12n
0819
(K12n
0819
)
A knot diagram
1
Linearized knot diagam
4 6 11 9 2 10 1 4 12 3 7 9
Solving Sequence
4,9 2,5
6 1 8 7 12 10 11 3
c
4
c
5
c
1
c
8
c
7
c
12
c
9
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h8.73090 × 10
293
u
77
− 3.56351 × 10
294
u
76
+ ··· + 7.84651 × 10
296
b − 4.65322 × 10
297
,
− 1.85338 × 10
298
u
77
+ 6.45142 × 10
298
u
76
+ ··· + 4.37678 × 10
300
a + 6.50906 × 10
300
,
u
78
− 4u
77
+ ··· − 34268u + 2789i
I
u
2
= h976963699145u
24
− 5356482432121u
23
+ ··· + 6473712830526b + 4457277781243,
− 4338891421343u
24
+ 18419785693814u
23
+ ··· + 12947425661052a − 28103666444157,
u
25
− 5u
24
+ ··· + 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 103 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
= h8.73 × 10
293
u
77
− 3.56 × 10
294
u
76
+ · · · + 7.85 × 10
296
b − 4.65 ×
10
297
, −1.85 × 10
298
u
77
+ 6.45 × 10
298
u
76
+ · · · + 4.38 × 10
300
a + 6.51 ×
10
300
, u
78
− 4u
77
+ · · · − 34268u + 2789i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
0.00423457u
77
− 0.0147401u
76
+ ··· + 47.3144u − 1.48718
−0.00111271u
77
+ 0.00454153u
76
+ ··· − 68.9860u + 5.93031
a
5
=
1
u
2
a
6
=
0.00437670u
77
− 0.0163847u
76
+ ··· + 19.7784u − 1.75814
−0.00313818u
77
+ 0.0102642u
76
+ ··· + 84.8849u − 8.41119
a
1
=
0.00312185u
77
− 0.0101986u
76
+ ··· − 21.6716u + 4.44313
−0.00111271u
77
+ 0.00454153u
76
+ ··· − 68.9860u + 5.93031
a
8
=
u
u
a
7
=
−0.00192164u
77
+ 0.0114186u
76
+ ··· − 261.075u + 19.1357
0.00123597u
77
− 0.00425560u
76
+ ··· − 33.1124u + 3.71756
a
12
=
0.00312185u
77
− 0.0101986u
76
+ ··· − 21.6716u + 4.44313
−0.00176996u
77
+ 0.00593289u
76
+ ··· + 0.741219u − 0.453273
a
10
=
−0.000969232u
77
+ 0.000832254u
76
+ ··· + 160.099u − 12.1813
−0.00313055u
77
+ 0.0146618u
76
+ ··· − 202.608u + 15.4460
a
11
=
−0.00124230u
77
+ 0.00728569u
76
+ ··· − 177.510u + 17.3463
0.00191628u
77
− 0.00793871u
76
+ ··· + 50.3738u − 5.09448
a
3
=
−0.00105957u
77
+ 0.00386563u
76
+ ··· − 11.5396u + 5.70652
0.00156637u
77
− 0.00526645u
76
+ ··· − 25.0713u + 1.19390
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00717324u
77
− 0.0329693u
76
+ ··· + 172.137u − 9.92485
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
78
− 2u
77
+ ··· + 5080u − 1808
c
2
, c
5
u
78
+ 4u
77
+ ··· − 177548u − 41707
c
3
, c
10
u
78
− u
77
+ ··· − 7u + 85
c
4
, c
8
u
78
+ 4u
77
+ ··· + 34268u + 2789
c
6
u
78
− 6u
77
+ ··· − 120616u − 6256
c
7
u
78
− 2u
77
+ ··· − 35004u − 5048
c
9
, c
12
u
78
+ 4u
77
+ ··· − 21648u − 1747
c
11
u
78
+ 2u
77
+ ··· + 1038u − 463
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
78
+ 86y
77
+ ··· + 33365824y + 3268864
c
2
, c
5
y
78
− 54y
77
+ ··· − 15298685406y + 1739473849
c
3
, c
10
y
78
− 51y
77
+ ··· − 50879y + 7225
c
4
, c
8
y
78
+ 74y
