12n
0504
(K12n
0504
)
A knot diagram
1
Linearized knot diagam
3 6 11 9 7 2 12 3 7 8 4 10
Solving Sequence
3,11 4,8
9 5 12 7 6 2 10 1
c
3
c
8
c
4
c
11
c
7
c
5
c
2
c
10
c
12
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.23441 × 10
152
u
80
+ 1.03277 × 10
152
u
79
+ ··· + 7.12803 × 10
149
b + 1.45911 × 10
152
,
− 1.08125 × 10
152
u
80
− 9.29614 × 10
151
u
79
+ ··· + 7.12803 × 10
149
a − 1.25045 × 10
152
,
u
81
− 25u
79
+ ··· − u − 1i
I
u
2
= h−u
19
− u
18
+ ··· + b − 1, −7529u
20
+ 16576u
19
+ ··· + 4369a + 66551, u
21
+ u
20
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 102 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
= h1.23 × 10
152
u
80
+ 1.03 × 10
152
u
79
+ · · · + 7.13 × 10
149
b + 1.46 ×
10
152
, −1.08 × 10
152
u
80
− 9.30 × 10
151
u
79
+ · · · + 7.13 × 10
149
a − 1.25 ×
10
152
, u
81
− 25u
79
+ · · · − u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
151.690u
80
+ 130.417u
79
+ ··· + 384.512u + 175.426
−173.177u
80
− 144.889u
79
+ ··· − 450.511u − 204.700
a
9
=
324.867u
80
+ 275.305u
79
+ ··· + 835.023u + 380.126
−173.177u
80
− 144.889u
79
+ ··· − 450.511u − 204.700
a
5
=
−217.115u
80
− 183.775u
79
+ ··· − 589.240u − 262.760
83.8333u
80
+ 71.1008u
79
+ ··· + 215.196u + 102.506
a
12
=
u
−u
3
+ u
a
7
=
303.584u
80
+ 259.429u
79
+ ··· + 777.896u + 355.169
−130.110u
80
− 108.535u
79
+ ··· − 338.033u − 153.969
a
6
=
−290.200u
80
− 249.523u
79
+ ··· − 729.435u − 337.494
85.7527u
80
+ 71.4068u
79
+ ··· + 225.793u + 102.293
a
2
=
−264.895u
80
− 226.810u
79
+ ··· − 666.097u − 306.595
95.4427u
80
+ 78.6904u
79
+ ··· + 251.393u + 112.450
a
10
=
183.583u
80
+ 153.132u
79
+ ··· + 480.308u + 219.882
−72.9647u
80
− 64.8472u
79
+ ··· − 178.991u − 84.6969
a
1
=
−169.452u
80
− 148.120u
79
+ ··· − 414.704u − 194.145
95.4427u
80
+ 78.6904u
79
+ ··· + 251.393u + 112.450
(ii) Obstruction class = −1
(iii) Cusp Shapes = −134.434u
80
− 107.850u
79
+ ··· − 374.672u − 167.881
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
81
+ 48u
80
+ ··· − 46u − 1
c
2
, c
6
u
81
− 4u
80
+ ··· − 10u + 1
c
3
, c
11
u
81
− 25u
79
+ ··· − u − 1
c
4
u
81
− 40u
79
+ ··· − 67990u + 12769
c
7
u
81
− 3u
80
+ ··· + 24u + 1
c
8
u
81
− u
80
+ ··· − 3486u − 4531
c
9
u
81
+ 10u
80
+ ··· + 31415u + 24751
c
10
u
81
+ 9u
80
+ ··· + 26u + 1
c
12
u
81
− 13u
80
+ ··· + 136052u − 20201
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
81
− 24y
80
+ ··· − 770y −1
c
2
, c
6
y
81
+ 48y
80
+ ··· − 46y −1
