12a
1084
(K12a
1084
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 9 2 11 12 5 3 8 6
Solving Sequence
7,11
8 12
3,9
2 6 5 10 4 1
c
7
c
11
c
8
c
2
c
6
c
5
c
10
c
3
c
1
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.41095 × 10
226
u
98
− 5.69026 × 10
226
u
97
+ ··· + 5.42259 × 10
227
b − 1.90870 × 10
229
,
− 2.17596 × 10
230
u
98
+ 3.39515 × 10
230
u
97
+ ··· + 5.43886 × 10
230
a + 4.44885 × 10
233
,
u
99
− 4u
98
+ ··· + 2545u + 1003i
I
u
2
= h2996823u
26
+ 3522809u
25
+ ··· + 792677b − 4094869,
− 533686u
26
+ 1883904u
25
+ ··· + 792677a + 5658204, u
27
+ 3u
26
+ ··· + 5u − 1i
* 2 irreducible components of dim
C
= 0, with total 126 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
= h5.41 × 10
226
u
98
− 5.69 × 10
226
u
97
+ · · · + 5.42 × 10
227
b − 1.91 ×
10
229
, −2.18 × 10
230
u
98
+ 3.40 × 10
230
u
97
+ · · · + 5.44 × 10
230
a + 4.45 ×
10
233
, u
99
− 4u
98
+ · · · + 2545u + 1003i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
0.400077u
98
− 0.624239u
97
+ ··· − 1633.59u − 817.975
−0.0997853u
98
+ 0.104936u
97
+ ··· + 340.396u + 35.1990
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
0.300292u
98
− 0.519303u
97
+ ··· − 1293.20u − 782.776
−0.0997853u
98
+ 0.104936u
97
+ ··· + 340.396u + 35.1990
a
6
=
0.0548331u
98
− 0.912289u
97
+ ··· + 1474.97u + 778.578
0.0336398u
98
− 0.236589u
97
+ ··· + 237.616u + 235.987
a
5
=
0.0408862u
98
− 1.05461u
97
+ ··· + 1912.99u + 1025.59
0.0737455u
98
− 0.370751u
97
+ ··· + 271.358u + 328.673
a
10
=
−0.695680u
98
+ 1.69937u
97
+ ··· + 1342.50u + 887.962
−0.590927u
98
+ 1.84609u
97
+ ··· + 488.653u − 21.2569
a
4
=
1.75208u
98
− 4.12027u
97
+ ··· − 3777.53u − 756.930
1.86946u
98
− 4.33276u
97
+ ··· − 4177.35u − 1429.35
a
1
=
1.75093u
98
− 3.19905u
97
+ ··· − 6038.12u − 2076.45
0.485526u
98
− 0.641300u
97
+ ··· − 2274.29u − 1238.76
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.887479u
98
+ 2.43148u
97
+ ··· + 1143.39u + 1477.84
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
99
− 8u
98
+ ··· + 19u − 1
c
2
, c
6
u
99
− 2u
98
+ ··· − 21137u − 8401
c
3
, c
10
u
99
+ u
98
+ ··· − 17146u − 20252
c
5
, c
9
u
99
− 3u
98
+ ··· − 1873u − 577
c
7
, c
8
, c
11
u
99
+ 4u
98
+ ··· + 2545u − 1003
c
12
u
99
+ 2u
98
+ ··· − 23310064u − 2254444
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
99
+ 56y
98
+ ··· + 87y −1
c
2
, c
6
y
99
− 80y
98
+ ··· − 692503643y −70576801
c
3
, c
10
y
99
+ 95y
98
+ ··· + 3720826236y −410143504
c
5
, c
9
y
99
+ 71y
98
+ ··· − 12786351y −332929
c
7
, c
8
, c
11
y
99
− 120y
98
+ ··· + 48189789y −1006009
c
12
y
99
− 42y
98
+ ··· + 169128066365000y −5082517749136
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671582 + 0.666153I
a = −0.81851 − 1.26445I
b = 1.39390 + 0.42952I
