12a
1068
(K12a
1068
)
A knot diagram
1
Linearized knot diagam
4 7 9 1 11 10 3 12 2 6 8 5
Solving Sequence
5,12
1 4
2,9
3 8 7 11 6 10
c
12
c
4
c
1
c
3
c
8
c
7
c
11
c
5
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.50029 × 10
216
u
98
+ 5.86036 × 10
216
u
97
+ ··· + 5.58008 × 10
215
b + 1.44724 × 10
217
,
2.25470 × 10
216
u
98
+ 9.19598 × 10
216
u
97
+ ··· + 5.58008 × 10
215
a + 5.61430 × 10
217
, u
99
+ 4u
98
+ ··· + 36u + 1i
I
u
2
= h4u
26
− 18u
25
+ ··· + b − 3, −4u
26
+ 16u
25
+ ··· + a + 4, u
27
− 3u
26
+ ··· − 4u + 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
= h1.50 × 10
216
u
98
+ 5.86 × 10
216
u
97
+ · · · + 5.58 × 10
215
b + 1.45 ×
10
217
, 2.25 × 10
216
u
98
+ 9.20 × 10
216
u
97
+ · · · + 5.58 × 10
215
a + 5.61 ×
10
217
, u
99
+ 4u
98
+ · · · + 36u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−4.04062u
98
− 16.4800u
97
+ ··· − 2163.01u − 100.613
−2.68866u
98
− 10.5023u
97
+ ··· − 730.857u − 25.9358
a
3
=
29.0429u
98
+ 111.972u
97
+ ··· + 6025.60u + 197.226
−3.10791u
98
− 12.2548u
97
+ ··· − 840.423u − 33.7257
a
8
=
−6.72927u
98
− 26.9823u
97
+ ··· − 2893.86u − 126.549
−2.68866u
98
− 10.5023u
97
+ ··· − 730.857u − 25.9358
a
7
=
−33.9952u
98
− 132.268u
97
+ ··· − 7939.55u − 282.211
1.29259u
98
+ 4.98101u
97
+ ··· + 349.365u + 15.2746
a
11
=
41.3416u
98
+ 161.620u
97
+ ··· + 11365.0u + 448.455
3.78798u
98
+ 14.6203u
97
+ ··· + 1051.78u + 38.9844
a
6
=
17.7191u
98
+ 68.5869u
97
+ ··· + 3201.82u + 77.1568
−4.02761u
98
− 15.3718u
97
+ ··· − 1226.90u − 53.2891
a
10
=
−7.06679u
98
− 28.2694u
97
+ ··· − 2947.05u − 127.980
−2.76743u
98
− 10.7591u
97
+ ··· − 748.335u − 26.6011
(ii) Obstruction class = −1
(iii) Cusp Shapes = 23.2492u
98
+ 90.4225u
97
+ ··· + 5217.51u + 181.119
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
99
− 4u
98
+ ··· + 36u − 1
c
2
, c
7
u
99
+ u
98
+ ··· − 2230u − 532
c
3
u
99
− u
98
+ ··· − 127450u + 3749
c
5
, c
6
, c
10
u
99
+ u
98
+ ··· + 472u − 103
c
8
, c
11
u
99
− 24u
97
+ ··· − 37u + 1
c
9
u
99
+ 3u
98
+ ··· − 3184124u + 9109661
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
99
+ 104y
98
+ ··· + 292y −1
c
2
, c
7
y
99
− 73y
98
+ ··· + 11428188y −283024
c
3
y
99
− 27y
98
+ ··· + 15140464222y −14055001
c
5
, c
6
, c
10
y
99
+ 109y
98
+ ··· − 84774y −10609
c
8
, c
11
y
99
− 48y
98
+ ··· + 671y −1
c
9
y
99
− 57y
98
+ ··· + 2009455767939712y −82985923534921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380785 + 0.967960I
a = −1.078150 + 0.090070I
b = 0.999599 − 0.621542I
7.29844 − 0.30926I 0
u = 0.380785 − 0.967960I
a = −1.078150 − 0.090070I
b = 0.999599 + 0.621542I
7.29844 + 0.30926I 0
u = −0.916031 + 0.535204I