77
+ ··· + 243548106y + 7778521
c
6
y
78
+ 36y
77
+ ··· − 7231852480y + 39137536
c
7
y
78
− 80y
77
+ ··· − 1613410640y + 25482304
c
9
, c
12
y
78
+ 44y
77
+ ··· − 160384742y + 3052009
c
11
y
78
+ 12y
77
+ ··· + 305074y + 214369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553189 + 0.771248I
a = 0.370110 + 1.114770I
b = 0.738176 − 0.268544I
−6.49552 − 2.40443I 0
u = 0.553189 − 0.771248I
a = 0.370110 − 1.114770I
b = 0.738176 + 0.268544I
−6.49552 + 2.40443I 0
u = 1.048370 + 0.137410I
a = 0.331336 + 0.088614I
b = −0.344501 + 0.666535I
−2.11440 − 0.16429I 0
u = 1.048370 − 0.137410I
a = 0.331336 − 0.088614I
b = −0.344501 − 0.666535I
−2.11440 + 0.16429I 0
u = 0.114213 + 0.927534I
a = −0.131174 − 0.243934I
b = −0.393728 − 0.447997I
−2.00138 − 3.96725I 0
u = 0.114213 − 0.927534I
a = −0.131174 + 0.243934I
b = −0.393728 + 0.447997I
−2.00138 + 3.96725I 0
u = 0.307499 + 1.047930I
a = −1.004590 + 0.203212I
b = −0.562101 − 0.775845I
−6.64128 + 1.36200I 0
u = 0.307499 − 1.047930I
a = −1.004590 − 0.203212I
b = −0.562101 + 0.775845I
−6.64128 − 1.36200I 0
u = 0.506668 + 1.014800I
a = 0.93502 − 1.34181I
b = −0.29598 + 1.91126I
1.53283 + 0.40725I 0
u = 0.506668 − 1.014800I
a = 0.93502 + 1.34181I
b = −0.29598 − 1.91126I
1.53283 − 0.40725I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.055201 + 0.814919I
a = −2.21047 + 0.40931I
b = 0.410233 − 0.651215I
−8.38983 − 7.51886I 0
u = −0.055201 − 0.814919I
a = −2.21047 − 0.40931I
b = 0.410233 + 0.651215I
−8.38983 + 7.51886I 0
u = 0.153693 + 0.735214I
a = 0.106501 + 0.447614I
b = −1.59181 − 0.10677I
−4.53096 + 2.37951I 0
u = 0.153693 − 0.735214I
a = 0.106501 − 0.447614I
b = −1.59181 + 0.10677I
−4.53096 − 2.37951I 0
u = −0.011668 + 0.741741I
a = −0.560820 − 0.866649I
b = 1.80811 + 0.17443I
−8.63150 + 7.73689I 0. − 5.72745I
u = −0.011668 − 0.741741I
a = −0.560820 + 0.866649I
b = 1.80811 − 0.17443I
−8.63150 − 7.73689I 0. + 5.72745I
u = −0.023067 + 1.262340I
a = −0.701945 − 1.138780I
b = 0.04894 + 1.73577I
1.29122 − 1.24492I 0
u = −0.023067 − 1.262340I
a = −0.701945 + 1.138780I
b = 0.04894 − 1.73577I
1.29122 + 1.24492I 0
u = 0.075082 + 1.267450I
a = 0.197226 − 1.233860I
b = −0.94859 + 1.44442I
1.42815 + 2.75123I 0
u = 0.075082 − 1.267450I
a = 0.197226 + 1.233860I
b = −0.94859 − 1.44442I
1.42815 − 2.75123I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077051 + 0.718984I
a = 2.13234 + 0.24501I
b = −0.173438 + 0.213573I
−4.57506 − 3.15137I 0. + 4.31486I
u = 0.077051 − 0.718984I
a = 2.13234 − 0.24501I
b = −0.173438 − 0.213573I
−4.57506 + 3.15137I 0. − 4.31486I
u = 0.536366 + 0.406535I
a = −0.87103 − 2.28655I
b = −0.316632 + 0.555371I
−7.45234 − 1.28627I −6.12884 − 2.41040I
u = 0.536366 − 0.406535I
a = −0.87103 + 2.28655I
b = −0.316632 − 0.555371I