−3.01360 − 7.08917I 0
u = 0.671582 − 0.666153I
a = −0.81851 + 1.26445I
b = 1.39390 − 0.42952I
−3.01360 + 7.08917I 0
u = 0.625140 + 0.686233I
a = 0.834216 + 0.986532I
b = −1.391950 − 0.146302I
−5.26496 − 2.40033I 0
u = 0.625140 − 0.686233I
a = 0.834216 − 0.986532I
b = −1.391950 + 0.146302I
−5.26496 + 2.40033I 0
u = 0.422701 + 0.807441I
a = −1.30778 − 0.63709I
b = 1.236250 − 0.119711I
−2.18481 + 2.18176I 0
u = 0.422701 − 0.807441I
a = −1.30778 + 0.63709I
b = 1.236250 + 0.119711I
−2.18481 − 2.18176I 0
u = −0.896243 + 0.006019I
a = −0.228443 + 0.713126I
b = −0.836938 − 0.795713I
1.52179 − 2.96179I 0
u = −0.896243 − 0.006019I
a = −0.228443 − 0.713126I
b = −0.836938 + 0.795713I
1.52179 + 2.96179I 0
u = 0.561471 + 0.662733I
a = 0.709135 + 1.118490I
b = −1.366860 − 0.093390I
−5.13995 − 2.31729I 0
u = 0.561471 − 0.662733I
a = 0.709135 − 1.118490I
b = −1.366860 + 0.093390I
−5.13995 + 2.31729I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.632131 + 0.587585I
a = −0.128876 + 0.582565I
b = −1.121870 − 0.038053I
−4.62953 − 2.16317I 0
u = 0.632131 − 0.587585I
a = −0.128876 − 0.582565I
b = −1.121870 + 0.038053I
−4.62953 + 2.16317I 0
u = 1.15287
a = −0.329540
b = −0.490126
−2.39809 0
u = −0.647182 + 0.484954I
a = 0.81717 − 1.19305I
b = −0.064411 + 0.544461I
−5.31603 + 1.89708I 0
u = −0.647182 − 0.484954I
a = 0.81717 + 1.19305I
b = −0.064411 − 0.544461I
−5.31603 − 1.89708I 0
u = −0.656533 + 0.429069I
a = −0.31014 + 1.49332I
b = 0.055583 − 1.009320I
−2.21186 + 7.67640I 0
u = −0.656533 − 0.429069I
a = −0.31014 − 1.49332I
b = 0.055583 + 1.009320I
−2.21186 − 7.67640I 0
u = −0.884666 + 0.838961I
a = 0.548928 − 1.096780I
b = −1.38567 + 0.40064I
−6.8912 + 12.6306I 0
u = −0.884666 − 0.838961I
a = 0.548928 + 1.096780I
b = −1.38567 − 0.40064I
−6.8912 − 12.6306I 0
u = 0.389722 + 0.629908I
a = −0.832777 + 0.668407I
b = 0.292539 − 0.596900I
0.39264 − 3.39831I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389722 − 0.629908I
a = −0.832777 − 0.668407I
b = 0.292539 + 0.596900I
0.39264 + 3.39831I 0
u = 0.459085 + 0.568866I
a = −0.162137 + 0.715721I
b = 0.927472 − 0.541537I
−1.47108 + 3.63726I 0
u = 0.459085 − 0.568866I
a = −0.162137 − 0.715721I
b = 0.927472 + 0.541537I
−1.47108 − 3.63726I 0
u = 0.565793 + 0.435926I
a = 1.24415 − 1.19701I
b = 1.048280 + 0.361406I
−1.81044 − 7.03502I 0
u = 0.565793 − 0.435926I
a = 1.24415 + 1.19701I
b = 1.048280 − 0.361406I
−1.81044 + 7.03502I 0
u = 0.509382 + 0.498338I
a = 0.132878 − 1.139320I
b = 0.344177 + 0.527838I
−0.086668 − 0.470961I 0
u = 0.509382 − 0.498338I
a = 0.132878 + 1.139320I
b = 0.344177 − 0.527838I
−0.086668 + 0.470961I 0
u = −0.232634 + 1.269800I
a = 0.987311 − 0.040384I
b = −1.269770 − 0.132436I
−4.83968 − 6.00928I 0
u = −0.232634 − 1.269800I
a = 0.987311 + 0.040384I