c
3
, c
11
y
81
− 50y
80
+ ··· + 13y −1
c
4
y
81
− 80y
80
+ ··· + 9648824956y −163047361
c
7
y
81
− y
80
+ ··· + 68y −1
c
8
y
81
− 23y
80
+ ··· + 1638264662y −20529961
c
9
y
81
− 78y
80
+ ··· + 90529436459y −612612001
c
10
y
81
− 5y
80
+ ··· + 92y −1
c
12
y
81
− 37y
80
+ ··· − 298277160y −408080401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902305 + 0.379132I
a = −0.541466 + 0.988112I
b = −1.32681 − 1.87079I
−6.54251 + 2.36585I 0
u = −0.902305 − 0.379132I
a = −0.541466 − 0.988112I
b = −1.32681 + 1.87079I
−6.54251 − 2.36585I 0
u = −0.960722 + 0.366305I
a = −0.43622 − 1.63083I
b = 0.460770 + 0.120247I
−2.14981 − 3.01376I 0
u = −0.960722 − 0.366305I
a = −0.43622 + 1.63083I
b = 0.460770 − 0.120247I
−2.14981 + 3.01376I 0
u = 1.011240 + 0.299411I
a = 0.436443 + 0.645111I
b = 1.21365 − 2.14492I
−1.46165 + 2.09415I 0
u = 1.011240 − 0.299411I
a = 0.436443 − 0.645111I
b = 1.21365 + 2.14492I
−1.46165 − 2.09415I 0
u = 1.009510 + 0.325728I
a = 0.54837 − 2.02019I
b = −0.737204 + 0.175634I
−5.81489 + 7.27123I 0
u = 1.009510 − 0.325728I
a = 0.54837 + 2.02019I
b = −0.737204 − 0.175634I
−5.81489 − 7.27123I 0
u = −0.964311 + 0.454853I
a = −0.210966 + 0.098303I
b = −1.009290 + 0.240162I
−1.62903 − 2.11796I 0
u = −0.964311 − 0.454853I
a = −0.210966 − 0.098303I
b = −1.009290 − 0.240162I
−1.62903 + 2.11796I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.648411 + 0.654308I
a = −0.695906 + 0.027482I
b = 0.355885 + 1.177700I
−1.75332 + 2.51421I 0
u = 0.648411 − 0.654308I
a = −0.695906 − 0.027482I
b = 0.355885 − 1.177700I
−1.75332 − 2.51421I 0
u = 1.09655
a = 0.468450
b = 0.654070
1.81674 0
u = 1.013360 + 0.419477I
a = 0.79390 − 1.50335I
b = −0.506195 − 0.174838I
−5.33253 − 1.57015I 0
u = 1.013360 − 0.419477I
a = 0.79390 + 1.50335I
b = −0.506195 + 0.174838I
−5.33253 + 1.57015I 0
u = −0.886429 + 0.150741I
a = 0.71362 − 1.59397I
b = 0.277004 + 0.899802I
0.26570 − 4.55441I 0
u = −0.886429 − 0.150741I
a = 0.71362 + 1.59397I
b = 0.277004 − 0.899802I
0.26570 + 4.55441I 0
u = 1.088310 + 0.200271I
a = −1.125980 − 0.191011I
b = −0.925517 − 0.209416I
2.44803 + 1.62087I 0
u = 1.088310 − 0.200271I
a = −1.125980 + 0.191011I
b = −0.925517 + 0.209416I
2.44803 − 1.62087I 0
u = −0.315200 + 0.827015I
a = 0.985815 + 0.065165I
b = 0.573644 + 0.998964I
−3.44192 − 2.58172I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.315200 − 0.827015I
a = 0.985815 − 0.065165I
b = 0.573644 − 0.998964I
−3.44192 + 2.58172I 0
