11a
344
(K11a
344
)
A knot diagram
1
Linearized knot diagam
9 7 1 8 11 10 2 4 3 5 6
Solving Sequence
5,10
11 6 7
1,3
2 8 4 9
c
10
c
5
c
6
c
11
c
2
c
7
c
4
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.87710 × 10
61
u
75
+ 3.95359 × 10
60
u
74
+ ··· + 4.66648 × 10
61
b + 9.74216 × 10
61
,
− 1.83090 × 10
62
u
75
+ 2.54599 × 10
61
u
74
+ ··· + 3.26653 × 10
62
a + 2.76516 × 10
62
, u
76
+ u
75
+ ··· − 12u − 7i
I
u
2
= h−u
7
+ 3u
5
− 2u
3
+ u
2
+ b − u − 1, u
11
− u
10
− 5u
9
+ 4u
8
+ 9u
7
− 5u
6
− 5u
5
+ u
4
− 2u
3
− u
2
+ a + u + 4,
u
12
− 6u
10
+ 13u
8
− u
7
− 10u
6
+ 4u
5
− 2u
4
− 5u
3
+ 4u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 88 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
= h−3.88×10
61
u
75
+3.95×10
60
u
74
+· · ·+4.67×10
61
b+9.74×10
61
, −1.83×
10
62
u
75
+2.55×10
61
u
74
+· · ·+3.27×10
62
a+2.77×10
62
, u
76
+u
75
+· · ·−12u−7i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
0.560502u
75
− 0.0779417u
74
+ ··· − 9.59790u − 0.846512
0.830840u
75
− 0.0847233u
74
+ ··· − 1.54729u − 2.08769
a
2
=
−0.329680u
75
− 0.0658791u
74
+ ··· − 7.74953u + 0.366663
1.74221u
75
− 0.275080u
74
+ ··· − 3.59422u − 3.39247
a
8
=
0.535153u
75
− 0.116974u
74
+ ··· − 4.19208u − 8.38576
−0.960929u
75
+ 0.121521u
74
+ ··· + 6.18648u + 6.54630
a
4
=
−0.315830u
75
+ 0.0000729843u
74
+ ··· − 8.58111u + 1.08231
1.95879u
75
− 0.464009u
74
+ ··· − 5.04491u − 5.66772
a
9
=
0.128996u
75
+ 0.0215062u
74
+ ··· − 10.2764u + 4.42926
1.77769u
75
− 0.255216u
74
+ ··· − 8.27842u − 11.8010
a
9
=
0.128996u
75
+ 0.0215062u
74
+ ··· − 10.2764u + 4.42926
1.77769u
75
− 0.255216u
74
+ ··· − 8.27842u − 11.8010
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.332173u
75
+ 1.45404u
74
+ ··· − 12.2591u − 8.45946
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 5u
75
+ ··· + u − 2
c
2
, c
7
u
76
− u
75
+ ··· − 23u − 101
c
3
u
76
− 11u
75
+ ··· + 9u + 11
c
4
, c
8
u
76
− 2u
75
+ ··· + 198u − 29
c
5
, c
10
, c
11
u
76
− u
75
+ ··· + 12u − 7
c
6
u
76
+ 3u
75
+ ··· − 3283u + 4312
c
9
u
76
+ 7u
74
+ ··· − 7948u − 1013
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 3y
75
+ ··· + 63y + 4
c
2
, c
7
y
76
+ 53y
75
+ ··· + 200865y + 10201
c
3
y
76
− 11y
75
+ ··· − 2567y + 121
c
4
, c
8
y
76
+ 46y
75
+ ··· − 29344y + 841
c
5
, c
10
, c
11
y
76
− 67y
75
+ ··· + 500y + 49