−7.45234 + 1.28627I −6.12884 + 2.41040I
u = −1.305890 + 0.287986I
a = 0.634714 + 0.012303I
b = 0.072979 − 0.725867I
−2.96317 − 3.30928I 0
u = −1.305890 − 0.287986I
a = 0.634714 − 0.012303I
b = 0.072979 + 0.725867I
−2.96317 + 3.30928I 0
u = 1.281170 + 0.411435I
a = −0.103190 + 0.368321I
b = 0.257930 + 0.155794I
−5.60477 − 1.57442I 0
u = 1.281170 − 0.411435I
a = −0.103190 − 0.368321I
b = 0.257930 − 0.155794I
−5.60477 + 1.57442I 0
u = −0.009798 + 1.367980I
a = 0.376007 + 1.350890I
b = 0.28274 − 1.78454I
2.81039 − 0.70774I 0
u = −0.009798 − 1.367980I
a = 0.376007 − 1.350890I
b = 0.28274 + 1.78454I
2.81039 + 0.70774I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475180 + 1.284860I
a = −0.29910 + 1.40610I
b = −0.25565 − 1.85967I
2.66302 − 4.36792I 0
u = 0.475180 − 1.284860I
a = −0.29910 − 1.40610I
b = −0.25565 + 1.85967I
2.66302 + 4.36792I 0
u = 0.03926 + 1.42863I
a = 0.197338 + 1.087340I
b = 0.340589 − 1.360110I
3.02947 − 1.19479I 0
u = 0.03926 − 1.42863I
a = 0.197338 − 1.087340I
b = 0.340589 + 1.360110I
3.02947 + 1.19479I 0
u = 0.02389 + 1.47698I
a = −0.247155 + 0.531188I
b = −0.266358 − 1.259730I
−1.68490 − 3.66956I 0
u = 0.02389 − 1.47698I
a = −0.247155 − 0.531188I
b = −0.266358 + 1.259730I
−1.68490 + 3.66956I 0
u = −1.39206 + 0.50023I
a = −0.627615 − 0.116524I
b = −0.103857 + 0.490501I
−7.16752 + 3.44665I 0
u = −1.39206 − 0.50023I
a = −0.627615 + 0.116524I
b = −0.103857 − 0.490501I
−7.16752 − 3.44665I 0
u = −0.221090 + 0.455313I
a = 0.729764 + 0.654361I
b = 0.256358 + 0.109918I
1.119390 − 0.786078I 4.39131 + 2.78793I
u = −0.221090 − 0.455313I
a = 0.729764 − 0.654361I
b = 0.256358 − 0.109918I
1.119390 + 0.786078I 4.39131 − 2.78793I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49652 + 0.07217I
a = −0.519087 − 0.019323I
b = 0.074392 + 0.704796I
−8.08211 − 9.03884I 0
u = −1.49652 − 0.07217I
a = −0.519087 + 0.019323I
b = 0.074392 − 0.704796I
−8.08211 + 9.03884I 0
u = 0.34732 + 1.47622I
a = 0.103642 + 1.259970I
b = −0.61410 − 1.70543I
2.82205 − 4.87434I 0
u = 0.34732 − 1.47622I
a = 0.103642 − 1.259970I
b = −0.61410 + 1.70543I
2.82205 + 4.87434I 0
u = 0.204950 + 0.421347I
a = 1.036100 − 0.700476I
b = 1.50993 + 0.40819I
−8.61803 − 3.17392I −4.16545 − 1.45630I
u = 0.204950 − 0.421347I
a = 1.036100 + 0.700476I
b = 1.50993 − 0.40819I
−8.61803 + 3.17392I −4.16545 + 1.45630I
u = 0.29953 + 1.53190I
a = −0.387107 − 1.030900I
b = 0.85234 + 1.55687I
1.18794 − 6.61851I 0
u = 0.29953 − 1.53190I
a = −0.387107 + 1.030900I
b = 0.85234 − 1.55687I
1.18794 + 6.61851I 0
u = −0.16833 + 1.56106I
a = 0.274182 + 1.088300I
b = −0.14730 − 1.65952I
5.43050 − 3.25360I 0
u = −0.16833 − 1.56106I
a = 0.274182 − 1.088300I
b = −0.14730 + 1.65952I
5.43050 + 3.25360I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17704 + 1.59692I
