12n
0618
(K12n
0618
)
A knot diagram
1
Linearized knot diagam
3 8 6 1 12 1 11 2 6 5 8 10
Solving Sequence
2,8 3,6
4 9 10 1 12 5 11 7
c
2
c
3
c
8
c
9
c
1
c
12
c
5
c
11
c
7
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.78413 × 10
157
u
83
+ 4.41545 × 10
158
u
82
+ ··· + 6.49095 × 10
157
b + 2.25203 × 10
160
,
1.03935 × 10
160
u
83
+ 1.05276 × 10
160
u
82
+ ··· + 3.18057 × 10
159
a + 1.00444 × 10
162
,
u
84
− u
83
+ ··· − 111u + 49i
I
u
2
= h−5u
30
− 2u
29
+ ··· + b − 4, −3u
30
+ 2u
29
+ ··· + a − 1, u
31
+ 8u
29
+ ··· − 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 115 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
= h2.78 × 10
157
u
83
+ 4.42 × 10
158
u
82
+ · · · + 6.49 × 10
157
b + 2.25 ×
10
160
, 1.04 × 10
160
u
83
+ 1.05 × 10
160
u
82
+ · · · + 3.18 × 10
159
a + 1.00 ×
10
162
, u
84
− u
83
+ · · · − 111u + 49i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
6
=
−3.26781u
83
− 3.30996u
82
+ ··· + 487.028u − 315.806
−0.428925u
83
− 6.80246u
82
+ ··· + 728.359u − 346.949
a
4
=
−1.16716u
83
− 1.19878u
82
+ ··· + 112.821u − 87.6721
0.148106u
83
− 0.591608u
82
+ ··· + 30.7174u − 25.5279
a
9
=
u
u
a
10
=
−2.43860u
83
+ 2.86253u
82
+ ··· − 210.519u + 45.7678
−0.688297u
83
− 0.498914u
82
+ ··· + 43.5911u − 43.6754
a
1
=
u
2
+ 1
−u
4
a
12
=
5.77871u
83
− 5.15966u
82
+ ··· + 404.557u − 35.3569
4.36764u
83
+ 3.76892u
82
+ ··· − 546.433u + 386.589
a
5
=
−0.405428u
83
− 1.49265u
82
+ ··· + 134.373u − 79.1284
1.55554u
83
− 2.95746u
82
+ ··· + 251.078u − 103.417
a
11
=
5.77871u
83
− 5.15966u
82
+ ··· + 404.557u − 35.3569
9.19323u
83
+ 0.355636u
82
+ ··· − 331.991u + 416.922
a
7
=
−2.31774u
83
− 3.78616u
82
+ ··· + 504.281u − 305.207
−0.356820u
83
− 11.5652u
82
+ ··· + 1284.14u − 608.102
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.61656u
83
− 5.45770u
82
+ ··· + 670.848u − 462.720
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 51u
83
+ ··· + 45793u + 2401
c
2
, c
8
u
84
+ u
83
+ ··· + 111u + 49
c
3
u
84
+ 8u
83
+ ··· − 11118u + 1361
c
4
u
84
− 9u
83
+ ··· − 217846165u + 89630771
c
5
u
84
− 3u
83
+ ··· − 1457u + 173
c
6
u
84
− 41u
82
+ ··· + 1075379u + 53761
c
7
, c
11
u
84
+ u
83
+ ··· + 14u + 1
c
9
u
84
+ 3u
83
+ ··· + 5494435u + 643211
c
10
u
84
+ u
83
+ ··· + 7748u + 16641
c
12
u
84
+ 4u
83
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
− 25y
83
+ ··· + 451388937y + 5764801
c
2
, c
8
y
84
+ 51y
83
+ ··· + 45793y + 2401
c
3
y
84
− 94y
83
+ ··· + 3281550y + 1852321
c
4
y
84
− 69y
83
+ ··· − 93715556363356613y + 8033675110054441
c
5
y
84
+ 19y
83
+ ··· − 9004789y + 29929
c
6
y
84
− 82y
83
+ ··· − 150205571231y + 2890245121
c
7
, c
11
y
84
− 63y
83
+ ··· − 68y + 1
c
9
y
84
− 47y
83
+ ··· + 6919320761307y + 413720390521