c
6
y
76
+ 25y
75
+ ··· − 18824281y + 18593344
c
9
y
76
+ 14y
75
+ ··· + 25053492y + 1026169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968679 + 0.306013I
a = 0.936744 + 0.290091I
b = −0.54901 − 1.35285I
3.49997 − 1.86931I 0
u = −0.968679 − 0.306013I
a = 0.936744 − 0.290091I
b = −0.54901 + 1.35285I
3.49997 + 1.86931I 0
u = −0.402726 + 0.858164I
a = −0.228589 − 0.621929I
b = −0.323000 + 0.715407I
3.74004 + 2.56276I 0. − 11.02950I
u = −0.402726 − 0.858164I
a = −0.228589 + 0.621929I
b = −0.323000 − 0.715407I
3.74004 − 2.56276I 0. + 11.02950I
u = 0.150149 + 0.934780I
a = 0.047146 + 0.930784I
b = −0.424630 − 0.704027I
3.32458 − 0.03587I −1.51662 + 0.I
u = 0.150149 − 0.934780I
a = 0.047146 − 0.930784I
b = −0.424630 + 0.704027I
3.32458 + 0.03587I −1.51662 + 0.I
u = 0.931604 + 0.510293I
a = 0.912239 − 0.333719I
b = −0.686062 + 1.169450I
0.53464 + 7.36666I 0
u = 0.931604 − 0.510293I
a = 0.912239 + 0.333719I
b = −0.686062 − 1.169450I
0.53464 − 7.36666I 0
u = 0.248826 + 0.843265I
a = −0.23673 − 2.05712I
b = 0.89742 + 1.31819I
2.65342 − 12.13500I −5.18296 + 8.02614I
u = 0.248826 − 0.843265I
a = −0.23673 + 2.05712I
b = 0.89742 − 1.31819I
2.65342 + 12.13500I −5.18296 − 8.02614I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.009890 + 0.581338I
a = −0.128172 + 0.337314I
b = −0.026272 − 0.785988I
0.66505 − 5.23954I 0
u = 1.009890 − 0.581338I
a = −0.128172 − 0.337314I
b = −0.026272 + 0.785988I
0.66505 + 5.23954I 0
u = −1.184460 + 0.087532I
a = −1.25675 − 1.30618I
b = 0.195439 + 0.281765I
−3.89513 − 3.10544I 0
u = −1.184460 − 0.087532I
a = −1.25675 + 1.30618I
b = 0.195439 − 0.281765I
−3.89513 + 3.10544I 0
u = −0.201569 + 0.767240I
a = −0.23031 + 2.38711I
b = 0.90138 − 1.50036I
5.85346 + 5.89693I −1.84592 − 6.16015I
u = −0.201569 − 0.767240I
a = −0.23031 − 2.38711I
b = 0.90138 + 1.50036I
5.85346 − 5.89693I −1.84592 + 6.16015I
u = 0.062116 + 0.761993I
a = −0.46367 + 1.82956I
b = −0.435791 − 0.829410I
3.69493 − 3.40892I −2.10008 + 7.62336I
u = 0.062116 − 0.761993I
a = −0.46367 − 1.82956I
b = −0.435791 + 0.829410I
3.69493 + 3.40892I −2.10008 − 7.62336I
u = 1.203070 + 0.312929I
a = −0.066873 + 0.897972I
b = 0.327385 − 0.987472I
0.209490 − 0.491453I 0
u = 1.203070 − 0.312929I
a = −0.066873 − 0.897972I
b = 0.327385 + 0.987472I