b = −1.269770 + 0.132436I
−4.83968 + 6.00928I 0
u = −0.626540 + 0.273548I
a = 0.93551 − 2.09001I
b = −1.234250 + 0.462376I
−8.25997 + 1.73585I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626540 − 0.273548I
a = 0.93551 + 2.09001I
b = −1.234250 − 0.462376I
−8.25997 − 1.73585I 0
u = −0.362556 + 0.575051I
a = −1.68279 − 0.01512I
b = −0.143843 + 0.295187I
−1.23465 − 4.31084I 0
u = −0.362556 − 0.575051I
a = −1.68279 + 0.01512I
b = −0.143843 − 0.295187I
−1.23465 + 4.31084I 0
u = 0.676867 + 0.044621I
a = 0.94289 + 1.18081I
b = 0.469702 + 0.239598I
0.632736 + 0.678056I 0
u = 0.676867 − 0.044621I
a = 0.94289 − 1.18081I
b = 0.469702 − 0.239598I
0.632736 − 0.678056I 0
u = −0.647432 + 0.189841I
a = −0.72737 + 1.72532I
b = 1.49112 − 0.35700I
−7.01581 − 2.36185I 0
u = −0.647432 − 0.189841I
a = −0.72737 − 1.72532I
b = 1.49112 + 0.35700I
−7.01581 + 2.36185I 0
u = 1.339350 + 0.111965I
a = 0.148541 + 0.088908I
b = −0.442208 + 0.756719I
−1.48538 − 0.70299I 0
u = 1.339350 − 0.111965I
a = 0.148541 − 0.088908I
b = −0.442208 − 0.756719I
−1.48538 + 0.70299I 0
u = −1.42141 + 0.18001I
a = 0.259621 + 0.430934I
b = 0.296118 − 0.499010I
−6.11710 + 2.82126I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42141 − 0.18001I
a = 0.259621 − 0.430934I
b = 0.296118 + 0.499010I
−6.11710 − 2.82126I 0
u = −0.502166 + 0.238090I
a = −0.996833 − 0.817909I
b = −0.908820 + 0.518858I
2.03936 + 3.39507I 0.73878 − 7.34492I
u = −0.502166 − 0.238090I
a = −0.996833 + 0.817909I
b = −0.908820 − 0.518858I
2.03936 − 3.39507I 0.73878 + 7.34492I
u = −0.486584 + 0.268353I
a = 1.16169 − 3.08951I
b = −1.136470 − 0.000745I
−7.76651 + 0.21651I −10.72357 + 1.56326I
u = −0.486584 − 0.268353I
a = 1.16169 + 3.08951I
b = −1.136470 + 0.000745I
−7.76651 − 0.21651I −10.72357 − 1.56326I
u = −1.44027 + 0.22382I
a = −0.490873 − 0.025787I
b = 0.225206 + 0.508462I
−5.48236 + 6.48741I 0
u = −1.44027 − 0.22382I
a = −0.490873 + 0.025787I
b = 0.225206 − 0.508462I
−5.48236 − 6.48741I 0
u = −0.490936 + 0.178178I
a = 0.24238 + 3.11516I
b = 1.382040 − 0.014841I
−6.44341 + 3.68086I −13.6904 − 4.8990I
u = −0.490936 − 0.178178I
a = 0.24238 − 3.11516I
b = 1.382040 + 0.014841I
−6.44341 − 3.68086I −13.6904 + 4.8990I
u = −1.48618 + 0.00613I
a = 0.098528 + 0.813606I
b = 0.315796 − 0.762481I
−6.09592 + 1.64565I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48618 − 0.00613I
a = 0.098528 − 0.813606I
b = 0.315796 + 0.762481I
−6.09592 − 1.64565I 0
u = −0.178980 + 0.439864I
a = 1.056880 + 0.579358I
b = −0.531876 − 0.756279I
3.23925 − 1.18451I 3.17617 + 1.25796I
u = −0.178980 − 0.439864I
a = 1.056880 − 0.579358I
b = −0.531876 + 0.756279I
3.23925 + 1.18451I 3.17617 − 1.25796I
u = 0.465205 + 0.093431I
a = −0.07254 + 2.27543I
b = 0.204842 − 1.190100I