a = −0.176905 − 0.839760I
b = −0.263205 + 0.915211I
−0.97845 − 4.15453I 0
u = 0.17704 − 1.59692I
a = −0.176905 + 0.839760I
b = −0.263205 − 0.915211I
−0.97845 + 4.15453I 0
u = −0.29112 + 1.58392I
a = −0.152746 − 0.944156I
b = −0.01316 + 1.73867I
7.27487 + 1.92167I 0
u = −0.29112 − 1.58392I
a = −0.152746 + 0.944156I
b = −0.01316 − 1.73867I
7.27487 − 1.92167I 0
u = 0.388485
a = 0.927393
b = −0.631738
−1.00985 −12.6520
u = 1.53299 + 0.52551I
a = −0.211769 + 0.366617I
b = 0.076365 − 0.940501I
−6.05906 − 1.96066I 0
u = 1.53299 − 0.52551I
a = −0.211769 − 0.366617I
b = 0.076365 + 0.940501I
−6.05906 + 1.96066I 0
u = 0.374839
a = −2.68128
b = 1.00371
−2.35857 −3.30110
u = 0.20137 + 1.63065I
a = 0.130556 − 0.944222I
b = 0.55294 + 1.46514I
4.81816 − 4.74145I 0
u = 0.20137 − 1.63065I
a = 0.130556 + 0.944222I
b = 0.55294 − 1.46514I
4.81816 + 4.74145I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293964 + 0.193189I
a = 2.35944 − 1.93322I
b = −0.116758 − 0.750759I
−1.75040 − 2.19758I 1.64597 + 5.00211I
u = −0.293964 − 0.193189I
a = 2.35944 + 1.93322I
b = −0.116758 + 0.750759I
−1.75040 + 2.19758I 1.64597 − 5.00211I
u = −0.67229 + 1.53955I
a = 0.082487 + 0.856688I
b = 0.46676 − 1.67544I
−3.49260 + 4.22399I 0
u = −0.67229 − 1.53955I
a = 0.082487 − 0.856688I
b = 0.46676 + 1.67544I
−3.49260 − 4.22399I 0
u = −0.62154 + 1.56682I
a = −0.091762 − 1.041160I
b = −0.55284 + 1.78046I
1.49105 + 10.50710I 0
u = −0.62154 − 1.56682I
a = −0.091762 + 1.041160I
b = −0.55284 − 1.78046I
1.49105 − 10.50710I 0
u = −0.21186 + 1.68170I
a = −0.291089 + 0.900756I
b = 0.06045 − 1.76893I
1.11465 + 9.02133I 0
u = −0.21186 − 1.68170I
a = −0.291089 − 0.900756I
b = 0.06045 + 1.76893I
1.11465 − 9.02133I 0
u = −0.60617 + 1.62101I
a = −0.006642 + 1.105160I
b = 0.63247 − 1.78811I
−2.8260 + 16.6173I 0
u = −0.60617 − 1.62101I
a = −0.006642 − 1.105160I
b = 0.63247 + 1.78811I
−2.8260 − 16.6173I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.77282 + 1.58292I
a = 0.159041 − 1.000460I
b = 0.31194 + 1.41896I
−2.41294 − 6.47356I 0
u = 0.77282 − 1.58292I
a = 0.159041 + 1.000460I
b = 0.31194 − 1.41896I
−2.41294 + 6.47356I 0
u = 0.25569 + 1.74590I
a = −0.087303 + 1.078660I
b = −0.56741 − 1.48246I
2.38693 − 8.45936I 0
u = 0.25569 − 1.74590I
a = −0.087303 − 1.078660I
b = −0.56741 + 1.48246I
2.38693 + 8.45936I 0
u = −0.10904 + 1.76638I
a = 0.223972 − 0.709148I
b = 0.14466 + 1.77376I
5.45948 + 1.85005I 0
u = −0.10904 − 1.76638I
a = 0.223972 + 0.709148I
b = 0.14466 − 1.77376I
5.45948 − 1.85005I 0
u = 0.124598 + 0.178716I
a = 3.11035 − 0.22996I
b = −0.556865 − 0.502010I
−1.74371 − 0.46019I −4.13695 − 0.26951I
u = 0.124598 − 0.178716I
a = 3.11035 + 0.22996I
b = −0.556865 + 0.502010I
−1.74371 + 0.46019I −4.13695 + 0.26951I
12
II.
