12a
1258
(K12a
1258
)
A knot diagram
1
Linearized knot diagam
5 7 9 10 2 11 12 1 4 6 3 8
Solving Sequence
7,12
8 1
3,9
4 2 11 6 5 10
c
7
c
12
c
8
c
3
c
2
c
11
c
6
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.55261 × 10
241
u
98
− 6.00163 × 10
241
u
97
+ ··· + 4.24303 × 10
242
b − 1.66484 × 10
242
,
− 4.48746 × 10
242
u
98
− 1.03495 × 10
243
u
97
+ ··· + 2.30336 × 10
243
a − 1.49280 × 10
244
,
u
99
+ 3u
98
+ ··· + 74u + 19i
I
u
2
= hu
20
+ u
19
+ ··· + b + 1, 11u
20
+ 6u
19
+ ··· + 2a + 23, u
21
− 14u
19
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 120 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−2.55 × 10
241
u
98
− 6.00 × 10
241
u
97
+ · · · + 4.24 × 10
242
b − 1.66 ×
10
242
, −4.49 × 10
242
u
98
− 1.03 × 10
243
u
97
+ · · · + 2.30 × 10
243
a − 1.49 ×
10
244
, u
99
+ 3u
98
+ · · · + 74u + 19i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
0.194822u
98
+ 0.449324u
97
+ ··· + 23.8610u + 6.48099
0.0601601u
98
+ 0.141447u
97
+ ··· + 1.99506u + 0.392369
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
0.292740u
98
+ 0.655874u
97
+ ··· + 30.4673u + 7.32334
0.0214966u
98
+ 0.0592174u
97
+ ··· + 0.553157u + 0.0275512
a
2
=
0.254983u
98
+ 0.590771u
97
+ ··· + 25.8561u + 6.87336
0.0601601u
98
+ 0.141447u
97
+ ··· + 1.99506u + 0.392369
a
11
=
0.0406568u
98
+ 0.0789464u
97
+ ··· + 5.22744u − 0.333209
0.0270023u
98
+ 0.0262813u
97
+ ··· + 1.59997u + 0.408942
a
6
=
0.123531u
98
+ 0.319533u
97
+ ··· + 12.3956u + 5.03543
0.100580u
98
+ 0.217161u
97
+ ··· + 7.38599u + 1.96953
a
5
=
0.141766u
98
+ 0.350890u
97
+ ··· + 17.4096u + 3.36732
0.0519563u
98
+ 0.120722u
97
+ ··· + 3.19261u + 0.366127
a
10
=
0.0473159u
98
+ 0.197736u
97
+ ··· + 21.0124u − 0.138025
−0.0392609u
98
− 0.00751575u
97
+ ··· − 3.64472u − 1.70638
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.432175u
98
− 1.12277u
97
+ ··· − 14.7712u − 6.70211
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
99
− 2u
98
+ ··· − 168u + 49
c
2
u
99
− 2u
98
+ ··· + 163u + 17
c
3
, c
4
, c
9
u
99
− u
98
+ ··· − 634u − 23
c
6
, c
10
u
99
− 36u
97
+ ··· + 52u − 7
c
7
, c
8
, c
12
u
99
− 3u
98
+ ··· + 74u − 19
c
11
u
99
− 5u
98
+ ··· + 465u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
99
− 60y
98
+ ··· + 121030y −2401
c
2
y
99
− 20y
98
+ ··· + 25889y −289
c
3
, c
4
, c
9
y
99
− 95y
98
+ ··· + 306322y −529
c
6
, c
10
y
99
− 72y
98
+ ··· + 660y −49
c
7
, c
8
, c
12
y
99
− 103y
98
+ ··· − 6038y −361
c
11
y
99
− 7y
98
+ ··· + 930y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638994 + 0.739104I
a = 0.228661 + 0.744090I
b = −0.793896 − 0.324299I
−3.35882 − 2.76331I 0
u = 0.638994 − 0.739104I
a = 0.228661 − 0.744090I
b = −0.793896 + 0.324299I
−3.35882 + 2.76331I 0
u = 0.511185 + 0.944135I
a = 0.163975 + 1.264040I
b = −1.00260 − 1.02085I
6.54384 − 12.43480I 0
u = 0.511185 − 0.944135I
a = 0.163975 − 1.264040I
b = −1.00260 + 1.02085I
6.54384 + 12.43480I 0
u = 0.540446 + 0.735322I
