13050 + 1.44697I
b = −0.309577 − 1.131200I
−4.70079 + 3.78323I −5.54818 − 3.30856I
u = 1.116360 + 0.351305I
a = −1.05780 − 0.95057I
b = 0.666696 + 0.237202I
−4.33281 − 4.26606I 0
u = 1.116360 − 0.351305I
a = −1.05780 + 0.95057I
b = 0.666696 − 0.237202I
−4.33281 + 4.26606I 0
u = 1.097800 + 0.427856I
a = 1.57748 + 0.94414I
b = −0.811505 + 1.002040I
2.99739 − 6.42104I 0
u = 1.097800 − 0.427856I
a = 1.57748 − 0.94414I
b = −0.811505 − 1.002040I
2.99739 + 6.42104I 0
u = 0.922762 + 0.740121I
a = −0.415168 − 0.652065I
b = 0.271496 + 0.211929I
3.08566 − 4.17180I 0
u = 0.922762 − 0.740121I
a = −0.415168 + 0.652065I
b = 0.271496 − 0.211929I
3.08566 + 4.17180I 0
u = −0.991780 + 0.652953I
a = −1.84179 + 0.76782I
b = 0.394401 + 1.134090I
0.43873 + 7.49699I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.991780 − 0.652953I
a = −1.84179 − 0.76782I
b = 0.394401 − 1.134090I
0.43873 − 7.49699I 0
u = 1.162730 + 0.284953I
a = −0.009432 + 0.485623I
b = 0.27944 + 1.42871I
−9.09751 + 0.85503I 0
u = 1.162730 − 0.284953I
a = −0.009432 − 0.485623I
b = 0.27944 − 1.42871I
−9.09751 − 0.85503I 0
u = −0.743234 + 0.302673I
a = 1.265020 + 0.224679I
b = −0.598633 + 1.007620I
1.64504 − 0.79136I −7.66851 − 3.15531I
u = −0.743234 − 0.302673I
a = 1.265020 − 0.224679I
b = −0.598633 − 1.007620I
1.64504 + 0.79136I −7.66851 + 3.15531I
u = −1.118710 + 0.488890I
a = 1.89475 − 0.05980I
b = −0.542651 − 1.179660I
−6.90163 + 2.26075I 0
u = −1.118710 − 0.488890I
a = 1.89475 + 0.05980I
b = −0.542651 + 1.179660I
−6.90163 − 2.26075I 0
u = −1.145040 + 0.505621I
a = −0.597188 + 0.555247I
b = 1.028760 − 0.304158I
−3.26600 + 3.64539I 0
u = −1.145040 − 0.505621I
a = −0.597188 − 0.555247I
b = 1.028760 + 0.304158I
−3.26600 − 3.64539I 0
u = −0.183670 + 0.715881I
a = 1.45549 − 0.28504I
b = −0.716431 − 0.354969I
−0.514533 + 0.940856I −1.24894 − 2.13001I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.183670 − 0.715881I
a = 1.45549 + 0.28504I
b = −0.716431 + 0.354969I
−0.514533 − 0.940856I −1.24894 + 2.13001I
u = −1.139740 + 0.579388I
a = −1.94101 + 0.08618I
b = 0.512467 + 1.158430I
−7.02831 + 8.88570I 0
u = −1.139740 − 0.579388I
a = −1.94101 − 0.08618I
b = 0.512467 − 1.158430I
−7.02831 − 8.88570I 0
u = −0.634187 + 0.341977I
a = −1.90217 + 0.43344I
b = 0.915109 + 0.975916I
4.92844 + 3.68094I −2.52917 − 1.30807I
u = −0.634187 − 0.341977I
a = −1.90217 − 0.43344I
b = 0.915109 − 0.975916I
4.92844 − 3.68094I −2.52917 + 1.30807I
u = −1.136150 + 0.610179I
a = 0.747989 − 0.641986I
b = −1.136880 + 0.243931I
−1.34866 + 10.46180I 0
u = −1.136150 − 0.610179I
a = 0.747989 + 0.641986I
b = −1.136880 − 0.243931I
−1.34866 − 10.46180I 0
u = −1.070200 + 0.734551I
a = 1.296960 − 0.360784I
b = −0.378710 − 1.178060I
0.09459 + 4.85619I 0
u = −1.070200 − 0.734551I
a = 1.296960 + 0.360784I
b = −0.378710 + 1.178060I
0.09459 − 4.85619I 0
u = 0.637063 + 0.218185I