I
u
2
= h9.77×10
11
u
24
−5.36×10
12
u
23
+· · ·+6.47×10
12
b+4.46×10
12
, −4.34×
10
12
u
24
+1.84×10
13
u
23
+· · ·+1.29×10
13
a−2.81×10
13
, u
25
−5u
24
+· · ·+3u−1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
0.335116u
24
− 1.42266u
23
+ ··· + 5.29501u + 2.17060
−0.150912u
24
+ 0.827420u
23
+ ··· − 0.635972u − 0.688520
a
5
=
1
u
2
a
6
=
−0.614994u
24
+ 2.94621u
23
+ ··· − 7.16614u − 0.634781
u
2
− u + 1
a
1
=
0.184204u
24
− 0.595240u
23
+ ··· + 4.65904u + 1.48208
−0.150912u
24
+ 0.827420u
23
+ ··· − 0.635972u − 0.688520
a
8
=
u
u
a
7
=
0.229860u
24
− 1.44105u
23
+ ··· + 1.04749u − 1.64934
0.128729u
24
− 0.630969u
23
+ ··· + 1.80423u + 0.310561
a
12
=
0.184204u
24
− 0.595240u
23
+ ··· + 4.65904u + 1.48208
−0.314929u
24
+ 1.69908u
23
+ ··· − 1.42911u − 0.362741
a
10
=
−0.344035u
24
+ 2.02980u
23
+ ··· + 0.0575888u + 1.32610
−0.0277911u
24
+ 0.128303u
23
+ ··· − 0.167822u − 0.0136182
a
11
=
0.275453u
24
− 1.26473u
23
+ ··· + 3.47503u + 0.585338
−0.119004u
24
+ 0.636924u
23
+ ··· − 0.168916u − 0.0515499
a
3
=
0.210239u
24
− 1.36998u
23
+ ··· + 0.684989u + 1.06823
−0.00238683u
24
− 0.00328565u
23
+ ··· − 0.927415u + 0.130104
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
5670551455370
3236856415263
u
24
−
56154175919473
6473712830526
u
23
+ ··· +
134776490182523
6473712830526
u −
652739685965
6473712830526
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
25
− u
24
+ ··· − 8u − 4
c
2
u
25
+ 3u
24
+ ··· + 21u − 13
c
3
u
25
− 7u
23
+ ··· + 6u + 1
c
4
u
25
− 5u
24
+ ··· + 3u − 1
c
5
u
25
− 3u
24
+ ··· + 21u + 13
c
6
u
25
+ u
24
+ ··· − 12u + 4
c
7
u
25
− u
24
+ ··· + 8u + 8
c
8
u
25
+ 5u
24
+ ··· + 3u + 1
c
9
u
25
+ 3u
24
+ ··· + 7u + 7
c
10
u
25
− 7u
23
+ ··· + 6u − 1
c
11
u
25
− u
24
+ ··· − 7u − 1
c
12
u
25
− 3u
24
+ ··· + 7u − 7
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 19y
24
+ ··· − 64y −16
c
2
, c
5
y
25
− 21y
24
+ ··· + 2703y −169
c
3
, c
10
y
25
− 14y
24
+ ··· + 52y −1
c
4
, c
8
y
25
+ 15y
24
+ ··· + 27y −1
c
6
y
25
+ 13y
24
+ ··· − 48y −16
c
7
y
25
− 15y
24
+ ··· − 608y −64
c
9
, c
12
y
25
+ 17y
24
+ ··· − 525y −49
c
11
y
25
+ y
24
+ ··· + 23y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741112 + 0.504146I
a = 0.116829 − 0.353061I