u = −0.767732 + 0.423882I
a = −0.205242 − 0.622535I
b = −0.380848 + 0.219729I
−1.39485 − 1.84663I 0
u = −0.767732 − 0.423882I
a = −0.205242 + 0.622535I
b = −0.380848 − 0.219729I
−1.39485 + 1.84663I 0
u = −0.013086 + 1.134480I
a = 0.213787 − 0.203235I
b = 0.247143 + 0.087637I
0.64631 + 2.82490I 0
u = −0.013086 − 1.134480I
a = 0.213787 + 0.203235I
b = 0.247143 − 0.087637I
0.64631 − 2.82490I 0
u = −1.076550 + 0.360738I
a = −0.635040 + 0.553652I
b = −1.23910 − 2.13479I
−4.75622 − 7.90439I 0
u = −1.076550 − 0.360738I
a = −0.635040 − 0.553652I
b = −1.23910 + 2.13479I
−4.75622 + 7.90439I 0
u = 0.183779 + 1.122460I
a = −0.802444 − 0.673376I
b = −1.306840 − 0.417115I
−9.90972 − 0.66625I 0
u = 0.183779 − 1.122460I
a = −0.802444 + 0.673376I
b = −1.306840 + 0.417115I
−9.90972 + 0.66625I 0
u = −0.170398 + 1.126680I
a = 0.689681 − 0.781080I
b = 1.106720 − 0.668721I
−5.19483 + 5.53843I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170398 − 1.126680I
a = 0.689681 + 0.781080I
b = 1.106720 + 0.668721I
−5.19483 − 5.53843I 0
u = 1.065720 + 0.407914I
a = −1.189530 − 0.619382I
b = −1.72330 + 0.89309I
0.68423 + 7.22736I 0
u = 1.065720 − 0.407914I
a = −1.189530 + 0.619382I
b = −1.72330 − 0.89309I
0.68423 − 7.22736I 0
u = 0.165603 + 1.132270I
a = −0.726014 − 0.887409I
b = −1.19140 − 0.88628I
−8.76483 − 11.09010I 0
u = 0.165603 − 1.132270I
a = −0.726014 + 0.887409I
b = −1.19140 + 0.88628I
−8.76483 + 11.09010I 0
u = 0.852441 + 0.001116I
a = −0.658643 + 1.180880I
b = −0.044733 − 1.206010I
1.046830 − 0.649414I 5.50516 + 0.I
u = 0.852441 − 0.001116I
a = −0.658643 − 1.180880I
b = −0.044733 + 1.206010I
1.046830 + 0.649414I 5.50516 + 0.I
u = −0.597478 + 0.470710I
a = −0.292709 + 0.767245I
b = −0.478827 + 0.650933I
−0.13061 + 2.12477I 1.60050 − 2.94701I
u = −0.597478 − 0.470710I
a = −0.292709 − 0.767245I
b = −0.478827 − 0.650933I
−0.13061 − 2.12477I 1.60050 + 2.94701I
u = −1.192220 + 0.350482I
a = 1.217880 − 0.419708I
b = 0.805797 + 0.821329I
3.57269 − 4.92095I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.192220 − 0.350482I
a = 1.217880 + 0.419708I
b = 0.805797 − 0.821329I
3.57269 + 4.92095I 0
u = −1.169650 + 0.444904I
a = 1.370680 − 0.316177I
b = 0.86662 + 1.45089I
3.36884 − 5.55592I 0
u = −1.169650 − 0.444904I
a = 1.370680 + 0.316177I
b = 0.86662 − 1.45089I
3.36884 + 5.55592I 0
u = −1.236580 + 0.299380I
a = 1.247280 − 0.439033I
b = 0.527525 + 0.682155I
3.49137 − 4.92888I 0
u = −1.236580 − 0.299380I