c
10
y
84
+ 23y
83
+ ··· + 12729508892y + 276922881
c
12
y
84
+ 6y
83
+ ··· + 104y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624339 + 0.776376I
a = −0.402447 + 0.827895I
b = 0.577955 + 0.944921I
2.98746 − 1.05041I 0
u = 0.624339 − 0.776376I
a = −0.402447 − 0.827895I
b = 0.577955 − 0.944921I
2.98746 + 1.05041I 0
u = −0.984757 + 0.028992I
a = −1.305870 − 0.531353I
b = −0.167274 + 0.135617I
−3.43240 − 4.70886I 0
u = −0.984757 − 0.028992I
a = −1.305870 + 0.531353I
b = −0.167274 − 0.135617I
−3.43240 + 4.70886I 0
u = 0.070205 + 0.974127I
a = 0.676828 − 0.681396I
b = −0.77441 − 1.73440I
−0.62510 + 3.04588I 0
u = 0.070205 − 0.974127I
a = 0.676828 + 0.681396I
b = −0.77441 + 1.73440I
−0.62510 − 3.04588I 0
u = 0.152041 + 1.034940I
a = −1.074540 − 0.801428I
b = 0.312399 − 0.793279I
−5.11490 + 2.83585I 0
u = 0.152041 − 1.034940I
a = −1.074540 + 0.801428I
b = 0.312399 + 0.793279I
−5.11490 − 2.83585I 0
u = 0.057583 + 0.947885I
a = −0.93954 + 2.00808I
b = −0.21235 + 2.27623I
1.035170 + 0.344979I 0
u = 0.057583 − 0.947885I
a = −0.93954 − 2.00808I
b = −0.21235 − 2.27623I
1.035170 − 0.344979I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056600 + 0.170943I
a = −1.159070 + 0.193628I
b = −0.127728 + 0.182476I
−7.93661 − 2.97178I 0
u = 1.056600 − 0.170943I
a = −1.159070 − 0.193628I
b = −0.127728 − 0.182476I
−7.93661 + 2.97178I 0
u = 1.064760 + 0.140239I
a = −1.61256 − 0.31819I
b = −0.007697 + 0.448028I
−8.8561 − 11.2574I 0
u = 1.064760 − 0.140239I
a = −1.61256 + 0.31819I
b = −0.007697 − 0.448028I
−8.8561 + 11.2574I 0
u = 0.266496 + 0.883595I
a = −1.17684 − 2.39946I
b = −1.07953 − 2.21939I
−2.41310 + 6.12076I 0. − 7.70810I
u = 0.266496 − 0.883595I
a = −1.17684 + 2.39946I
b = −1.07953 + 2.21939I
−2.41310 − 6.12076I 0. + 7.70810I
u = −0.618147 + 0.892022I
a = 0.240538 − 0.019613I
b = −0.764502 − 0.092969I
−2.45152 + 0.05749I 0
u = −0.618147 − 0.892022I
a = 0.240538 + 0.019613I
b = −0.764502 + 0.092969I
−2.45152 − 0.05749I 0
u = 0.400936 + 1.008700I
a = 0.099014 − 1.279680I
b = −0.25180 − 2.23090I
−3.64938 + 5.14792I 0
u = 0.400936 − 1.008700I
a = 0.099014 + 1.279680I
b = −0.25180 + 2.23090I
−3.64938 − 5.14792I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.252494 + 0.875622I
a = 0.960910 − 0.430174I
b = 0.601016 − 0.096506I
−0.43979 − 1.58507I 0. + 4.81532I
u = −0.252494 − 0.875622I
a = 0.960910 + 0.430174I
b = 0.601016 + 0.096506I
−0.43979 + 1.58507I 0. − 4.81532I
u = −0.855464 + 0.674714I
a = 0.028517 − 0.741459I
b = 0.571683 + 0.220653I
−0.681532 + 0.899140I 0
u = −0.855464 − 0.674714I
a = 0.028517 + 0.741459I
b = 0.571683 − 0.220653I
−0.681532 − 0.899140I 0
u = −0.155261 + 1.079100I
a = −0.325368 + 0.475644I
b = −0.34063 + 1.77064I