b = 1.218660 − 0.276562I
−9.23157 + 3.66581I −12.91546 − 4.91536I
u = −0.741112 − 0.504146I
a = 0.116829 + 0.353061I
b = 1.218660 + 0.276562I
−9.23157 − 3.66581I −12.91546 + 4.91536I
u = 0.829941 + 0.296486I
a = 0.918807 + 0.518041I
b = −0.194389 + 0.648589I
−2.47394 + 1.82700I −7.17952 − 1.07328I
u = 0.829941 − 0.296486I
a = 0.918807 − 0.518041I
b = −0.194389 − 0.648589I
−2.47394 − 1.82700I −7.17952 + 1.07328I
u = 0.970904 + 0.587520I
a = 0.376179 + 1.206820I
b = 0.224159 − 0.206009I
−7.99692 − 1.72986I −16.4749 + 4.4091I
u = 0.970904 − 0.587520I
a = 0.376179 − 1.206820I
b = 0.224159 + 0.206009I
−7.99692 + 1.72986I −16.4749 − 4.4091I
u = 0.078121 + 1.150140I
a = 0.10712 − 1.54071I
b = −0.60157 + 1.77907I
2.50588 + 1.87323I −1.02310 − 2.28296I
u = 0.078121 − 1.150140I
a = 0.10712 + 1.54071I
b = −0.60157 − 1.77907I
2.50588 − 1.87323I −1.02310 + 2.28296I
u = 0.142180 + 0.821206I
a = −1.17694 − 0.83275I
b = −0.601242 + 0.453878I
−5.60658 − 2.15689I −2.19337 + 1.94259I
u = 0.142180 − 0.821206I
a = −1.17694 + 0.83275I
b = −0.601242 − 0.453878I
−5.60658 + 2.15689I −2.19337 − 1.94259I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096098 + 1.258110I
a = 0.65267 + 1.46440I
b = −0.00381 − 1.87685I
3.12298 − 1.71886I 0.16611 + 4.53358I
u = −0.096098 − 1.258110I
a = 0.65267 − 1.46440I
b = −0.00381 + 1.87685I
3.12298 + 1.71886I 0.16611 − 4.53358I
u = −0.647184 + 0.050857I
a = −0.74957 + 1.59582I
b = 1.134710 + 0.306453I
−10.19640 + 7.70200I −10.96604 − 4.89541I
u = −0.647184 − 0.050857I
a = −0.74957 − 1.59582I
b = 1.134710 − 0.306453I
−10.19640 − 7.70200I −10.96604 + 4.89541I
u = 1.36240 + 0.47131I
a = −0.245222 + 0.228355I
b = 0.043781 − 0.599815I
−4.97268 − 1.46866I −1.44139 + 0.68762I
u = 1.36240 − 0.47131I
a = −0.245222 − 0.228355I
b = 0.043781 + 0.599815I
−4.97268 + 1.46866I −1.44139 − 0.68762I
u = −0.370655 + 0.327033I
a = −1.36917 + 1.30864I
b = −1.032240 + 0.303743I
−5.69473 − 2.61851I −8.99601 + 3.18795I
u = −0.370655 − 0.327033I
a = −1.36917 − 1.30864I
b = −1.032240 − 0.303743I
−5.69473 + 2.61851I −8.99601 − 3.18795I
u = 0.26880 + 1.49571I
a = 0.197658 + 1.156570I
b = −0.78824 − 1.61341I
2.47325 − 5.67148I −3.70840 + 7.21556I
u = 0.26880 − 1.49571I
a = 0.197658 − 1.156570I