a = 1.247280 + 0.439033I
b = 0.527525 − 0.682155I
3.49137 + 4.92888I 0
u = 1.169700 + 0.502563I
a = −1.159140 + 0.011019I
b = −0.388968 + 1.350540I
3.00360 + 2.72726I 0
u = 1.169700 − 0.502563I
a = −1.159140 − 0.011019I
b = −0.388968 − 1.350540I
3.00360 − 2.72726I 0
u = 0.724961
a = 0.141553
b = −3.03101
−3.09176 −12.2130
u = −0.666916 + 0.195048I
a = −0.156382 − 0.607093I
b = 2.72346 − 0.31841I
−7.46556 − 5.35134I −7.82165 + 7.22544I
u = −0.666916 − 0.195048I
a = −0.156382 + 0.607093I
b = 2.72346 + 0.31841I
−7.46556 + 5.35134I −7.82165 − 7.22544I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978674 + 0.931902I
a = −0.280037 + 0.224847I
b = −0.074527 + 0.737144I
1.13541 + 2.26803I 0
u = 0.978674 − 0.931902I
a = −0.280037 − 0.224847I
b = −0.074527 − 0.737144I
1.13541 − 2.26803I 0
u = 1.301260 + 0.414651I
a = 0.580151 + 0.104656I
b = 0.952867 − 0.457869I
5.36895 + 2.14990I 0
u = 1.301260 − 0.414651I
a = 0.580151 − 0.104656I
b = 0.952867 + 0.457869I
5.36895 − 2.14990I 0
u = −1.305270 + 0.493311I
a = −0.662219 + 0.141141I
b = −1.024370 − 0.588649I
4.77612 − 8.26020I 0
u = −1.305270 − 0.493311I
a = −0.662219 − 0.141141I
b = −1.024370 + 0.588649I
4.77612 + 8.26020I 0
u = −0.032146 + 0.601351I
a = −0.704884 + 1.212550I
b = −0.396728 + 0.822881I
0.20204 + 1.49826I 1.38934 − 4.06041I
u = −0.032146 − 0.601351I
a = −0.704884 − 1.212550I
b = −0.396728 − 0.822881I
0.20204 − 1.49826I 1.38934 + 4.06041I
u = 0.589104 + 0.077999I
a = 3.02288 + 0.38505I
b = 1.43654 + 0.15109I
−7.40845 − 4.70430I −8.71870 + 1.25287I
u = 0.589104 − 0.077999I
a = 3.02288 − 0.38505I
b = 1.43654 − 0.15109I
−7.40845 + 4.70430I −8.71870 − 1.25287I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28056 + 0.60613I
a = 0.936300 + 0.444957I
b = 1.49356 − 1.15454I
−6.48713 + 6.72299I 0
u = 1.28056 − 0.60613I
a = 0.936300 − 0.444957I
b = 1.49356 + 1.15454I
−6.48713 − 6.72299I 0
u = 1.35655 + 0.41748I
a = −1.011780 − 0.542288I
b = −0.462888 + 1.153850I
1.69314 + 7.01569I 0
u = 1.35655 − 0.41748I
a = −1.011780 + 0.542288I
b = −0.462888 − 1.153850I
1.69314 − 7.01569I 0
u = −1.29675 + 0.60148I
a = −1.036220 + 0.360848I
b = −1.29084 − 1.29622I
−1.66431 − 11.60560I 0
u = −1.29675 − 0.60148I
a = −1.036220 − 0.360848I
b = −1.29084 + 1.29622I
−1.66431 + 11.60560I 0
u = 1.30382 + 0.60686I
a = 1.123340 + 0.392064I
b = 1.29633 − 1.46900I
−5.2024 + 17.2034I 0
u = 1.30382 − 0.60686I
a = 1.123340 − 0.392064I
b = 1.29633 + 1.46900I
−5.2024 − 17.2034I 0