0.209490 + 0.491453I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.234810 + 0.206791I
a = −0.721753 + 0.756146I
b = 0.135004 − 0.637912I
−1.62348 − 1.28005I 0
u = 1.234810 − 0.206791I
a = −0.721753 − 0.756146I
b = 0.135004 + 0.637912I
−1.62348 + 1.28005I 0
u = −0.211230 + 0.692166I
a = 0.32479 − 2.42437I
b = −0.579010 + 0.798991I
−1.61113 + 5.99074I −7.07123 − 7.64863I
u = −0.211230 − 0.692166I
a = 0.32479 + 2.42437I
b = −0.579010 − 0.798991I
−1.61113 − 5.99074I −7.07123 + 7.64863I
u = −1.264020 + 0.200993I
a = −0.743336 − 1.099380I
b = −1.81254 + 0.02250I
−3.68056 − 0.68832I 0
u = −1.264020 − 0.200993I
a = −0.743336 + 1.099380I
b = −1.81254 − 0.02250I
−3.68056 + 0.68832I 0
u = −0.637024 + 0.316684I
a = −0.0814032 + 0.0833784I
b = −0.235620 + 0.937335I
3.01317 + 1.73011I −2.31903 − 3.39119I
u = −0.637024 − 0.316684I
a = −0.0814032 − 0.0833784I
b = −0.235620 − 0.937335I
3.01317 − 1.73011I −2.31903 + 3.39119I
u = −1.284140 + 0.219366I
a = 0.183447 − 1.023270I
b = 0.352547 + 1.162330I
0.12887 + 2.52959I 0
u = −1.284140 − 0.219366I
a = 0.183447 + 1.023270I
b = 0.352547 − 1.162330I
0.12887 − 2.52959I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.075482 + 0.672046I
a = 0.64227 + 1.93805I
b = −0.534886 − 0.748714I
1.83137 − 1.88031I −3.15463 + 4.07325I
u = 0.075482 − 0.672046I
a = 0.64227 − 1.93805I
b = −0.534886 + 0.748714I
1.83137 + 1.88031I −3.15463 − 4.07325I
u = 0.369901 + 0.560002I
a = 1.17517 − 0.88223I
b = −0.380653 + 0.890018I
−1.20192 − 1.77591I −8.18323 + 1.57822I
u = 0.369901 − 0.560002I
a = 1.17517 + 0.88223I
b = −0.380653 − 0.890018I
−1.20192 + 1.77591I −8.18323 − 1.57822I
u = 1.310420 + 0.247828I
a = 1.47529 − 0.24769I
b = 0.571098 + 0.537826I
−0.27749 − 3.56587I 0
u = 1.310420 − 0.247828I
a = 1.47529 + 0.24769I
b = 0.571098 − 0.537826I
−0.27749 + 3.56587I 0
u = −1.33405
a = −0.863799
b = −1.01726
−5.87122 0
u = 1.325920 + 0.160373I
a = 0.78766 − 1.54148I
b = 0.93014 + 1.41946I
−5.55889 + 0.47303I 0
u = 1.325920 − 0.160373I
a = 0.78766 + 1.54148I
b = 0.93014 − 1.41946I
−5.55889 − 0.47303I 0
u = −1.308300 + 0.270202I
a = 0.64800 + 1.41204I
b = 0.832561 − 0.888141I
−2.49885 + 5.30835I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.308300 − 0.270202I
a = 0.64800 − 1.41204I
b = 0.832561 + 0.888141I
−2.49885 − 5.30835I 0
u = −1.305040 + 0.319754I
a = 1.38303 + 0.97569I