a = −0.575578 − 0.742046I
b = −1.138750 + 0.708186I
8.2842 + 12.1910I 0
u = −0.916031 − 0.535204I
a = −0.575578 + 0.742046I
b = −1.138750 − 0.708186I
8.2842 − 12.1910I 0
u = 0.081133 + 0.917673I
a = −0.891072 + 0.177720I
b = 0.291147 + 0.429752I
4.97123 − 1.60465I 0
u = 0.081133 − 0.917673I
a = −0.891072 − 0.177720I
b = 0.291147 − 0.429752I
4.97123 + 1.60465I 0
u = −0.861368 + 0.321070I
a = −1.299810 − 0.217264I
b = −0.810628 + 0.586401I
9.09344 − 1.46018I 0
u = −0.861368 − 0.321070I
a = −1.299810 + 0.217264I
b = −0.810628 − 0.586401I
9.09344 + 1.46018I 0
u = 0.190324 + 1.068550I
a = −0.237611 + 0.115075I
b = −1.257530 − 0.134290I
0.28001 − 2.62311I 0
u = 0.190324 − 1.068550I
a = −0.237611 − 0.115075I
b = −1.257530 + 0.134290I
0.28001 + 2.62311I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808953 + 0.423145I
a = 0.554722 − 0.715807I
b = 0.989338 + 0.318623I
−2.61211 − 3.25013I 0
u = 0.808953 − 0.423145I
a = 0.554722 + 0.715807I
b = 0.989338 − 0.318623I
−2.61211 + 3.25013I 0
u = 0.634538 + 0.901713I
a = 0.140566 − 0.301929I
b = 0.868536 − 0.046181I
−1.32841 − 1.88863I 0
u = 0.634538 − 0.901713I
a = 0.140566 + 0.301929I
b = 0.868536 + 0.046181I
−1.32841 + 1.88863I 0
u = 0.994467 + 0.486650I
a = −0.691397 + 0.442067I
b = −1.033900 − 0.585558I
3.54877 − 5.37076I 0
u = 0.994467 − 0.486650I
a = −0.691397 − 0.442067I
b = −1.033900 + 0.585558I
3.54877 + 5.37076I 0
u = −0.715566 + 0.532179I
a = 0.457943 + 1.155560I
b = 1.145500 − 0.504808I
0.80367 + 8.22347I 0
u = −0.715566 − 0.532179I
a = 0.457943 − 1.155560I
b = 1.145500 + 0.504808I
0.80367 − 8.22347I 0
u = −0.574131 + 0.616338I
a = −0.268689 + 0.221406I
b = −0.447700 − 0.999113I
10.34210 + 6.07405I 0
u = −0.574131 − 0.616338I
a = −0.268689 − 0.221406I
b = −0.447700 + 0.999113I
10.34210 − 6.07405I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.907557 + 0.730013I
a = 0.124855 − 0.182401I
b = −0.906542 − 0.595760I
8.77349 − 6.14037I 0
u = −0.907557 − 0.730013I
a = 0.124855 + 0.182401I
b = −0.906542 + 0.595760I
8.77349 + 6.14037I 0
u = −0.622216 + 0.510793I
a = −0.042605 + 0.326293I
b = 1.068350 + 0.348839I
0.80525 − 3.61642I 0
u = −0.622216 − 0.510793I
a = −0.042605 − 0.326293I
b = 1.068350 − 0.348839I
0.80525 + 3.61642I 0
u = 0.770064 + 0.954381I
a = −0.082133 + 0.202671I
b = −0.628584 + 0.505927I
4.90385 − 0.82779I 0
u = 0.770064 − 0.954381I
a = −0.082133 − 0.202671I
b = −0.628584 − 0.505927I
4.90385 + 0.82779I 0
u = −0.123577 + 1.234730I
a = −1.06774 − 1.68429I
b = 0.0518778 − 0.0095839I
10.91520 + 4.80273I 0
u = −0.123577 − 1.234730I
a = −1.06774 + 1.68429I
b = 0.0518778 + 0.0095839I
10.91520 − 4.80273I 0