1.36006 − 1.43745I −12.0554 + 7.7332I
u = 0.465205 − 0.093431I
a = −0.07254 − 2.27543I
b = 0.204842 + 1.190100I
1.36006 + 1.43745I −12.0554 − 7.7332I
u = 1.54191 + 0.03849I
a = −0.790361 + 0.168672I
b = −1.305740 − 0.260764I
−4.84551 − 4.27483I 0
u = 1.54191 − 0.03849I
a = −0.790361 − 0.168672I
b = −1.305740 + 0.260764I
−4.84551 + 4.27483I 0
u = 1.55153
a = 0.691794
b = 1.41813
−8.58947 0
u = 1.56140 + 0.07649I
a = −0.27530 + 1.40786I
b = −1.140370 − 0.297190I
−14.8432 − 1.4473I 0
u = 1.56140 − 0.07649I
a = −0.27530 − 1.40786I
b = −1.140370 + 0.297190I
−14.8432 + 1.4473I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56585 + 0.01882I
a = −0.050219 − 0.867231I
b = 0.22809 + 1.70840I
−5.74012 + 1.79605I 0
u = −1.56585 − 0.01882I
a = −0.050219 + 0.867231I
b = 0.22809 − 1.70840I
−5.74012 − 1.79605I 0
u = 1.56534 + 0.05266I
a = 0.653824 − 1.146550I
b = 1.43207 + 0.25279I
−13.5869 − 4.5151I 0
u = 1.56534 − 0.05266I
a = 0.653824 + 1.146550I
b = 1.43207 − 0.25279I
−13.5869 + 4.5151I 0
u = −0.431395
a = 1.13469
b = 0.946642
−1.70568 −3.51530
u = −1.05293 + 1.16373I
a = −0.552771 + 0.656982I
b = 1.295040 − 0.191585I
−9.47040 + 4.51904I 0
u = −1.05293 − 1.16373I
a = −0.552771 − 0.656982I
b = 1.295040 + 0.191585I
−9.47040 − 4.51904I 0
u = 0.284081 + 0.308258I
a = −0.439234 − 1.143360I
b = 0.214478 + 0.317345I
−0.189428 − 0.841299I −4.65351 + 7.98617I
u = 0.284081 − 0.308258I
a = −0.439234 + 1.143360I
b = 0.214478 − 0.317345I
−0.189428 + 0.841299I −4.65351 − 7.98617I
u = −1.57655 + 0.11657I
a = 1.105590 + 0.283380I
b = 1.302210 − 0.195925I
−9.12473 + 8.98920I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57655 − 0.11657I
a = 1.105590 − 0.283380I
b = 1.302210 + 0.195925I
−9.12473 − 8.98920I 0
u = −1.57232 + 0.17577I
a = −0.525222 − 0.887076I
b = −1.49086 + 0.22367I
−12.31410 + 5.28789I 0
u = −1.57232 − 0.17577I
a = −0.525222 + 0.887076I
b = −1.49086 − 0.22367I
−12.31410 − 5.28789I 0
u = 1.60156 + 0.07631I
a = −0.080976 + 1.002640I
b = −1.39765 − 0.86415I
−15.9884 − 3.0243I 0
u = 1.60156 − 0.07631I
a = −0.080976 − 1.002640I
b = −1.39765 + 0.86415I
−15.9884 + 3.0243I 0
u = 1.60206 + 0.11818I
a = 0.083430 − 0.863594I
b = 0.13553 + 1.48784I
−9.94507 − 9.67187I 0
u = 1.60206 − 0.11818I
a = 0.083430 + 0.863594I
b = 0.13553 − 1.48784I
−9.94507 + 9.67187I 0
u = 1.60254 + 0.12020I
a = 0.054616 + 0.921423I
b = −0.244997 − 1.142180I
−13.03140 − 4.01637I 0
u = 1.60254 − 0.12020I
a = 0.054616 − 0.921423I
b = −0.244997 + 1.142180I
−13.03140 + 4.01637I 0
u = 1.60624 + 0.05496I
a = 0.120137 − 0.790933I
b = 1.72208 + 0.68668I
−14.8594 + 1.4437I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60624 − 0.05496I
a = 0.120137 + 0.790933I
b = 1.72208 − 0.68668I
−14.8594 − 1.4437I 0
u = −1.60055 + 0.19017I