b = 0.543065 − 0.675937I
−0.57872 + 7.31208I 0
u = −1.305040 − 0.319754I
a = 1.38303 − 0.97569I
b = 0.543065 + 0.675937I
−0.57872 − 7.31208I 0
u = 1.327950 + 0.244567I
a = 0.244688 + 0.775435I
b = −1.90753 + 0.89944I
−4.47754 − 6.67234I 0
u = 1.327950 − 0.244567I
a = 0.244688 − 0.775435I
b = −1.90753 − 0.89944I
−4.47754 + 6.67234I 0
u = −0.564347 + 0.281716I
a = −0.419798 − 0.783383I
b = 0.808778 + 0.477749I
−3.26194 − 2.66752I −12.49560 + 1.19911I
u = −0.564347 − 0.281716I
a = −0.419798 + 0.783383I
b = 0.808778 − 0.477749I
−3.26194 + 2.66752I −12.49560 − 1.19911I
u = 0.368179 + 0.508001I
a = 0.96836 − 1.48644I
b = 0.126296 + 1.052670I
−1.29394 − 1.64438I −9.75127 + 4.13442I
u = 0.368179 − 0.508001I
a = 0.96836 + 1.48644I
b = 0.126296 − 1.052670I
−1.29394 + 1.64438I −9.75127 − 4.13442I
u = −0.075467 + 0.609557I
a = −1.85586 − 0.84943I
b = 1.75807 + 0.52628I
−0.03422 + 3.55485I −4.57668 − 5.47640I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075467 − 0.609557I
a = −1.85586 + 0.84943I
b = 1.75807 − 0.52628I
−0.03422 − 3.55485I −4.57668 + 5.47640I
u = −0.044203 + 0.612297I
a = −1.23990 − 1.62222I
b = −0.389998 + 0.831508I
4.00054 + 0.42281I −1.53362 + 1.17105I
u = −0.044203 − 0.612297I
a = −1.23990 + 1.62222I
b = −0.389998 − 0.831508I
4.00054 − 0.42281I −1.53362 − 1.17105I
u = 1.389280 + 0.027409I
a = 0.100143 − 0.840012I
b = 0.943148 − 0.485048I
−3.13133 + 2.04238I 0
u = 1.389280 − 0.027409I
a = 0.100143 + 0.840012I
b = 0.943148 + 0.485048I
−3.13133 − 2.04238I 0
u = −1.334670 + 0.401679I
a = 0.525115 + 0.884565I
b = 0.751457 − 0.668315I
−1.28728 + 4.79520I 0
u = −1.334670 − 0.401679I
a = 0.525115 − 0.884565I
b = 0.751457 + 0.668315I
−1.28728 − 4.79520I 0
u = 1.379300 + 0.285950I
a = 0.77351 − 1.51750I
b = 0.669261 + 1.000640I
−6.65323 − 9.56425I 0
u = 1.379300 − 0.285950I
a = 0.77351 + 1.51750I
b = 0.669261 − 1.000640I
−6.65323 + 9.56425I 0
u = 1.38264 + 0.31570I
a = −1.22325 + 1.23732I
b = −1.13602 − 1.53413I
0.83133 − 9.81598I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38264 − 0.31570I
a = −1.22325 − 1.23732I
b = −1.13602 + 1.53413I
0.83133 + 9.81598I 0
u = −1.40631 + 0.21816I
a = −1.026610 − 0.485658I
b = −0.272085 + 1.269180I
−6.84634 + 4.36487I 0
u = −1.40631 − 0.21816I
a = −1.026610 + 0.485658I
b = −0.272085 − 1.269180I
−6.84634 − 4.36487I 0