u = −0.003388 + 1.272120I
a = 0.915951 − 0.583969I
b = −1.52579 + 0.30597I
1.48489 + 1.58514I 0
u = −0.003388 − 1.272120I
a = 0.915951 + 0.583969I
b = −1.52579 − 0.30597I
1.48489 − 1.58514I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.240720 + 1.252590I
a = −1.038950 + 0.271205I
b = 1.124750 + 0.115853I
6.14932 − 1.00815I 0
u = −0.240720 − 1.252590I
a = −1.038950 − 0.271205I
b = 1.124750 − 0.115853I
6.14932 + 1.00815I 0
u = 0.709928 + 0.123175I
a = 0.663884 − 0.511483I
b = 1.052080 + 0.916210I
4.65542 − 3.59845I 0
u = 0.709928 − 0.123175I
a = 0.663884 + 0.511483I
b = 1.052080 − 0.916210I
4.65542 + 3.59845I 0
u = −0.372442 + 0.611930I
a = 0.58103 − 1.74962I
b = −1.095300 + 0.309250I
0.26345 + 2.62023I 0
u = −0.372442 − 0.611930I
a = 0.58103 + 1.74962I
b = −1.095300 − 0.309250I
0.26345 − 2.62023I 0
u = 0.584980 + 0.353698I
a = −0.030160 + 1.413860I
b = −0.894830 − 0.022267I
−1.45461 − 0.14764I 0
u = 0.584980 − 0.353698I
a = −0.030160 − 1.413860I
b = −0.894830 + 0.022267I
−1.45461 + 0.14764I 0
u = 0.236471 + 1.318320I
a = −0.05193 − 2.23086I
b = 0.93339 + 1.19290I
9.12685 − 6.97856I 0
u = 0.236471 − 1.318320I
a = −0.05193 + 2.23086I
b = 0.93339 − 1.19290I
9.12685 + 6.97856I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484489 + 0.446016I
a = −0.222432 − 0.700483I
b = 0.180754 + 0.863249I
3.72537 + 3.36221I 0
u = −0.484489 − 0.446016I
a = −0.222432 + 0.700483I
b = 0.180754 − 0.863249I
3.72537 − 3.36221I 0
u = −0.071334 + 1.372250I
a = 0.48461 − 1.50093I
b = −1.028430 + 0.639743I
2.79128 + 1.44895I 0
u = −0.071334 − 1.372250I
a = 0.48461 + 1.50093I
b = −1.028430 − 0.639743I
2.79128 − 1.44895I 0
u = −0.145077 + 1.385060I
a = −0.27987 + 1.86042I
b = 1.18889 − 0.99715I
7.12843 + 5.25158I 0
u = −0.145077 − 1.385060I
a = −0.27987 − 1.86042I
b = 1.18889 + 0.99715I
7.12843 − 5.25158I 0
u = 0.086189 + 1.400630I
a = −0.351019 + 1.124700I
b = 0.475218 − 0.574761I
5.31989 − 2.36934I 0
u = 0.086189 − 1.400630I
a = −0.351019 − 1.124700I
b = 0.475218 + 0.574761I
5.31989 + 2.36934I 0
u = 0.152955 + 1.396230I
a = 0.54193 + 1.75034I
b = −0.931903 − 0.988146I
4.04235 − 4.91926I 0
u = 0.152955 − 1.396230I
a = 0.54193 − 1.75034I
b = −0.931903 + 0.988146I
4.04235 + 4.91926I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547574 + 0.214398I
a = 1.56284 + 0.57855I
b = 0.239576 − 0.404718I
3.17897 − 0.15464I 2.53527 − 1.97824I
u = −0.547574 − 0.214398I
a = 1.56284 − 0.57855I
b = 0.239576 + 0.404718I
3.17897 + 0.15464I 2.53527 + 1.97824I
u = −0.02049 + 1.42222I
a = −0.701489 + 0.531251I
b = 1.79195 − 0.31139I
6.70624 + 2.98104I 0
u = −0.02049 − 1.42222I
a = −0.701489 − 0.531251I