a = −0.198672 − 0.849455I
b = −1.62688 + 0.39160I
−12.79020 + 5.57261I 0
u = −1.60055 − 0.19017I
a = −0.198672 + 0.849455I
b = −1.62688 − 0.39160I
−12.79020 − 5.57261I 0
u = −1.60485 + 0.15048I
a = −0.502230 − 0.340729I
b = −1.46981 + 0.03824I
−12.27220 + 4.78564I 0
u = −1.60485 − 0.15048I
a = −0.502230 + 0.340729I
b = −1.46981 − 0.03824I
−12.27220 − 4.78564I 0
u = −1.60258 + 0.19607I
a = 0.169020 + 0.982199I
b = 1.63051 − 0.67539I
−10.6448 + 10.2694I 0
u = −1.60258 − 0.19607I
a = 0.169020 − 0.982199I
b = 1.63051 + 0.67539I
−10.6448 − 10.2694I 0
u = 1.62021 + 0.16614I
a = −0.315343 − 0.768944I
b = −0.216820 + 0.664390I
−8.17640 + 1.14930I 0
u = 1.62021 − 0.16614I
a = −0.315343 + 0.768944I
b = −0.216820 − 0.664390I
−8.17640 − 1.14930I 0
u = −1.62325 + 0.26012I
a = 0.124507 + 0.886797I
b = 1.234980 − 0.275110I
−8.93307 + 2.05082I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62325 − 0.26012I
a = 0.124507 − 0.886797I
b = 1.234980 + 0.275110I
−8.93307 − 2.05082I 0
u = −1.68381 + 0.16522I
a = 0.311492 − 0.243654I
b = 1.216690 + 0.286899I
−8.81041 − 0.18615I 0
u = −1.68381 − 0.16522I
a = 0.311492 + 0.243654I
b = 1.216690 − 0.286899I
−8.81041 + 0.18615I 0
u = 1.67684 + 0.25771I
a = −0.190408 + 1.009440I
b = −1.55979 − 0.58138I
−15.4166 − 16.8496I 0
u = 1.67684 − 0.25771I
a = −0.190408 − 1.009440I
b = −1.55979 + 0.58138I
−15.4166 + 16.8496I 0
u = 1.72467 + 0.29018I
a = 0.085552 − 0.899049I
b = 1.49426 + 0.47195I
−18.5482 − 9.7894I 0
u = 1.72467 − 0.29018I
a = 0.085552 + 0.899049I
b = 1.49426 − 0.47195I
−18.5482 + 9.7894I 0
u = 2.00123 + 0.53247I
a = 0.067451 + 0.592695I
b = −1.238420 − 0.242163I
−11.31000 − 2.08418I 0
u = 2.00123 − 0.53247I
a = 0.067451 − 0.592695I
b = −1.238420 + 0.242163I
−11.31000 + 2.08418I 0
14
II.
I
u
2
= h3.00 × 10
6
u
26
+ 3.52 × 10
6
u
25
+ · · · + 7.93 × 10
5
b − 4.09 × 10
6
, −5.34 ×
10
5
u
26
+1.88×10
6
u
25
+· · · +7.93×10
5
a+5.66×10
6
, u
27
+3u
26
+· · · +5u −1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
0.673270u
26
− 2.37664u
25
+ ··· + 25.0995u − 7.13810
−3.78064u
26
− 4.44419u
25
+ ··· − 21.2698u + 5.16587
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−3.10737u
26
− 6.82083u
25
+ ··· + 3.82971u − 1.97222
−3.78064u
26
− 4.44419u
25
+ ··· − 21.2698u + 5.16587
a
6
=
−1.18091u
26
− 3.85843u
25
+ ··· + 6.21017u − 5.38505
−1.70258u
26
− 2.82854u
25
+ ··· − 3.08295u + 1.50340
a
5
=
−0.122342u
26
− 2.57030u
25
+ ··· + 10.5145u − 7.58720
−1.42936u
26
− 2.56048u
25
+ ··· − 2.39396u + 1.29629
a
10
=
3.66248u
26
+ 8.90937u
25
+ ··· + 4.93561u + 6.12557
−2.59489u
26
− 4.46514u
25
+ ··· − 9.49678u + 0.521665
a
4
=
−1.09427u
26
− 3.45639u
25
+ ··· + 4.42081u − 5.18096
−3.64276u
26
− 4.52291u
25
+ ··· − 13.9435u + 3.89601
a
1
=
−4.06341u