u = 1.42980 + 0.07326I
a = −0.490884 − 0.045086I
b = −1.101020 + 0.554963I
−9.55152 + 1.46003I 0
u = 1.42980 − 0.07326I
a = −0.490884 + 0.045086I
b = −1.101020 − 0.554963I
−9.55152 − 1.46003I 0
u = −1.43258 + 0.21432I
a = −0.770404 + 0.141503I
b = 0.531412 + 1.110610I
−6.96863 + 4.63471I 0
u = −1.43258 − 0.21432I
a = −0.770404 − 0.141503I
b = 0.531412 − 1.110610I
−6.96863 − 4.63471I 0
u = −1.41403 + 0.34833I
a = −1.03057 − 1.23596I
b = −1.07132 + 1.35240I
−2.6277 + 16.4336I 0
u = −1.41403 − 0.34833I
a = −1.03057 + 1.23596I
b = −1.07132 − 1.35240I
−2.6277 − 16.4336I 0
u = 1.45271 + 0.36773I
a = 0.481096 − 0.525580I
b = 0.743722 + 0.594956I
−2.09696 − 7.08063I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45271 − 0.36773I
a = 0.481096 + 0.525580I
b = 0.743722 − 0.594956I
−2.09696 + 7.08063I 0
u = −1.53494 + 0.03855I
a = 0.132344 − 0.251214I
b = 0.750588 − 0.550715I
−8.13102 + 6.65132I 0
u = −1.53494 − 0.03855I
a = 0.132344 + 0.251214I
b = 0.750588 + 0.550715I
−8.13102 − 6.65132I 0
u = 0.375740
a = 0.100271
b = 0.540684
−0.725667 −13.9610
u = −0.099162 + 0.335506I
a = 2.71273 − 3.59350I
b = −0.665037 + 0.775565I
−1.09766 − 2.44518I −6.25239 − 1.93768I
u = −0.099162 − 0.335506I
a = 2.71273 + 3.59350I
b = −0.665037 − 0.775565I
−1.09766 + 2.44518I −6.25239 + 1.93768I
12
II. I
u
2
=
h−u
7
+3u
5
−2u
3
+u
2
+b−u−1, u
11
−u
10
+· · ·+a+4, u
12
−6u
10
+· · ·+2u+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−u
11
+ u
10
+ 5u
9
− 4u
8
− 9u
7
+ 5u
6
+ 5u
5
− u
4
+ 2u
3
+ u
2
− u − 4
u
7
− 3u
5
+ 2u
3
− u
2
+ u + 1
a
2
=
−u
11
+ 5u
9
+ u
8
− 9u
7
− 3u
6
+ 6u
5
+ 2u
4
− u
3
+ 2u
2
+ u − 3
u
7
− 3u
5
− u
4
+ 2u
3
+ u
2
+ u + 1
a
8
=
−u
11
+ u
10
+ 6u
9
− 5u
8
− 13u
7
+ 10u
6
+ 9u
5
− 9u
4
+ 5u
3
+ 3u
2
− 7u
u
11
+ u
10
− 5u
9
− 4u
8
+ 8u
7
+ 3u
6
− 4u
5
+ 5u
4
− 5u
2
− 1
a
4
=
−u
11
+ 5u
9
+ u
8
− 9u
7
− 3u
6
+ 6u
5
+ 2u
4
− u
3
+ 3u
2
+ u − 4
u
10
− 4u
8
+ u
7
+ 5u
6
− 4u
5
− u
4
+ 4u
3
− 2u
2
+ u + 1
a
9
=
u
10
− 2u
9
− 5u
8
+ 9u
7
+ 8u
6
− 14u
5
+ 6u
3
− 9u
2
+ 3u + 4
u
9
− 4u
7
+ 5u
5
− u
4
+ 2u
2
− 2u − 1
a
9
=
u
10
− 2u
9
− 5u
8
+ 9u
7
+ 8u
6
− 14u
5
+ 6u
3
− 9u
2
+ 3u + 4
u
9
− 4u
7
+ 5u
5
− u
4
+ 2u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
11
+ 12u
9
− u
8
− 36u
7
+ 6u
6
+ 37u
5
− 16u
4
+ 2u
3
+ 16u
2
− 15u − 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 2u