b = 1.79195 + 0.31139I
6.70624 − 2.98104I 0
u = −0.27716 + 1.40128I
a = 0.45484 + 1.34405I
b = 0.712181 − 0.569531I
8.25008 + 3.15430I 0
u = −0.27716 − 1.40128I
a = 0.45484 − 1.34405I
b = 0.712181 + 0.569531I
8.25008 − 3.15430I 0
u = −0.01731 + 1.43658I
a = 0.16463 + 1.87472I
b = −0.790510 − 0.509312I
8.08050 + 0.40274I 0
u = −0.01731 − 1.43658I
a = 0.16463 − 1.87472I
b = −0.790510 + 0.509312I
8.08050 − 0.40274I 0
u = −0.00477 + 1.46661I
a = −0.862324 − 1.050040I
b = 0.947756 + 0.787724I
7.01175 − 2.09262I 0
u = −0.00477 − 1.46661I
a = −0.862324 + 1.050040I
b = 0.947756 − 0.787724I
7.01175 + 2.09262I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15332 + 1.46090I
a = −0.55488 − 1.56502I
b = 0.389356 + 1.027810I
9.89339 + 5.67837I 0
u = −0.15332 − 1.46090I
a = −0.55488 + 1.56502I
b = 0.389356 − 1.027810I
9.89339 − 5.67837I 0
u = 0.450858 + 0.256702I
a = −0.177543 + 0.990337I
b = −1.071810 − 0.572179I
−1.22302 − 2.67007I −7.39915 + 10.94039I
u = 0.450858 − 0.256702I
a = −0.177543 − 0.990337I
b = −1.071810 + 0.572179I
−1.22302 + 2.67007I −7.39915 − 10.94039I
u = 0.22256 + 1.46568I
a = 0.390336 + 1.238280I
b = −0.623858 − 0.415482I
4.50771 − 3.11816I 0
u = 0.22256 − 1.46568I
a = 0.390336 − 1.238280I
b = −0.623858 + 0.415482I
4.50771 + 3.11816I 0
u = 0.06659 + 1.48445I
a = 0.271142 − 1.371170I
b = 1.164310 + 0.524284I
14.4517 − 5.4304I 0
u = 0.06659 − 1.48445I
a = 0.271142 + 1.371170I
b = 1.164310 − 0.524284I
14.4517 + 5.4304I 0
u = −0.488613
a = −0.894239
b = −1.17090
−1.64387 −8.18420
u = 0.27861 + 1.49474I
a = −0.22098 − 1.40771I
b = 1.061660 + 0.599311I
3.61668 − 7.15621I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27861 − 1.49474I
a = −0.22098 + 1.40771I
b = 1.061660 − 0.599311I
3.61668 + 7.15621I 0
u = −0.446853 + 0.111335I
a = 1.50560 − 0.11020I
b = 1.052330 − 0.677785I
2.28317 + 3.15343I 4.58442 + 1.03106I
u = −0.446853 − 0.111335I
a = 1.50560 + 0.11020I
b = 1.052330 + 0.677785I
2.28317 − 3.15343I 4.58442 − 1.03106I
u = −0.19941 + 1.53402I
a = 0.61915 + 1.37411I
b = −0.60331 − 1.38982I
17.3600 + 8.9631I 0
u = −0.19941 − 1.53402I
a = 0.61915 − 1.37411I
b = −0.60331 + 1.38982I
17.3600 − 8.9631I 0
u = −0.36021 + 1.51331I
a = −0.258402 − 1.132070I
b = −1.158180 + 0.594833I
15.0187 + 3.1095I 0
u = −0.36021 − 1.51331I
a = −0.258402 + 1.132070I
b = −1.158180 − 0.594833I
15.0187 − 3.1095I 0
u = −0.24901 + 1.53942I
a = −0.40345 + 1.63875I
b = 1.158500 − 0.694088I
7.60750 + 11.78010I 0
u = −0.24901 − 1.53942I
a = −0.40345 − 1.63875I
b = 1.158500 + 0.694088I
7.60750 − 11.78010I 0
u = −0.14537 + 1.56497I
a = 0.82793 − 1.44795I
b = −0.931355 + 0.541931I