−2.09724 − 2.85559I 0
u = −0.155261 − 1.079100I
a = −0.325368 − 0.475644I
b = −0.34063 − 1.77064I
−2.09724 + 2.85559I 0
u = 0.621232 + 0.914123I
a = −0.876179 + 0.130572I
b = −0.478088 + 0.940852I
2.55309 + 5.96851I 0
u = 0.621232 − 0.914123I
a = −0.876179 − 0.130572I
b = −0.478088 − 0.940852I
2.55309 − 5.96851I 0
u = −0.889487 + 0.087296I
a = 1.49853 + 0.36339I
b = 0.478615 + 0.423569I
−7.16342 − 1.69036I −8.17295 + 4.28512I
u = −0.889487 − 0.087296I
a = 1.49853 − 0.36339I
b = 0.478615 − 0.423569I
−7.16342 + 1.69036I −8.17295 − 4.28512I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099728 + 0.867946I
a = 0.624002 − 0.596405I
b = −0.691779 − 0.310908I
−0.40378 − 2.13241I −4.45473 + 4.83431I
u = 0.099728 − 0.867946I
a = 0.624002 + 0.596405I
b = −0.691779 + 0.310908I
−0.40378 + 2.13241I −4.45473 − 4.83431I
u = −0.344209 + 0.802582I
a = 0.954239 + 0.172222I
b = 0.469133 + 0.722529I
−0.30736 − 1.52896I −2.00000 + 5.06207I
u = −0.344209 − 0.802582I
a = 0.954239 − 0.172222I
b = 0.469133 − 0.722529I
−0.30736 + 1.52896I −2.00000 − 5.06207I
u = 0.521057 + 0.696756I
a = 2.25645 + 0.55350I
b = 1.84405 − 0.56915I
−2.02874 − 2.80140I −3.16614 + 3.38466I
u = 0.521057 − 0.696756I
a = 2.25645 − 0.55350I
b = 1.84405 + 0.56915I
−2.02874 + 2.80140I −3.16614 − 3.38466I
u = −1.129490 + 0.150367I
a = 1.80812 − 0.45022I
b = −0.505344 + 0.948878I
−6.41608 + 0.87005I 0
u = −1.129490 − 0.150367I
a = 1.80812 + 0.45022I
b = −0.505344 − 0.948878I
−6.41608 − 0.87005I 0
u = 0.317066 + 1.096700I
a = −0.80464 − 1.22601I
b = −0.73642 − 2.85554I
−4.04887 + 7.70346I 0
u = 0.317066 − 1.096700I
a = −0.80464 + 1.22601I
b = −0.73642 + 2.85554I
−4.04887 − 7.70346I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.231757 + 1.181000I
a = −0.730973 − 1.200560I
b = 0.07606 − 1.88946I
−5.80217 − 6.52422I 0
u = −0.231757 − 1.181000I
a = −0.730973 + 1.200560I
b = 0.07606 + 1.88946I
−5.80217 + 6.52422I 0
u = 0.793678 + 0.911216I
a = −0.083385 + 0.248184I
b = −0.386082 + 0.069923I
5.63036 + 2.99540I 0
u = 0.793678 − 0.911216I
a = −0.083385 − 0.248184I
b = −0.386082 − 0.069923I
5.63036 − 2.99540I 0
u = 0.279077 + 0.740387I
a = 1.271060 − 0.044685I
b = 1.87377 + 0.06065I
−4.18434 − 0.93777I −10.44340 − 1.29773I
u = 0.279077 − 0.740387I
a = 1.271060 + 0.044685I
b = 1.87377 − 0.06065I
−4.18434 + 0.93777I −10.44340 + 1.29773I
u = 0.769600 + 0.104576I
a = 1.88696 + 0.52531I
b = 0.429347 − 0.248742I
−2.63396 − 1.15147I −2.64253 − 2.45768I
u = 0.769600 − 0.104576I
a = 1.88696 − 0.52531I
b = 0.429347 + 0.248742I
−2.63396 + 1.15147I −2.64253 + 2.45768I
u = 0.416078 + 1.182460I
a = 0.208724 − 1.368180I
b = 0.86755 − 2.06309I
−6.34523 + 2.87444I 0
u = 0.416078 − 1.182460I
a = 0.208724 + 1.368180I
b = 0.86755 + 2.06309I