9
+ 2u
8
− u
7
− u
5
+ u
4
+ u
3
− u
2
− u + 1
c
2
u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1
c
3
u
12
− 2u
10
− u
9
+ 2u
8
+ 2u
7
+ 3u
6
+ 4u
5
+ 2u
4
+ u
3
+ 3u
2
+ 3u + 1
c
4
u
12
− u
11
+ 5u
10
− 3u
9
+ 12u
8
− 6u
7
+ 17u
6
− 4u
5
+ 14u
4
− u
3
+ 6u
2
+ 1
c
5
u
12
− 6u
10
+ 13u
8
+ u
7
− 10u
6
− 4u
5
− 2u
4
+ 5u
3
+ 4u
2
− 2u + 1
c
6
u
12
+ 2u
10
− 3u
9
+ 4u
8
+ 4u
7
+ 12u
6
+ 7u
5
+ 3u
4
+ 4u
3
+ 4u
2
− 2u + 1
c
7
u
12
+ 6u
10
− u
9
+ 14u
8
− 4u
7
+ 17u
6
− 6u
5
+ 12u
4
− 3u
3
+ 5u
2
− u + 1
c
8
u
12
+ u
11
+ 5u
10
+ 3u
9
+ 12u
8
+ 6u
7
+ 17u
6
+ 4u
5
+ 14u
4
+ u
3
+ 6u
2
+ 1
c
9
u
12
+ u
11
− u
10
− u
9
+ u
8
+ u
7
+ u
5
+ 2u
4
− 2u
3
+ 1
c
10
, c
11
u
12
− 6u
10
+ 13u
8
− u
7
− 10u
6
+ 4u
5
− 2u
4
− 5u
3
+ 4u
2
+ 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 4y
10
− 4y
9
+ 10y
8
+ y
7
+ y
5
+ 5y
4
− 5y
3
+ 5y
2
− 3y + 1
c
2
, c
7
y
12
+ 12y
11
+ ··· + 9y + 1
c
3
y
12
− 4y
11
+ 8y
10
− 3y
9
+ 14y
7
− 7y
6
+ 6y
5
+ 6y
4
− 7y
3
+ 7y
2
− 3y + 1
c
4
, c
8
y
12
+ 9y
11
+ ··· + 12y + 1
c
5
, c
10
, c
11
y
12
− 12y
11
+ ··· + 4y + 1
c
6
y
12
+ 4y
11
+ ··· + 4y + 1
c
9
y
12
− 3y
11
+ 5y
10
− 5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
− 4y
3
+ 4y
2
+ 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215104 + 0.798845I
a = −0.413477 + 0.669068I
b = −0.377143 − 0.565754I
3.50536 − 1.91915I −4.46198 + 0.73730I
u = 0.215104 − 0.798845I
a = −0.413477 − 0.669068I
b = −0.377143 + 0.565754I
3.50536 + 1.91915I −4.46198 − 0.73730I
u = 1.181970 + 0.217891I
a = 0.539675 + 0.842839I
b = 0.241684 − 0.971815I
0.83736 − 1.52744I −4.49507 + 0.61060I
u = 1.181970 − 0.217891I
a = 0.539675 − 0.842839I
b = 0.241684 + 0.971815I
0.83736 + 1.52744I −4.49507 − 0.61060I
u = −1.286840 + 0.093791I
a = −0.86850 − 1.39935I
b = −1.299930 + 0.350855I
−4.83854 − 1.75409I −13.7193 + 4.0775I
u = −1.286840 − 0.093791I
a = −0.86850 + 1.39935I
b = −1.299930 − 0.350855I
−4.83854 + 1.75409I −13.7193 − 4.0775I
u = −1.334400 + 0.365970I
a = 0.637376 + 0.770937I
b = 0.740658 − 0.383732I
−1.29267 + 6.23322I −8.20976 − 5.43660I
u = −1.334400 − 0.365970I
a = 0.637376 − 0.770937I
b = 0.740658 + 0.383732I
−1.29267 − 6.23322I −8.20976 + 5.43660I
u = 1.43060 + 0.17503I
a = 0.821437 + 0.356941I
b = −0.793895 + 0.868621I
−6.80152 − 5.19940I −9.91514 + 9.30773I