u = 0.368457 + 0.423875I
a = 0.70058 + 2.15721I
b = 1.144710 − 0.026537I
−1.34736 − 3.65138I −6.40050 + 3.27750I
u = 0.368457 − 0.423875I
a = 0.70058 − 2.15721I
b = 1.144710 + 0.026537I
−1.34736 + 3.65138I −6.40050 − 3.27750I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.002369 + 0.507248I
a = −1.31039 + 1.21972I
b = −0.441129 + 0.625857I
0.12904 + 1.47742I 0.85859 − 4.88287I
u = −0.002369 − 0.507248I
a = −1.31039 − 1.21972I
b = −0.441129 − 0.625857I
0.12904 − 1.47742I 0.85859 + 4.88287I
u = 1.61293
a = 0.420426
b = −0.170339
1.22427 0
u = −0.378742 + 0.055619I
a = −3.23578 − 0.29152I
b = −1.335370 − 0.015602I
−3.66407 + 0.00055I −3.29899 + 0.32726I
u = −0.378742 − 0.055619I
a = −3.23578 + 0.29152I
b = −1.335370 + 0.015602I
−3.66407 − 0.00055I −3.29899 − 0.32726I
u = −1.67266 + 0.23707I
a = −0.403242 − 0.141145I
b = 0.422530 − 0.302754I
−2.75985 + 5.35327I 0
u = −1.67266 − 0.23707I
a = −0.403242 + 0.141145I
b = 0.422530 + 0.302754I
−2.75985 − 5.35327I 0
u = 0.067184 + 0.302298I
a = 1.13766 − 3.28658I
b = 1.54834 − 0.44871I
−7.40668 + 4.90606I −5.02431 − 3.21161I
u = 0.067184 − 0.302298I
a = 1.13766 + 3.28658I
b = 1.54834 + 0.44871I
−7.40668 − 4.90606I −5.02431 + 3.21161I
u = −1.56337 + 0.79423I
a = 0.246662 − 0.263030I
b = 0.605441 + 0.629873I
−4.14648 − 5.92038I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56337 − 0.79423I
a = 0.246662 + 0.263030I
b = 0.605441 − 0.629873I
−4.14648 + 5.92038I 0
13
II. I
u
2
= h−u
19
− u
18
+ · · · + b − 1, −7529u
20
+ 16576u
19
+ · · · + 4369a +
66551, u
21
+ u
20
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
1.72328u
20
− 3.79400u
19
+ ··· + 7.36301u − 15.2325
u
19
+ u
18
+ ··· − 6u
2
+ 1
a
9
=
1.72328u
20
− 4.79400u
19
+ ··· + 7.36301u − 16.2325
u
19
+ u
18
+ ··· − 6u
2
+ 1
a
5
=
−8.57542u
20
− 1.45502u
19
+ ··· − 26.2774u + 12.2559
−4.44610u
20
+ 0.689403u
19
+ ··· − 18.0385u + 8.07507
a
12
=
u
−u
3
+ u
a
7
=
2.57679u
20
− 5.24079u
19
+ ··· + 10.3401u − 19.4260
0.0691234u
20
+ 0.310826u
19
+ ··· − 0.176699u − 0.893111
a
6
=
6.02930u
20
+ 0.489357u
19
+ ··· + 14.0046u − 12.9613
9.33257u
20
+ 1.16434u
19
+ ··· + 26.5207u − 15.3500
a
2
=
8.32982u
20
+ 7.55596u
19
+ ··· + 22.3953u + 4.99016
11.4024u
20
+ 5.12726u
19
+ ··· + 30.3754u − 9.82811
a
10
=
−17.6077u
20
− 10.1035u
19
+ ··· − 38.7512u + 9.75235
−8.07507u
20
− 2.62898u
19
+ ··· − 19.7617u + 10.9634
a
1
=
19.7322u
20
+ 12.6832u
19
+ ··· + 52.7707u − 4.83795
11.4024u
20