7.58537 + 4.66034I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14537 − 1.56497I
a = 0.82793 + 1.44795I
b = −0.931355 − 0.541931I
7.58537 − 4.66034I 0
u = 0.303921 + 0.301418I
a = 0.484939 + 0.687513I
b = −0.050441 − 0.295647I
−0.151501 − 0.860358I −3.67340 + 7.82157I
u = 0.303921 − 0.301418I
a = 0.484939 − 0.687513I
b = −0.050441 + 0.295647I
−0.151501 + 0.860358I −3.67340 − 7.82157I
u = 0.14950 + 1.57868I
a = 0.218886 − 1.212920I
b = −0.266157 + 1.215160I
13.34460 − 3.44425I 0
u = 0.14950 − 1.57868I
a = 0.218886 + 1.212920I
b = −0.266157 − 1.215160I
13.34460 + 3.44425I 0
u = −0.32728 + 1.55643I
a = 0.17280 − 1.59481I
b = −1.27617 + 0.85627I
15.0673 + 16.7358I 0
u = −0.32728 − 1.55643I
a = 0.17280 + 1.59481I
b = −1.27617 − 0.85627I
15.0673 − 16.7358I 0
u = 0.34061 + 1.56064I
a = 0.104948 + 1.330500I
b = −1.28754 − 0.72555I
10.2362 − 10.1957I 0
u = 0.34061 − 1.56064I
a = 0.104948 − 1.330500I
b = −1.28754 + 0.72555I
10.2362 + 10.1957I 0
u = −0.391447
a = −1.50474
b = −1.03773
−1.66971 −6.70640
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132488 + 0.329921I
a = 4.62802 − 2.84343I
b = 0.770323 + 0.470588I
8.28620 − 4.57392I 2.18985 + 8.66184I
u = 0.132488 − 0.329921I
a = 4.62802 + 2.84343I
b = 0.770323 − 0.470588I
8.28620 + 4.57392I 2.18985 − 8.66184I
u = −0.00439 + 1.69977I
a = −0.715193 + 0.460101I
b = 0.467243 − 0.410517I
16.8314 − 1.2465I 0
u = −0.00439 − 1.69977I
a = −0.715193 − 0.460101I
b = 0.467243 + 0.410517I
16.8314 + 1.2465I 0
u = −0.19462 + 1.71124I
a = 0.288108 + 0.497754I
b = −0.442079 − 0.604819I
17.2396 − 1.7990I 0
u = −0.19462 − 1.71124I
a = 0.288108 − 0.497754I
b = −0.442079 + 0.604819I
17.2396 + 1.7990I 0
u = −0.125192
a = 13.2053
b = −0.469237
2.89635 10.3080
u = −0.0876198 + 0.0177221I
a = 4.04055 − 8.18611I
b = 1.41561 − 0.34626I
1.67204 + 2.65205I −6.65996 + 0.50003I
u = −0.0876198 − 0.0177221I
a = 4.04055 + 8.18611I
b = 1.41561 + 0.34626I
1.67204 − 2.65205I −6.65996 − 0.50003I
14
II. I
u
2
=
h4u
26
−18u
25
+· · ·+b−3, −4u
26
+16u
25
+· · ·+a+4, u
27
−3u
26
+· · ·−4u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
4u
26
− 16u
25
+ ··· + 24u − 4
−4u
26
+ 18u
25
+ ··· − 20u + 3
a
3
=
−3u
26
+ 9u
25
+ ··· − 10u + 4
u
24
− 3u
23
+ ··· + 7u − 2
a
8
=
2u
25
− 6u
24
+ ··· + 4u − 1
−4u
26
+ 18u
25
+ ··· − 20u + 3
a
7
=
u
4
− u
3
+ 3u
2
− 2u + 2
3u
26
− u
25
+ ··· − 9u + 2
a
11
=
u
26
+ 2u
25
+ ··· − 3u + 2
2u
26
− 6u
25
+ ··· − 9u
2
− 1
a
6
=
−u
26
+ 3u
25
+ ··· − 5u
2
+ 2u
10u
26
− 20u
25
+ ··· − 8u + 3
a
10
=
−u
25
+ 3u
24
+ ··· + 8u − 1
−6u
26
+ 30u
25
+ ··· − 39u + 8
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −7u
26
− 6u
25
− 57u
24