u = 1.43060 − 0.17503I
a = 0.821437 − 0.356941I
b = −0.793895 − 0.868621I
−6.80152 + 5.19940I −9.91514 − 9.30773I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.206431 + 0.331897I
a = −3.71651 − 0.52155I
b = 0.988629 + 0.507298I
−1.27959 + 3.15177I −9.69878 − 7.80238I
u = −0.206431 − 0.331897I
a = −3.71651 + 0.52155I
b = 0.988629 − 0.507298I
−1.27959 − 3.15177I −9.69878 + 7.80238I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 2u
9
+ 2u
8
− u
7
− u
5
+ u
4
+ u
3
− u
2
− u + 1)
· (u
76
+ 5u
75
+ ··· + u − 2)
c
2
(u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1)
· (u
76
− u
75
+ ··· − 23u − 101)
c
3
(u
12
− 2u
10
− u
9
+ 2u
8
+ 2u
7
+ 3u
6
+ 4u
5
+ 2u
4
+ u
3
+ 3u
2
+ 3u + 1)
· (u
76
− 11u
75
+ ··· + 9u + 11)
c
4
(u
12
− u
11
+ 5u
10
− 3u
9
+ 12u
8
− 6u
7
+ 17u
6
− 4u
5
+ 14u
4
− u
3
+ 6u
2
+ 1)
· (u
76
− 2u
75
+ ··· + 198u − 29)
c
5
(u
12
− 6u
10
+ 13u
8
+ u
7
− 10u
6
− 4u
5
− 2u
4
+ 5u
3
+ 4u
2
− 2u + 1)
· (u
76
− u
75
+ ··· + 12u − 7)
c
6
(u
12
+ 2u
10
− 3u
9
+ 4u
8
+ 4u
7
+ 12u
6
+ 7u
5
+ 3u
4
+ 4u
3
+ 4u
2
− 2u + 1)
· (u
76
+ 3u
75
+ ··· − 3283u + 4312)
c
7
(u
12
+ 6u
10
− u
9
+ 14u
8
− 4u
7
+ 17u
6
− 6u
5
+ 12u
4
− 3u
3
+ 5u
2
− u + 1)
· (u
76
− u
75
+ ··· − 23u − 101)
c
8
(u
12
+ u
11
+ 5u
10
+ 3u
9
+ 12u
8
+ 6u
7
+ 17u
6
+ 4u
5
+ 14u
4
+ u
3
+ 6u
2
+ 1)
· (u
76
− 2u
75
+ ··· + 198u − 29)
c
9
(u
12
+ u
11
− u
10
− u
9
+ u
8
+ u
7
+ u
5
+ 2u
4
− 2u
3
+ 1)
· (u
76
+ 7u
74
+ ··· − 7948u − 1013)
c
10
, c
11
(u
12
− 6u
10
+ 13u
8
− u
7
− 10u
6
+ 4u
5
− 2u
4
− 5u
3
+ 4u
2
+ 2u + 1)
· (u
76
− u
75
+ ··· + 12u − 7)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
12
+ 4y
10
− 4y
9
+ 10y
8
+ y
7
+ y
5
+ 5y
4
− 5y
3
+ 5y
2
− 3y + 1)
· (y
76
− 3y
75
+ ··· + 63y + 4)
c
2
, c
7
(y
12
+ 12y
11
+ ··· + 9y + 1)(y
76
+ 53y
75
+ ··· + 200865y + 10201)
c
3
(y
12
− 4y
11
+ 8y
10
− 3y
9
+ 14y
7
− 7y
6
+ 6y
5
+ 6y
4
− 7y
3
+ 7y
2
− 3y + 1)
· (y
76
− 11y
75
+ ··· − 2567y + 121)
c
4
, c
8
(y
12
+ 9y
11
+ ··· + 12y + 1)(y
76
+ 46y
75
+ ··· − 29344y + 841)
c
5
, c
10
, c
11
(y
12
− 12y
11
+ ··· + 4y + 1)(y
76
− 67y
75
+ ··· + 500y + 49)
c
6
(y
12
+ 4y
11
+ ··· + 4y + 1)
· (y
76
+ 25y
75
+ ··· − 18824281y + 18593344)
c
9
(y
12
− 3y
11
+ 5y
10
− 5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
− 4y
3
+ 4y
2
+ 1)
· (y
76
+ 14y
75
+ ··· + 25053492y + 1026169)
19