+ 5.12726u
19
+ ··· + 30.3754u − 9.82811
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
142174
4369
u
20
−
43479
4369
u
19
+ ··· −
429897
4369
u +
119686
4369
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
21
− 11u
20
+ ··· − 4u + 1
c
2
u
21
− u
20
+ ··· − 2u − 1
c
3
u
21
+ u
20
+ ··· + u − 1
c
4
u
21
+ u
20
+ ··· + 6u − 1
c
6
u
21
+ u
20
+ ··· − 2u + 1
c
7
u
21
− 2u
20
+ ··· − 2u + 1
c
8
u
21
− 4u
19
+ ··· + 2u + 1
c
9
u
21
+ 11u
20
+ ··· + 7u + 1
c
10
u
21
− 10u
20
+ ··· − 8u + 1
c
11
u
21
− u
20
+ ··· + u + 1
c
12
u
21
− 2u
20
+ ··· − 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
21
+ 3y
20
+ ··· − 4y −1
c
2
, c
6
y
21
+ 11y
20
+ ··· − 4y −1
c
3
, c
11
y
21
− 15y
20
+ ··· + 15y −1
c
4
y
21
− 5y
20
+ ··· − 14y −1
c
7
y
21
− 6y
20
+ ··· + 6y −1
c
8
y
21
− 8y
20
+ ··· − 12y −1
c
9
y
21
− 7y
20
+ ··· − 11y −1
c
10
y
21
− 6y
20
+ ··· − 2y −1
c
12
y
21
− 6y
20
+ ··· + 6y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888681 + 0.424494I
a = −0.320823 − 0.407542I
b = 0.037005 + 1.158720I
0.01292 + 1.95369I 2.10409 − 3.40241I
u = 0.888681 − 0.424494I
a = −0.320823 + 0.407542I
b = 0.037005 − 1.158720I
0.01292 − 1.95369I 2.10409 + 3.40241I
u = 0.807708
a = 0.989331
b = 2.32361
−2.65595 8.30830
u = −0.780642 + 0.008696I
a = −1.47938 − 0.67723I
b = −1.99501 + 0.09159I
−6.71198 − 4.94074I 3.19350 + 3.55851I
u = −0.780642 − 0.008696I
a = −1.47938 + 0.67723I
b = −1.99501 − 0.09159I
−6.71198 + 4.94074I 3.19350 − 3.55851I
u = −1.171510 + 0.413563I
a = 1.41786 − 0.22856I
b = 0.650009 + 1.073900I
2.50065 − 3.95422I 0.25209 + 3.41763I
u = −1.171510 − 0.413563I
a = 1.41786 + 0.22856I
b = 0.650009 − 1.073900I
2.50065 + 3.95422I 0.25209 − 3.41763I
u = 1.199990 + 0.355792I
a = −1.27775 − 0.66921I
b = −0.821752 + 1.103720I
2.38428 + 5.99565I 1.10633 − 7.42127I
u = 1.199990 − 0.355792I
a = −1.27775 + 0.66921I
b = −0.821752 − 1.103720I
2.38428 − 5.99565I 1.10633 + 7.42127I
u = 0.193620 + 1.274390I
a = −0.178684 + 0.310534I
b = −0.018473 + 0.489168I
0.97197 + 2.90581I 14.3385 − 11.9690I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.193620 − 1.274390I
a = −0.178684 − 0.310534I
b = −0.018473 − 0.489168I
0.97197 − 2.90581I 14.3385 + 11.9690I
u = 1.321630 + 0.400034I
a = −0.771560 − 0.180940I
b = −0.819522 + 0.795198I
5.96726 + 2.57833I 8.01202 − 3.81094I
u = 1.321630 − 0.400034I
a = −0.771560 + 0.180940I
b = −0.819522 − 0.795198I
5.96726 − 2.57833I 8.01202 + 3.81094I
u = −1.305240 + 0.463057I