26
− 6.40875u
25
+ ··· − 8.28744u + 1.23141
−2.48321u
26
− 3.27273u
25
+ ··· − 10.3527u + 2.66927
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2226709
792677
u
26
−
4791574
792677
u
25
+ ··· +
14581222
792677
u −
4258801
792677
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 3u
26
+ ··· + 9u − 3
c
2
u
27
− u
26
+ ··· + 3u − 1
c
3
u
27
+ 15u
25
+ ··· + 5u + 1
c
4
u
27
+ 3u
26
+ ··· + 9u + 3
c
5
u
27
− 2u
26
+ ··· + 5u − 1
c
6
u
27
+ u
26
+ ··· + 3u + 1
c
7
, c
8
u
27
+ 3u
26
+ ··· + 5u − 1
c
9
u
27
+ 2u
26
+ ··· + 5u + 1
c
10
u
27
+ 15u
25
+ ··· + 5u − 1
c
11
u
27
− 3u
26
+ ··· + 5u + 1
c
12
u
27
+ u
26
+ ··· + 37u − 13
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
27
+ 23y
26
+ ··· − 141y −9
c
2
, c
6
y
27
− 17y
26
+ ··· + 9y −1
c
3
, c
10
y
27
+ 30y
26
+ ··· + 17y −1
c
5
, c
9
y
27
+ 18y
26
+ ··· − 3y −1
c
7
, c
8
, c
11
y
27
− 37y
26
+ ··· + 33y −1
c
12
y
27
− 7y
26
+ ··· + 251y −169
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03811
a = −0.159209
b = −0.784252
−2.84980 −16.4580
u = 0.748175 + 0.105655I
a = 0.279333 + 0.368664I
b = 0.882795 − 0.680720I
1.83419 + 2.65297I −0.36090 + 4.60742I
u = 0.748175 − 0.105655I
a = 0.279333 − 0.368664I
b = 0.882795 + 0.680720I
1.83419 − 2.65297I −0.36090 − 4.60742I
u = 1.294530 + 0.034789I
a = −0.259219 + 0.497403I
b = −0.182701 + 0.600701I
−1.83917 − 1.49800I −9.12397 + 5.41258I
u = 1.294530 − 0.034789I
a = −0.259219 − 0.497403I
b = −0.182701 − 0.600701I
−1.83917 + 1.49800I −9.12397 − 5.41258I
u = −1.259050 + 0.350704I
a = 0.119528 − 0.626909I
b = 0.653247 + 0.049288I
−7.24454 + 1.88805I −13.81478 − 1.79703I
u = −1.259050 − 0.350704I
a = 0.119528 + 0.626909I
b = 0.653247 − 0.049288I
−7.24454 − 1.88805I −13.81478 + 1.79703I
u = 0.252879 + 0.611917I
a = 1.47088 + 1.30440I
b = −1.389330 + 0.017865I
−5.27887 − 3.53952I −7.30701 + 5.60328I
u = 0.252879 − 0.611917I
a = 1.47088 − 1.30440I
b = −1.389330 − 0.017865I
−5.27887 + 3.53952I −7.30701 − 5.60328I
u = −1.365240 + 0.167447I
a = 0.449300 + 0.369934I
b = −0.429753 + 0.338426I
−5.94774 + 7.32226I −10.71991 − 7.51124I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.365240 − 0.167447I
a = 0.449300 − 0.369934I
b = −0.429753 − 0.338426I
−5.94774 − 7.32226I −10.71991 + 7.51124I
u = −0.201115 + 0.528834I
a = −1.46674 − 0.51422I
b = −0.639093 − 0.316370I
−1.80312 − 5.03781I −10.29717 + 6.83310I
u = −0.201115 − 0.528834I
a = −1.46674 + 0.51422I
b = −0.639093 + 0.316370I
−1.80312 + 5.03781I −10.29717 − 6.83310I
u = −0.439489 + 0.267686I
a = −1.47387 + 2.97217I
b = 1.190120 − 0.233496I
−7.57088 + 1.18253I −7.77665 − 3.74760I
u = −0.439489 − 0.267686I
a = −1.47387 − 2.97217I
b = 1.190120 + 0.233496I
−7.57088 − 1.18253I −7.77665 + 3.74760I
u = −1.52232 + 0.01840I