b = −0.78824 + 1.61341I
2.47325 + 5.67148I −3.70840 − 7.21556I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16498 + 1.68985I
a = 0.151027 + 0.785264I
b = 0.13998 − 1.73711I
5.73609 − 1.54923I 1.91065 − 4.75162I
u = 0.16498 − 1.68985I
a = 0.151027 − 0.785264I
b = 0.13998 + 1.73711I
5.73609 + 1.54923I 1.91065 + 4.75162I
u = 0.43658 + 1.65754I
a = −0.084607 − 0.845179I
b = 0.375139 + 1.295270I
−0.34144 − 5.76799I −5.64984 + 6.08143I
u = 0.43658 − 1.65754I
a = −0.084607 + 0.845179I
b = 0.375139 − 1.295270I
−0.34144 + 5.76799I −5.64984 − 6.08143I
u = 0.202283
a = 3.21043
b = −0.829879
−0.445338 3.94260
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− u
24
+ ··· − 8u − 4)(u
78
− 2u
77
+ ··· + 5080u − 1808)
c
2
(u
25
+ 3u
24
+ ··· + 21u − 13)(u
78
+ 4u
77
+ ··· − 177548u − 41707)
c
3
(u
25
− 7u
23
+ ··· + 6u + 1)(u
78
− u
77
+ ··· − 7u + 85)
c
4
(u
25
− 5u
24
+ ··· + 3u − 1)(u
78
+ 4u
77
+ ··· + 34268u + 2789)
c
5
(u
25
− 3u
24
+ ··· + 21u + 13)(u
78
+ 4u
77
+ ··· − 177548u − 41707)
c
6
(u
25
+ u
24
+ ··· − 12u + 4)(u
78
− 6u
77
+ ··· − 120616u − 6256)
c
7
(u
25
− u
24
+ ··· + 8u + 8)(u
78
− 2u
77
+ ··· − 35004u − 5048)
c
8
(u
25
+ 5u
24
+ ··· + 3u + 1)(u
78
+ 4u
77
+ ··· + 34268u + 2789)
c
9
(u
25
+ 3u
24
+ ··· + 7u + 7)(u
78
+ 4u
77
+ ··· − 21648u − 1747)
c
10
(u
25
− 7u
23
+ ··· + 6u − 1)(u
78
− u
77
+ ··· − 7u + 85)
c
11
(u
25
− u
24
+ ··· − 7u − 1)(u
78
+ 2u
77
+ ··· + 1038u − 463)
c
12
(u
25
− 3u
24
+ ··· + 7u − 7)(u
78
+ 4u
77
+ ··· − 21648u − 1747)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
+ 19y
24
+ ··· − 64y −16)
· (y
78
+ 86y
77
+ ··· + 33365824y + 3268864)
c
2
, c
5
(y
25
− 21y
24
+ ··· + 2703y −169)
· (y
78
− 54y
77
+ ··· − 15298685406y + 1739473849)
c
3
, c
10
(y
25
− 14y
24
+ ··· + 52y −1)(y
78
− 51y
77
+ ··· − 50879y + 7225)
c
4
, c
8
(y
25
+ 15y
24
+ ··· + 27y −1)
· (y
78
+ 74y
77
+ ··· + 243548106y + 7778521)
c
6
(y
25
+ 13y
24
+ ··· − 48y −16)
· (y
78
+ 36y
77
+ ··· − 7231852480y + 39137536)
c
7
(y
25
− 15y
24
+ ··· − 608y −64)
· (y
78
− 80y
77
+ ··· − 1613410640y + 25482304)
c
9
, c
12
(y
25
+ 17y
24
+ ··· − 525y −49)
· (y
78
+ 44y
77
+ ··· − 160384742y + 3052009)
c
11
(y
25
+ y
24
+ ··· + 23y −1)(y
78
+ 12y
77
+ ··· + 305074y + 214369)
22