a = 0.877968 − 0.064829I
b = 0.704657 + 0.794595I
5.59416 − 8.12880I 7.29693 + 6.03982I
u = −1.305240 − 0.463057I
a = 0.877968 + 0.064829I
b = 0.704657 − 0.794595I
5.59416 + 8.12880I 7.29693 − 6.03982I
u = −0.312750 + 0.395125I
a = −0.41319 + 2.25464I
b = −0.197554 + 0.419489I
−0.253263 + 0.438961I −2.82903 + 1.96774I
u = −0.312750 − 0.395125I
a = −0.41319 − 2.25464I
b = −0.197554 − 0.419489I
−0.253263 − 0.438961I −2.82903 − 1.96774I
u = 0.486254 + 0.103220I
a = −0.39298 + 2.58099I
b = 0.600680 + 0.211205I
−0.41271 − 3.61050I 1.11773 + 4.65529I
u = 0.486254 − 0.103220I
a = −0.39298 − 2.58099I
b = 0.600680 − 0.211205I
−0.41271 + 3.61050I 1.11773 − 4.65529I
u = −1.42389 + 0.49409I
a = 0.043877 − 0.381971I
b = 0.698149 + 0.623289I
−3.79051 − 5.69804I 2.75371 + 3.99925I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42389 − 0.49409I
a = 0.043877 + 0.381971I
b = 0.698149 − 0.623289I
−3.79051 + 5.69804I 2.75371 − 3.99925I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
21
− 11u
20
+ ··· − 4u + 1)(u
81
+ 48u
80
+ ··· − 46u − 1)
c
2
(u
21
− u
20
+ ··· − 2u − 1)(u
81
− 4u
80
+ ··· − 10u + 1)
c
3
(u
21
+ u
20
+ ··· + u − 1)(u
81
− 25u
79
+ ··· − u − 1)
c
4
(u
21
+ u
20
+ ··· + 6u − 1)(u
81
− 40u
79
+ ··· − 67990u + 12769)
c
6
(u
21
+ u
20
+ ··· − 2u + 1)(u
81
− 4u
80
+ ··· − 10u + 1)
c
7
(u
21
− 2u
20
+ ··· − 2u + 1)(u
81
− 3u
80
+ ··· + 24u + 1)
c
8
(u
21
− 4u
19
+ ··· + 2u + 1)(u
81
− u
80
+ ··· − 3486u − 4531)
c
9
(u
21
+ 11u
20
+ ··· + 7u + 1)(u
81
+ 10u
80
+ ··· + 31415u + 24751)
c
10
(u
21
− 10u
20
+ ··· − 8u + 1)(u
81
+ 9u
80
+ ··· + 26u + 1)
c
11
(u
21
− u
20
+ ··· + u + 1)(u
81
− 25u
79
+ ··· − u − 1)
c
12
(u
21
− 2u
20
+ ··· − 2u + 1)(u
81
− 13u
80
+ ··· + 136052u − 20201)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
21
+ 3y
20
+ ··· − 4y −1)(y
81
− 24y
80
+ ··· − 770y −1)
c
2
, c
6
(y
21
+ 11y
20
+ ··· − 4y −1)(y
81
+ 48y
80
+ ··· − 46y −1)
c
3
, c
11
(y
21
− 15y
20
+ ··· + 15y −1)(y
81
− 50y
80
+ ··· + 13y −1)
c
4
(y
21
− 5y
20
+ ··· − 14y −1)
· (y
81
− 80y
80
+ ··· + 9648824956y −163047361)
c
7
(y
21
− 6y
20
+ ··· + 6y −1)(y
81
− y
80
+ ··· + 68y −1)
c
8
(y
21
− 8y
20
+ ··· − 12y −1)
· (y
81
− 23y
80
+ ··· + 1638264662y −20529961)
c
9
(y
21
− 7y
20
+ ··· − 11y −1)
· (y
81
− 78y
80
+ ··· + 90529436459y −612612001)
c
10
(y
21
− 6y
20
+ ··· − 2y −1)(y
81
− 5y
80
+ ··· + 92y −1)
c
12
(y
21
− 6y
20
+ ··· + 6y −1)
· (y
81
− 37y
80
+ ··· − 298277160y −408080401)
21