a = 0.139780 − 0.848382I
b = 0.037051 + 1.262990I
−4.52450 − 0.76353I −5.42241 + 0.28908I
u = −1.52232 − 0.01840I
a = 0.139780 + 0.848382I
b = 0.037051 − 1.262990I
−4.52450 + 0.76353I −5.42241 − 0.28908I
u = −1.54296 + 0.15604I
a = −0.544250 − 0.878566I
b = −1.57279 + 0.15201I
−11.64350 + 6.09468I −8.13310 − 7.08189I
u = −1.54296 − 0.15604I
a = −0.544250 + 0.878566I
b = −1.57279 − 0.15201I
−11.64350 − 6.09468I −8.13310 + 7.08189I
u = 1.55264 + 0.06966I
a = 0.246557 − 1.296030I
b = 1.246470 + 0.511230I
−14.4755 − 2.3233I −9.43970 + 3.30668I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55264 − 0.06966I
a = 0.246557 + 1.296030I
b = 1.246470 − 0.511230I
−14.4755 + 2.3233I −9.43970 − 3.30668I
u = −1.61874 + 0.47056I
a = 0.022489 + 0.795132I
b = 1.280130 − 0.170951I
−10.08060 + 2.82444I −12.89711 − 3.14465I
u = −1.61874 − 0.47056I
a = 0.022489 − 0.795132I
b = 1.280130 + 0.170951I
−10.08060 − 2.82444I −12.89711 + 3.14465I
u = 0.242146 + 0.071939I
a = 2.15135 + 3.13574I
b = −0.049870 − 0.913367I
1.75106 + 1.08204I 0.48346 + 1.66701I
u = 0.242146 − 0.071939I
a = 2.15135 − 3.13574I
b = −0.049870 + 0.913367I
1.75106 − 1.08204I 0.48346 − 1.66701I
u = 1.83948 + 0.21736I
a = −0.055534 + 0.721360I
b = −1.134140 − 0.322128I
−10.70870 − 1.45270I 0
u = 1.83948 − 0.21736I
a = −0.055534 − 0.721360I
b = −1.134140 + 0.322128I
−10.70870 + 1.45270I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 3u
26
+ ··· + 9u − 3)(u
99
− 8u
98
+ ··· + 19u − 1)
c
2
(u
27
− u
26
+ ··· + 3u − 1)(u
99
− 2u
98
+ ··· − 21137u − 8401)
c
3
(u
27
+ 15u
25
+ ··· + 5u + 1)(u
99
+ u
98
+ ··· − 17146u − 20252)
c
4
(u
27
+ 3u
26
+ ··· + 9u + 3)(u
99
− 8u
98
+ ··· + 19u − 1)
c
5
(u
27
− 2u
26
+ ··· + 5u − 1)(u
99
− 3u
98
+ ··· − 1873u − 577)
c
6
(u
27
+ u
26
+ ··· + 3u + 1)(u
99
− 2u
98
+ ··· − 21137u − 8401)
c
7
, c
8
(u
27
+ 3u
26
+ ··· + 5u − 1)(u
99
+ 4u
98
+ ··· + 2545u − 1003)
c
9
(u
27
+ 2u
26
+ ··· + 5u + 1)(u
99
− 3u
98
+ ··· − 1873u − 577)
c
10
(u
27
+ 15u
25
+ ··· + 5u − 1)(u
99
+ u
98
+ ··· − 17146u − 20252)
c
11
(u
27
− 3u
26
+ ··· + 5u + 1)(u
99
+ 4u
98
+ ··· + 2545u − 1003)
c
12
(u
27
+ u
26
+ ··· + 37u − 13)
· (u
99
+ 2u
98
+ ··· − 23310064u − 2254444)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
27
+ 23y
26
+ ··· − 141y −9)(y
99
+ 56y
98
+ ··· + 87y −1)
c
2
, c
6
(y
27
− 17y
26
+ ··· + 9y −1)
· (y
99
− 80y
98
+ ··· − 692503643y −70576801)
c
3
, c
10
(y
27
+ 30y
26
+ ··· + 17y −1)
· (y
99
+ 95y
98
+ ··· + 3720826236y −410143504)
c
5
, c
9
(y
27
+ 18y
26
+ ··· − 3y −1)
· (y
99
+ 71y
98
+ ··· − 12786351y −332929)
c
7
, c
8
, c
11
(y
27
− 37y
26
+ ··· + 33y −1)
· (y
99
− 120y
98
+ ··· + 48189789y −1006009)
c
12
(y
27
− 7y
26
+ ··· + 251y −169)
· (y
99
− 42y
98
+ ··· + 169128066365000y −5082517749136)
22