−6.34523 − 2.87444I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498312 + 0.543146I
a = 0.125771 − 0.693418I
b = −0.062607 + 1.020890I
−1.56776 − 4.58591I −3.52776 + 6.17506I
u = −0.498312 − 0.543146I
a = 0.125771 + 0.693418I
b = −0.062607 − 1.020890I
−1.56776 + 4.58591I −3.52776 − 6.17506I
u = −0.116360 + 1.267120I
a = 0.225728 − 0.913470I
b = 1.07436 − 2.04992I
−7.20975 − 0.95387I 0
u = −0.116360 − 1.267120I
a = 0.225728 + 0.913470I
b = 1.07436 + 2.04992I
−7.20975 + 0.95387I 0
u = −0.802349 + 1.014890I
a = −0.394246 + 0.208156I
b = −1.092340 − 0.494974I
−1.65167 − 7.02055I 0
u = −0.802349 − 1.014890I
a = −0.394246 − 0.208156I
b = −1.092340 + 0.494974I
−1.65167 + 7.02055I 0
u = 0.489018 + 1.198890I
a = −0.10819 − 1.72417I
b = −0.36299 − 2.86624I
−5.84133 + 5.81556I 0
u = 0.489018 − 1.198890I
a = −0.10819 + 1.72417I
b = −0.36299 + 2.86624I
−5.84133 − 5.81556I 0
u = −0.433364 + 1.274080I
a = −0.425292 + 1.337080I
b = −0.12528 + 2.11785I
−11.30970 − 6.31124I 0
u = −0.433364 − 1.274080I
a = −0.425292 − 1.337080I
b = −0.12528 − 2.11785I
−11.30970 + 6.31124I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524149 + 1.250560I
a = 0.39005 + 1.42843I
b = 0.39342 + 2.16528I
−10.64430 − 3.42952I 0
u = −0.524149 − 1.250560I
a = 0.39005 − 1.42843I
b = 0.39342 − 2.16528I
−10.64430 + 3.42952I 0
u = 0.519821 + 0.374551I
a = 1.88837 + 0.04418I
b = 0.179300 − 0.260934I
−1.87796 − 1.43458I −1.46731 − 0.52130I
u = 0.519821 − 0.374551I
a = 1.88837 − 0.04418I
b = 0.179300 + 0.260934I
−1.87796 + 1.43458I −1.46731 + 0.52130I
u = −0.486780 + 1.316210I
a = 0.140717 − 1.395610I
b = 0.40034 − 2.51194I
−7.59451 − 9.91142I 0
u = −0.486780 − 1.316210I
a = 0.140717 + 1.395610I
b = 0.40034 + 2.51194I
−7.59451 + 9.91142I 0
u = −0.51542 + 1.32110I
a = −0.251208 − 0.923395I
b = −0.74651 − 1.69422I
−7.40945 − 0.67992I 0
u = −0.51542 − 1.32110I
a = −0.251208 + 0.923395I
b = −0.74651 + 1.69422I
−7.40945 + 0.67992I 0
u = 0.58449 + 1.30757I
a = −0.14518 + 1.53271I
b = 0.23231 + 2.91128I
−12.4841 + 17.1391I 0
u = 0.58449 − 1.30757I
a = −0.14518 − 1.53271I
b = 0.23231 − 2.91128I
−12.4841 − 17.1391I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59528 + 1.30604I
a = −0.194602 + 1.083090I
b = −0.22396 + 1.95074I
−11.4630 + 8.9032I 0
u = 0.59528 − 1.30604I
a = −0.194602 − 1.083090I
b = −0.22396 − 1.95074I
−11.4630 − 8.9032I 0
u = 0.38684 + 1.38887I
a = 0.162602 + 1.055620I
b = −0.00363 + 2.00199I
−13.05160 + 2.06430I 0
u = 0.38684 − 1.38887I
a = 0.162602 − 1.055620I
b = −0.00363 − 2.00199I
−13.05160 − 2.06430I 0
u = 0.40196 + 1.41075I
a = −0.265295 + 0.937006I
b = −1.15968 + 2.03447I
−13.9236 − 6.0378I 0
u = 0.40196 − 1.41075I
a = −0.265295 − 0.937006I
b = −1.15968 − 2.03447I