− 163u
23
+ 27u
22
− 1594u
21
+ 2054u
20
− 8129u
19
+ 10974u
18
−
24708u
17
+ 29721u
16
− 47186u
15
+ 47876u
14
− 57143u
13
+ 47152u
12
− 42833u
11
+
27674u
10
−18847u
9
+9241u
8
−4614u
7
+1745u
6
−573u
5
+22u
4
+118u
3
−150u
2
+57u−22
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
27
− 3u
26
+ ··· − 4u + 1
c
2
u
27
− 9u
25
+ ··· − 7u
2
+ 1
c
3
u
27
− 2u
24
+ ··· + 11u
2
+ 1
c
4
u
27
+ 3u
26
+ ··· − 4u − 1
c
5
, c
6
u
27
+ 16u
25
+ ··· − 6u + 1
c
7
u
27
− 9u
25
+ ··· + 7u
2
− 1
c
8
u
27
+ 5u
26
+ ··· − 5u − 1
c
9
u
27
− 5u
25
+ ··· − 6u + 1
c
10
u
27
+ 16u
25
+ ··· − 6u − 1
c
11
u
27
− 5u
26
+ ··· − 5u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
27
+ 31y
26
+ ··· − 8y −1
c
2
, c
7
y
27
− 18y
26
+ ··· + 14y −1
c
3
y
27
− 14y
25
+ ··· − 22y −1
c
5
, c
6
, c
10
y
27
+ 32y
26
+ ··· − 6y −1
c
8
, c
11
y
27
− 21y
26
+ ··· + 27y −1
c
9
y
27
− 10y
26
+ ··· − 32y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529825 + 0.809918I
a = −0.055011 + 0.489943I
b = −0.957191 − 0.078245I
−1.56306 − 2.18322I −8.36006 + 8.63349I
u = 0.529825 − 0.809918I
a = −0.055011 − 0.489943I
b = −0.957191 + 0.078245I
−1.56306 + 2.18322I −8.36006 − 8.63349I
u = 0.267042 + 0.760078I
a = 0.751964 − 0.351572I
b = 1.266910 + 0.279218I
2.31208 − 3.21416I 1.95146 + 4.84868I
u = 0.267042 − 0.760078I
a = 0.751964 + 0.351572I
b = 1.266910 − 0.279218I
2.31208 + 3.21416I 1.95146 − 4.84868I
u = 0.567361 + 1.110970I
a = −0.431431 − 0.330212I
b = 0.774453 − 0.350896I
4.00066 − 0.48119I −3.66135 − 1.00155I
u = 0.567361 − 1.110970I
a = −0.431431 + 0.330212I
b = 0.774453 + 0.350896I
4.00066 + 0.48119I −3.66135 + 1.00155I
u = 0.059850 + 1.252320I
a = −1.65356 + 0.39903I
b = 1.67176 − 0.45128I
4.67985 + 2.02941I −2.20493 − 2.90597I
u = 0.059850 − 1.252320I
a = −1.65356 − 0.39903I
b = 1.67176 + 0.45128I
4.67985 − 2.02941I −2.20493 + 2.90597I
u = −0.174494 + 1.271190I
a = 0.90134 + 2.08409I
b = 0.721752 − 0.620445I
11.02560 + 5.82117I 4.75059 − 7.23956I
u = −0.174494 − 1.271190I
a = 0.90134 − 2.08409I
b = 0.721752 + 0.620445I
11.02560 − 5.82117I 4.75059 + 7.23956I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030883 + 1.290990I
a = 0.478980 − 0.478805I
b = −1.45287 + 0.32069I
2.18015 + 1.34894I 4.75960 + 0.I
u = 0.030883 − 1.290990I
a = 0.478980 + 0.478805I
b = −1.45287 − 0.32069I
2.18015 − 1.34894I 4.75960 + 0.I
u = −0.391975 + 0.461539I
a = 0.09757 + 2.50345I
b = 0.588105 + 0.363259I
8.14039 − 3.78112I −0.034946 − 0.532297I
u = −0.391975 − 0.461539I
a = 0.09757 − 2.50345I
b = 0.588105 − 0.363259I
8.14039 + 3.78112I −0.034946 + 0.532297I
u = 0.192166 + 1.399840I
a = −0.28477 − 1.97334I
b = 1.11005 + 1.12524I