a = −1.32663 − 1.92334I
b = 0.03800 − 1.49521I
−5.48699 + 1.94976I 2.72009 + 1.05128I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637063 − 0.218185I
a = −1.32663 + 1.92334I
b = 0.03800 + 1.49521I
−5.48699 − 1.94976I 2.72009 − 1.05128I
u = −0.311386 + 0.591390I
a = −0.80934 + 2.32791I
b = 0.226255 − 1.139810I
−4.49439 + 2.07707I −5.39720 − 3.30118I
u = −0.311386 − 0.591390I
a = −0.80934 − 2.32791I
b = 0.226255 + 1.139810I
−4.49439 − 2.07707I −5.39720 + 3.30118I
u = 0.985820 + 0.912507I
a = −0.636717 + 0.039730I
b = 0.201679 − 0.628086I
2.79450 − 4.44773I 0
u = 0.985820 − 0.912507I
a = −0.636717 − 0.039730I
b = 0.201679 + 0.628086I
2.79450 + 4.44773I 0
u = 1.359520 + 0.164573I
a = −0.399737 − 1.222220I
b = 0.068318 − 0.573572I
−4.98357 − 3.68959I 0
u = 1.359520 − 0.164573I
a = −0.399737 + 1.222220I
b = 0.068318 + 0.573572I
−4.98357 + 3.68959I 0
u = 1.258050 + 0.575219I
a = −1.49315 − 0.54735I
b = 0.651128 − 1.243060I
−6.14816 − 9.70514I 0
u = 1.258050 − 0.575219I
a = −1.49315 + 0.54735I
b = 0.651128 + 1.243060I
−6.14816 + 9.70514I 0
u = −1.290740 + 0.507998I
a = 0.736660 − 0.702992I
b = −0.356631 − 1.170940I
−0.49084 + 6.69889I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.290740 − 0.507998I
a = 0.736660 + 0.702992I
b = −0.356631 + 1.170940I
−0.49084 − 6.69889I 0
u = 1.240140 + 0.660502I
a = 1.56088 + 0.45637I
b = −0.65000 + 1.29438I
−4.6334 − 16.7910I 0
u = 1.240140 − 0.660502I
a = 1.56088 − 0.45637I
b = −0.65000 − 1.29438I
−4.6334 + 16.7910I 0
u = −1.38465 + 0.37974I
a = 0.139313 − 0.158138I
b = 0.414696 − 1.149390I
−7.77183 + 0.76959I 0
u = −1.38465 − 0.37974I
a = 0.139313 + 0.158138I
b = 0.414696 + 1.149390I
−7.77183 − 0.76959I 0
u = 0.417926 + 0.357171I
a = −0.87838 − 1.58477I
b = 0.857230 + 0.892954I
5.13693 + 2.84021I 1.05922 − 6.16779I
u = 0.417926 − 0.357171I
a = −0.87838 + 1.58477I
b = 0.857230 − 0.892954I
5.13693 − 2.84021I 1.05922 + 6.16779I
u = −1.47404 + 0.21229I
a = −0.048590 + 0.308635I
b = −0.384894 + 1.161020I
−8.06565 − 6.08851I 0
u = −1.47404 − 0.21229I
a = −0.048590 − 0.308635I
b = −0.384894 − 1.161020I
−8.06565 + 6.08851I 0
u = −0.238068 + 0.402940I
a = 1.102460 − 0.088285I
b = −0.300155 − 0.543538I
−0.171294 + 1.043260I −3.00612 − 6.15581I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238068 − 0.402940I
a = 1.102460 + 0.088285I
b = −0.300155 + 0.543538I
−0.171294 − 1.043260I −3.00612 + 6.15581I
13
II. I
u
2
=
h−5u
23
+u
22
+· · ·+b−1, 16u
23
−14u
22
+· · ·+a+33, u
24
−7u
22
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−16u
23
+ 14u
22
+ ··· − 24u − 33
5u
23
− u
22
+ ··· − 7u + 1
a
11
=
−u
−u
3
+ u
a
2
=
8u
23
− u
22
+ ··· − 16u + 10
u
23
− 7u
21
+ ··· − 2u − 1
a
7
=
−15u
23
+ 6u
22
+ ··· − 4u − 20
3u
23
− 4u
22
+ ··· + 13u + 8
a
8
=
−18u
23
+ 6u
22
+ ··· + u − 21
4u
23
− 4u
22
+ ··· + 11u + 9
a
1
=
9u
23
− u
22
+ ··· − 18u + 9