−13.9236 + 6.0378I 0
u = −0.39976 + 1.41147I
a = 0.524178 + 0.697717I
b = 2.23400 + 1.98841I
−11.64390 − 4.47794I 0
u = −0.39976 − 1.41147I
a = 0.524178 − 0.697717I
b = 2.23400 − 1.98841I
−11.64390 + 4.47794I 0
u = −0.59023 + 1.35145I
a = 0.29506 + 1.50766I
b = −0.38369 + 3.36097I
−10.23170 − 7.02272I 0
u = −0.59023 − 1.35145I
a = 0.29506 − 1.50766I
b = −0.38369 − 3.36097I
−10.23170 + 7.02272I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383340 + 0.185448I
a = 0.37154 + 1.61335I
b = −0.338406 + 0.477813I
1.21335 − 1.11387I 4.27095 + 2.48493I
u = −0.383340 − 0.185448I
a = 0.37154 − 1.61335I
b = −0.338406 − 0.477813I
1.21335 + 1.11387I 4.27095 − 2.48493I
u = 0.223249 + 0.317821I
a = 3.38242 − 0.25747I
b = 0.407420 + 0.951931I
−1.76322 − 4.93035I −2.22330 + 7.33828I
u = 0.223249 − 0.317821I
a = 3.38242 + 0.25747I
b = 0.407420 − 0.951931I
−1.76322 + 4.93035I −2.22330 − 7.33828I
13
II. I
u
2
=
h−5u
30
−2u
29
+· · ·+b −4, −3u
30
+2u
29
+· · ·+a −1, u
31
+8u
29
+· · ·−4u +1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
6
=
3u
30
− 2u
29
+ ··· + 4u + 1
5u
30
+ 2u
29
+ ··· − 10u + 4
a
4
=
2u
30
+ 3u
29
+ ··· − 10u + 4
6u
30
− 6u
29
+ ··· + 43u − 7
a
9
=
u
u
a
10
=
4u
30
+ u
29
+ ··· − 8u + 3
−5u
30
+ 3u
29
+ ··· + 7u − 3
a
1
=
u
2
+ 1
−u
4
a
12
=
2u
30
+ 6u
29
+ ··· − 20u + 5
−8u
30
+ u
29
+ ··· + 16u − 6
a
5
=
−u
30
+ u
29
+ ··· + 4u − 1
6u
30
− 9u
29
+ ··· + 55u − 9
a
11
=
2u
30
+ 6u
29
+ ··· − 20u + 5
−7u
30
+ 3u
29
+ ··· + 27u
2
− 6u
a
7
=
3u
30
− 2u
29
+ ··· − 27u
2
+ 4u
4u
30
+ 2u
29
+ ··· − 11u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
29
−14u
28
−28u
27
−96u
26
−127u
25
−356u
24
−374u
23
−870u
22
−790u
21
−1557u
20
−
1273u
19
− 2066u
18
− 1619u
17
− 2021u
16
− 1648u
15
− 1324u
14
− 1375u
13
− 374u
12
−
963u
11
+ 280u
10
−574u
9
+ 404u
8
−295u
7
+ 198u
6
−109u
5
+ 12u
4
−2u
3
−33u
2
+ 19u −14
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
31
− 16u
30
+ ··· − 8u + 1
c
2
u
31
+ 8u
29
+ ··· − 4u + 1
c
3
u
31
− 17u
30
+ ··· + 543u − 71
c
4
u
31
+ 4u
30
+ ··· + 292u + 149
c
5
u
31
− 2u
29
+ ··· + 2u + 1
c
6
u
31
− u
30
+ ··· + 4u + 1
c
7
u
31
− 7u
29
+ ··· − u − 1
c
8
u
31
+ 8u
29
+ ··· − 4u − 1
c
9
u
31
− 3u
29
+ ··· − 2u − 1
c
10
u
31
− 2u
29
+ ··· + u − 1
c
11
u
31
− 7u
29
+ ··· − u + 1
c
12
u
31
− 7u
30
+ ··· + 5u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 8y
30
+ ··· − 20y −1
c
2
, c
8
y
31
+ 16y
30
+ ··· − 8y −1
c
3
y
31
− 25y
30
+ ··· − 46377y −5041
c
4
y
31
− 16y
30
+ ··· − 83702y −22201
c
5
y
31
− 4y
30
+ ··· − 30y −1
c
6
y
31
− y
30
+ ··· − 20y −1
c
7
, c
11
y
31
− 14y
30
+ ··· + 25y −1
c
9
y
31
− 6y
30
+ ··· − 18y −1
c
10
y
31
− 4y
30
+ ··· − 23y −1
c
12
y
31
− 5y
30