7.14619 − 6.16599I 1.37328 + 7.84994I
u = 0.192166 − 1.399840I
a = −0.28477 + 1.97334I
b = 1.11005 − 1.12524I
7.14619 + 6.16599I 1.37328 − 7.84994I
u = 0.530911 + 0.240216I
a = 0.905097 − 0.380887I
b = 1.159280 + 0.725401I
1.91060 − 3.56104I −5.75759 + 9.42146I
u = 0.530911 − 0.240216I
a = 0.905097 + 0.380887I
b = 1.159280 − 0.725401I
1.91060 + 3.56104I −5.75759 − 9.42146I
u = −0.20013 + 1.42433I
a = −0.07006 − 1.51288I
b = −0.607531 + 0.291383I
7.48897 + 2.36651I − 60.10 − 0.822434I
u = −0.20013 − 1.42433I
a = −0.07006 + 1.51288I
b = −0.607531 − 0.291383I
7.48897 − 2.36651I − 60.10 + 0.822434I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17269 + 1.48110I
a = 0.57866 + 1.32623I
b = −0.752363 − 0.679230I
5.10932 − 3.84763I 3.16616 + 5.03771I
u = 0.17269 − 1.48110I
a = 0.57866 − 1.32623I
b = −0.752363 + 0.679230I
5.10932 + 3.84763I 3.16616 − 5.03771I
u = −0.433229
a = −3.79438
b = −0.627919
2.54905 −14.0320
u = 0.215989 + 0.342402I
a = 1.17353 + 1.40885I
b = −1.110620 − 0.350103I
−1.11587 − 1.97397I −6.20655 + 0.29675I
u = 0.215989 − 0.342402I
a = 1.17353 − 1.40885I
b = −1.110620 + 0.350103I
−1.11587 + 1.97397I −6.20655 − 0.29675I
u = −0.08350 + 1.73493I
a = −0.495123 + 0.240156I
b = 0.402235 + 0.073150I
16.4978 − 1.6817I 0
u = −0.08350 − 1.73493I
a = −0.495123 − 0.240156I
b = 0.402235 − 0.073150I
16.4978 + 1.6817I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
27
− 3u
26
+ ··· − 4u + 1)(u
99
− 4u
98
+ ··· + 36u − 1)
c
2
(u
27
− 9u
25
+ ··· − 7u
2
+ 1)(u
99
+ u
98
+ ··· − 2230u − 532)
c
3
(u
27
− 2u
24
+ ··· + 11u
2
+ 1)(u
99
− u
98
+ ··· − 127450u + 3749)
c
4
(u
27
+ 3u
26
+ ··· − 4u − 1)(u
99
− 4u
98
+ ··· + 36u − 1)
c
5
, c
6
(u
27
+ 16u
25
+ ··· − 6u + 1)(u
99
+ u
98
+ ··· + 472u − 103)
c
7
(u
27
− 9u
25
+ ··· + 7u
2
− 1)(u
99
+ u
98
+ ··· − 2230u − 532)
c
8
(u
27
+ 5u
26
+ ··· − 5u − 1)(u
99
− 24u
97
+ ··· − 37u + 1)
c
9
(u
27
− 5u
25
+ ··· − 6u + 1)(u
99
+ 3u
98
+ ··· − 3184124u + 9109661)
c
10
(u
27
+ 16u
25
+ ··· − 6u − 1)(u
99
+ u
98
+ ··· + 472u − 103)
c
11
(u
27
− 5u
26
+ ··· − 5u + 1)(u
99
− 24u
97
+ ··· − 37u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
27
+ 31y
26
+ ··· − 8y −1)(y
99
+ 104y
98
+ ··· + 292y −1)
c
2
, c
7
(y
27
− 18y
26
+ ··· + 14y −1)
· (y
99
− 73y
98
+ ··· + 11428188y −283024)
c
3
(y
27
− 14y
25
+ ··· − 22y −1)
· (y
99
− 27y
98
+ ··· + 15140464222y −14055001)
c
5
, c
6
, c
10
(y
27
+ 32y
26
+ ··· − 6y −1)(y
99
+ 109y
98
+ ··· − 84774y −10609)
c
8
, c
11
(y
27
− 21y
26
+ ··· + 27y −1)(y
99
− 48y
98
+ ··· + 671y −1)
c
9
(y
27
− 10y
26
+ ··· − 32y −1)
· (y
99
− 57y
98
+ ··· + 2009455767939712y −82985923534921)
22