u
23
− 7u
21
+ ··· − 2u − 1
a
5
=
−8u
23
+ 7u
22
+ ··· − 18u − 26
u
23
+ u
22
+ ··· − 5u + 1
a
9
=
u
3
u
5
− u
3
+ u
a
12
=
8u
23
− u
22
+ ··· − 16u + 9
−u
19
+ 6u
17
+ ··· + 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 25u
23
− 22u
22
− 171u
21
+ 195u
20
+ 576u
19
− 827u
18
− 1216u
17
+
2202u
16
+ 1672u
15
− 4057u
14
− 1435u
13
+ 5422u
12
+ 575u
11
− 5408u
10
+ 259u
9
+
4100u
8
− 511u
7
− 2403u
6
+ 358u
5
+ 1038u
4
− 121u
3
− 324u
2
+ 10u + 45
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
24
− 16u
23
+ ··· − 21u + 1
c
2
u
24
+ 8u
22
+ ··· + u + 1
c
3
u
24
− 7u
22
+ ··· + 2u + 1
c
4
u
24
+ 2u
23
+ ··· − 2u
2
+ 1
c
5
u
24
− 4u
23
+ ··· − 4u + 1
c
6
u
24
+ 8u
22
+ ··· − u + 1
c
7
u
24
+ 2u
22
+ ··· + u + 1
c
8
u
24
+ 4u
23
+ ··· + 4u + 1
c
9
u
24
− 14u
23
+ ··· − 16u + 1
c
10
u
24
− 7u
22
+ ··· − 2u + 1
c
11
u
24
+ 2u
22
+ ··· − u + 1
c
12
u
24
+ 8u
23
+ ··· − 203u + 103
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 32y
22
+ ··· − 23y + 1
c
2
, c
6
y
24
+ 16y
23
+ ··· + 21y + 1
c
3
, c
10
y
24
− 14y
23
+ ··· − 16y + 1
c
4
y
24
+ 18y
23
+ ··· − 4y + 1
c
5
, c
8
y
24
+ 16y
23
+ ··· + 20y + 1
c
7
, c
11
y
24
+ 4y
23
+ ··· − 11y + 1
c
9
y
24
+ 6y
23
+ ··· − 8y + 1
c
12
y
24
− 8y
23
+ ··· + 12145y + 10609
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.760804 + 0.607035I
a = −1.49179 + 0.04895I
b = 0.887524 − 0.776961I
5.70049 − 4.53187I 3.10527 + 6.80987I
u = 0.760804 − 0.607035I
a = −1.49179 − 0.04895I
b = 0.887524 + 0.776961I
5.70049 + 4.53187I 3.10527 − 6.80987I
u = 0.692071 + 0.781521I
a = 0.611885 − 0.793457I
b = −0.339703 + 0.732138I
3.33432 − 2.30280I −2.18873 + 5.34734I
u = 0.692071 − 0.781521I
a = 0.611885 + 0.793457I
b = −0.339703 − 0.732138I
3.33432 + 2.30280I −2.18873 − 5.34734I
u = −0.716982 + 0.459544I
a = −0.680089 + 0.749202I
b = 0.874697 − 1.033040I
4.95705 − 1.97528I −0.77501 − 2.33256I
u = −0.716982 − 0.459544I
a = −0.680089 − 0.749202I
b = 0.874697 + 1.033040I
4.95705 + 1.97528I −0.77501 + 2.33256I
u = −1.044620 + 0.486468I
a = 1.50313 − 1.01455I
b = −0.707939 − 1.076430I
3.79667 + 5.88099I 0.70835 − 4.51294I
u = −1.044620 − 0.486468I
a = 1.50313 + 1.01455I
b = −0.707939 + 1.076430I
3.79667 − 5.88099I 0.70835 + 4.51294I
u = 0.982224 + 0.632402I
a = 0.066377 + 0.727471I
b = −0.725173 − 0.698599I
4.98117 − 0.35208I 2.23151 + 0.17854I
u = 0.982224 − 0.632402I
a = 0.066377 − 0.727471I
b = −0.725173 + 0.698599I
4.98117 + 0.35208I 2.23151 − 0.17854I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.210080 + 0.127545I
a = 0.196543 + 0.090225I
b = 0.070686 + 1.309280I
−7.87423 − 3.04176I −7.80879 + 2.61074I
u = 1.210080 − 0.127545I
a = 0.196543 − 0.090225I
b = 0.070686 − 1.309280I
−7.87423 + 3.04176I −7.80879 − 2.61074I
u = −0.568852 + 0.486026I
a = 0.778900 + 0.647406I
b = −0.474721 + 1.003620I
2.29472 − 1.15093I 2.64163 + 1.71093I