+ ··· + 13y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265098 + 0.967882I
a = −0.28743 − 1.89453I
b = −0.49506 − 2.92170I
−3.29472 + 6.43312I −7.05697 − 9.59211I
u = 0.265098 − 0.967882I
a = −0.28743 + 1.89453I
b = −0.49506 + 2.92170I
−3.29472 − 6.43312I −7.05697 + 9.59211I
u = −0.313962 + 0.920721I
a = 0.511198 − 0.129308I
b = −0.893757 − 0.210031I
−0.217015 + 1.174960I −1.83905 + 2.61792I
u = −0.313962 − 0.920721I
a = 0.511198 + 0.129308I
b = −0.893757 + 0.210031I
−0.217015 − 1.174960I −1.83905 − 2.61792I
u = −0.669519 + 0.789204I
a = −0.518703 − 1.126310I
b = 0.563405 − 1.097350I
2.42460 + 0.73064I −4.84089 + 2.23011I
u = −0.669519 − 0.789204I
a = −0.518703 + 1.126310I
b = 0.563405 + 1.097350I
2.42460 − 0.73064I −4.84089 − 2.23011I
u = −0.189679 + 0.927863I
a = 1.04809 + 1.87907I
b = 0.30657 + 2.16466I
1.18607 − 0.83629I 1.46354 + 9.46145I
u = −0.189679 − 0.927863I
a = 1.04809 − 1.87907I
b = 0.30657 − 2.16466I
1.18607 + 0.83629I 1.46354 − 9.46145I
u = −1.05657
a = 1.66463
b = −0.229458
−6.35797 −6.30910
u = 0.718686 + 0.844084I
a = 0.780944 + 0.285872I
b = 1.257230 − 0.128860I
−0.09569 − 2.34713I −1.50519 + 3.38527I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718686 − 0.844084I
a = 0.780944 − 0.285872I
b = 1.257230 + 0.128860I
−0.09569 + 2.34713I −1.50519 − 3.38527I
u = −0.267932 + 0.847092I
a = 0.370904 − 0.228935I
b = −0.797009 + 1.085070I
0.10252 − 3.72692I 1.27618 + 7.56947I
u = −0.267932 − 0.847092I
a = 0.370904 + 0.228935I
b = −0.797009 − 1.085070I
0.10252 + 3.72692I 1.27618 − 7.56947I
u = 0.681648 + 0.893777I
a = −0.607976 − 0.954870I
b = −0.786717 − 0.392164I
−0.25933 + 7.71253I −0.77608 − 8.53261I
u = 0.681648 − 0.893777I
a = −0.607976 + 0.954870I
b = −0.786717 + 0.392164I
−0.25933 − 7.71253I −0.77608 + 8.53261I
u = 0.275652 + 0.825616I
a = 2.09397 − 0.85986I
b = 1.293070 − 0.245003I
−2.78013 − 4.08092I −7.65589 + 4.54600I
u = 0.275652 − 0.825616I
a = 2.09397 + 0.85986I
b = 1.293070 + 0.245003I
−2.78013 + 4.08092I −7.65589 − 4.54600I
u = −0.641006 + 0.933992I
a = −1.046320 − 0.393466I
b = −0.70177 − 1.23874I
1.96290 − 5.81995I −7.31112 + 5.01137I
u = −0.641006 − 0.933992I
a = −1.046320 + 0.393466I
b = −0.70177 + 1.23874I
1.96290 + 5.81995I −7.31112 − 5.01137I
u = −0.811801 + 0.910841I
a = 0.143518 + 0.320639I
b = 0.347483 + 0.203658I
5.52560 − 3.04659I −31.3952 + 17.9372I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.811801 − 0.910841I
a = 0.143518 − 0.320639I
b = 0.347483 − 0.203658I
5.52560 + 3.04659I −31.3952 − 17.9372I
u = 0.481778 + 1.173210I
a = 0.408417 − 1.203180I
b = 0.97414 − 1.75605I
−6.07463 + 2.05407I −6.49054 + 0.97231I
u = 0.481778 − 1.173210I
a = 0.408417 + 1.203180I
b = 0.97414 + 1.75605I
−6.07463 − 2.05407I −6.49054 − 0.97231I