u = −0.568852 − 0.486026I
a = 0.778900 − 0.647406I
b = −0.474721 − 1.003620I
2.29472 + 1.15093I 2.64163 − 1.71093I
u = 0.732837 + 0.096465I
a = 1.22326 + 2.46457I
b = −0.04279 + 1.41632I
−5.93011 + 2.08072I −15.0441 − 4.1088I
u = 0.732837 − 0.096465I
a = 1.22326 − 2.46457I
b = −0.04279 − 1.41632I
−5.93011 − 2.08072I −15.0441 + 4.1088I
u = 0.970626 + 0.826369I
a = 0.040532 − 0.461280I
b = 0.152881 + 0.624525I
2.52482 − 3.79144I −6.34052 − 1.00053I
u = 0.970626 − 0.826369I
a = 0.040532 + 0.461280I
b = 0.152881 − 0.624525I
2.52482 + 3.79144I −6.34052 + 1.00053I
u = −1.133250 + 0.654883I
a = −1.105590 + 0.663064I
b = 0.306177 + 1.173280I
0.26786 + 5.91058I −1.36806 − 6.09267I
u = −1.133250 − 0.654883I
a = −1.105590 − 0.663064I
b = 0.306177 − 1.173280I
0.26786 − 5.91058I −1.36806 + 6.09267I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.310450 + 0.138714I
a = −0.42360 + 1.66109I
b = 0.128205 + 0.671742I
−5.27306 + 3.87856I −18.3514 − 11.3041I
u = −1.310450 − 0.138714I
a = −0.42360 − 1.66109I
b = 0.128205 − 0.671742I
−5.27306 − 3.87856I −18.3514 + 11.3041I
u = −0.574501 + 0.081525I
a = 1.78044 − 3.44622I
b = −0.129839 + 0.528164I
−2.19997 − 2.85560I 0.68983 + 4.72031I
u = −0.574501 − 0.081525I
a = 1.78044 + 3.44622I
b = −0.129839 − 0.528164I
−2.19997 + 2.85560I 0.68983 − 4.72031I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 16u
23
+ ··· − 21u + 1)(u
81
+ 47u
80
+ ··· − 12u − 1)
c
2
(u
24
+ 8u
22
+ ··· + u + 1)(u
81
− u
80
+ ··· + 6u
2
+ 1)
c
3
(u
24
− 7u
22
+ ··· + 2u + 1)(u
81
− u
80
+ ··· + 13u + 47)
c
4
(u
24
+ 2u
23
+ ··· − 2u
2
+ 1)(u
81
− 3u
80
+ ··· + 1837u + 347)
c
5
(u
24
− 4u
23
+ ··· − 4u + 1)(u
81
− 3u
80
+ ··· − 35u − 49)
c
6
(u
24
+ 8u
22
+ ··· − u + 1)(u
81
− u
80
+ ··· + 6u
2
+ 1)
c
7
(u
24
+ 2u
22
+ ··· + u + 1)(u
81
+ 5u
80
+ ··· − 11394u + 9307)
c
8
(u
24
+ 4u
23
+ ··· + 4u + 1)(u
81
− 3u
80
+ ··· − 35u − 49)
c
9
(u
24
− 14u
23
+ ··· − 16u + 1)(u
81
+ 43u
80
+ ··· + 30249u + 2209)
c
10
(u
24
− 7u
22
+ ··· − 2u + 1)(u
81
− u
80
+ ··· + 13u + 47)
c
11
(u
24
+ 2u
22
+ ··· − u + 1)(u
81
+ 5u
80
+ ··· − 11394u + 9307)
c
12
(u
24
+ 8u
23
+ ··· − 203u + 103)(u
81
− u
80
+ ··· − 251686u + 41753)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
− 32y
22
+ ··· − 23y + 1)(y
81
− 9y
80
+ ··· − 28y −1)
c
2
, c
6
(y
24
+ 16y
23
+ ··· + 21y + 1)(y
81
+ 47y
80
+ ··· − 12y −1)
c
3
, c
10
(y
24
− 14y
23
+ ··· − 16y + 1)(y
81
− 43y
80
+ ··· + 30249y −2209)
c
4
(y
24
+ 18y
23
+ ··· − 4y + 1)(y
81
+ 37y
80
+ ··· − 3637607y −120409)
c
5
, c
8
(y
24
+ 16y
23
+ ··· + 20y + 1)(y
81
+ 27y
80
+ ··· − 50323y −2401)
c
7
, c
11
(y
24
+ 4y
23
+ ··· − 11y + 1)
· (y
81
+ 63y
80
+ ··· + 678266132y −86620249)
c
9
(y
24
+ 6y
23
+ ··· − 8y + 1)
· (y
81
+ 5y
80
+ ··· − 223295699y −4879681)
c
12
(y
24
− 8y
23
+ ··· + 12145y + 10609)
· (y
81
− 37y
80
+ ··· + 94686312444y −1743313009)
23