u = 0.470271 + 1.181590I
a = −0.24613 − 1.80567I
b = −0.60419 − 2.99873I
−6.11418 + 6.34194I −11.1554 − 10.3331I
u = 0.470271 − 1.181590I
a = −0.24613 + 1.80567I
b = −0.60419 + 2.99873I
−6.11418 − 6.34194I −11.1554 + 10.3331I
u = 0.589602 + 0.209264I
a = 2.48299 + 1.02644I
b = 0.787669 − 0.377602I
−3.13512 − 1.99092I −7.94938 + 3.76098I
u = 0.589602 − 0.209264I
a = 2.48299 − 1.02644I
b = 0.787669 + 0.377602I
−3.13512 + 1.99092I −7.94938 − 3.76098I
u = −0.466463 + 1.331720I
a = 0.099439 + 1.155400I
b = 0.56374 + 2.28352I
−10.68690 − 5.35793I −7.27535 + 3.05329I
u = −0.466463 − 1.331720I
a = 0.099439 − 1.155400I
b = 0.56374 − 2.28352I
−10.68690 + 5.35793I −7.27535 − 3.05329I
u = 0.405909 + 0.350244I
a = 0.43477 − 1.80577I
b = 0.799929 − 0.326264I
−3.32889 + 2.11246I −5.83416 − 3.67200I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405909 − 0.350244I
a = 0.43477 + 1.80577I
b = 0.799929 + 0.326264I
−3.32889 − 2.11246I −5.83416 + 3.67200I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 16u
30
+ ··· − 8u + 1)(u
84
+ 51u
83
+ ··· + 45793u + 2401)
c
2
(u
31
+ 8u
29
+ ··· − 4u + 1)(u
84
+ u
83
+ ··· + 111u + 49)
c
3
(u
31
− 17u
30
+ ··· + 543u − 71)(u
84
+ 8u
83
+ ··· − 11118u + 1361)
c
4
(u
31
+ 4u
30
+ ··· + 292u + 149)
· (u
84
− 9u
83
+ ··· − 217846165u + 89630771)
c
5
(u
31
− 2u
29
+ ··· + 2u + 1)(u
84
− 3u
83
+ ··· − 1457u + 173)
c
6
(u
31
− u
30
+ ··· + 4u + 1)(u
84
− 41u
82
+ ··· + 1075379u + 53761)
c
7
(u
31
− 7u
29
+ ··· − u − 1)(u
84
+ u
83
+ ··· + 14u + 1)
c
8
(u
31
+ 8u
29
+ ··· − 4u − 1)(u
84
+ u
83
+ ··· + 111u + 49)
c
9
(u
31
− 3u
29
+ ··· − 2u − 1)(u
84
+ 3u
83
+ ··· + 5494435u + 643211)
c
10
(u
31
− 2u
29
+ ··· + u − 1)(u
84
+ u
83
+ ··· + 7748u + 16641)
c
11
(u
31
− 7u
29
+ ··· − u + 1)(u
84
+ u
83
+ ··· + 14u + 1)
c
12
(u
31
− 7u
30
+ ··· + 5u + 1)(u
84
+ 4u
83
+ ··· + 8u + 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
31
+ 8y
30
+ ··· − 20y −1)
· (y
84
− 25y
83
+ ··· + 451388937y + 5764801)
c
2
, c
8
(y
31
+ 16y
30
+ ··· − 8y −1)(y
84
+ 51y
83
+ ··· + 45793y + 2401)
c
3
(y
31
− 25y
30
+ ··· − 46377y −5041)
· (y
84
− 94y
83
+ ··· + 3281550y + 1852321)
c
4
(y
31
− 16y
30
+ ··· − 83702y −22201)
· (y
84
− 69y
83
+ ··· − 93715556363356613y + 8033675110054441)
c
5
(y
31
− 4y
30
+ ··· − 30y −1)(y
84
+ 19y
83
+ ··· − 9004789y + 29929)
c
6
(y
31
− y
30
+ ··· − 20y −1)
· (y
84
− 82y
83
+ ··· − 150205571231y + 2890245121)
c
7
, c
11
(y
31
− 14y
30
+ ··· + 25y −1)(y
84
− 63y
83
+ ··· − 68y + 1)
c
9
(y
31
− 6y
30
+ ··· − 18y −1)
· (y
84
− 47y
83
+ ··· + 6919320761307y + 413720390521)
c
10
(y
31
− 4y
30
+ ··· − 23y −1)
· (y
84
+ 23y
83
+ ··· + 12729508892y + 276922881)
c
12
(y
31
− 5y
30
+ ··· + 13y −1)(y
84
+ 6y
83
+ ··· + 104y + 1)
24