a = 0.18350 − 1.66701I
b = 0.911733 + 0.865941I
9.94163 − 5.42512I 0
u = 0.540446 − 0.735322I
a = 0.18350 + 1.66701I
b = 0.911733 − 0.865941I
9.94163 + 5.42512I 0
u = −0.172232 + 0.883812I
a = 0.754439 − 0.973326I
b = −0.587200 + 0.722324I
3.85491 + 2.48956I 0
u = −0.172232 − 0.883812I
a = 0.754439 + 0.973326I
b = −0.587200 − 0.722324I
3.85491 − 2.48956I 0
u = −0.879167 + 0.061143I
a = 1.384480 + 0.052534I
b = 0.184132 − 0.062040I
2.42479 − 0.00213I 0
u = −0.879167 − 0.061143I
a = 1.384480 − 0.052534I
b = 0.184132 + 0.062040I
2.42479 + 0.00213I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.415960 + 0.773865I
a = −0.952838 − 0.274165I
b = 0.563722 + 0.793689I
0.74742 − 3.86475I 0
u = −0.415960 − 0.773865I
a = −0.952838 + 0.274165I
b = 0.563722 − 0.793689I
0.74742 + 3.86475I 0
u = 1.062410 + 0.380284I
a = −1.144630 + 0.599349I
b = −1.39357 − 0.51108I
3.54258 + 0.66396I 0
u = 1.062410 − 0.380284I
a = −1.144630 − 0.599349I
b = −1.39357 + 0.51108I
3.54258 − 0.66396I 0
u = −0.513689 + 0.678395I
a = −0.10183 + 1.44799I
b = 1.03582 − 1.05461I
0.41702 + 8.50479I 0
u = −0.513689 − 0.678395I
a = −0.10183 − 1.44799I
b = 1.03582 + 1.05461I
0.41702 − 8.50479I 0
u = −0.425029 + 1.086770I
a = −0.413391 + 0.592418I
b = 0.700812 − 0.301259I
1.91325 + 5.57658I 0
u = −0.425029 − 1.086770I
a = −0.413391 − 0.592418I
b = 0.700812 + 0.301259I
1.91325 − 5.57658I 0
u = 0.496443 + 0.664464I
a = −0.910416 + 0.679661I
b = 0.816921 − 0.775446I
9.99441 + 0.67991I 0
u = 0.496443 − 0.664464I
a = −0.910416 − 0.679661I
b = 0.816921 + 0.775446I
9.99441 − 0.67991I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743531 + 0.998930I
a = 0.594722 − 0.257668I
b = −0.597670 + 0.831620I
5.97682 + 6.13788I 0
u = 0.743531 − 0.998930I
a = 0.594722 + 0.257668I
b = −0.597670 − 0.831620I
5.97682 − 6.13788I 0
u = 1.251660 + 0.031833I
a = −0.0696663 + 0.0094888I
b = −0.49160 − 1.82486I
−1.66463 − 2.28211I 0
u = 1.251660 − 0.031833I
a = −0.0696663 − 0.0094888I
b = −0.49160 + 1.82486I
−1.66463 + 2.28211I 0
u = 0.079414 + 0.724598I
a = 0.288634 − 1.148690I
b = −1.03185 + 1.19062I
6.59290 − 4.64406I 6.89953 + 3.82909I
u = 0.079414 − 0.724598I
a = 0.288634 + 1.148690I
b = −1.03185 − 1.19062I
6.59290 + 4.64406I 6.89953 − 3.82909I
u = −1.304400 + 0.029599I
a = 0.718871 − 1.214870I
b = 0.895637 + 0.963892I
−0.08248 − 4.61626I 0
u = −1.304400 − 0.029599I
a = 0.718871 + 1.214870I
b = 0.895637 − 0.963892I
−0.08248 + 4.61626I 0
u = −0.235824 + 0.649282I
a = 0.45602 − 1.59993I
b = −0.093634 + 0.809627I
4.43577 + 3.18480I 7.02018 − 3.08430I
u = −0.235824 − 0.649282I
a = 0.45602 + 1.59993I
b = −0.093634 − 0.809627I
4.43577 − 3.18480I 7.02018 + 3.08430I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.296090 + 0.243555I
a = 0.154706 + 0.132203I
b = −0.52140 − 1.78708I
2.34220 + 8.10002I 0
u = −1.296090 − 0.243555I
a = 0.154706 − 0.132203I
b = −0.52140 + 1.78708I
2.34220 − 8.10002I 0
u = 1.32749
a = 1.13738
b = 1.95283
6.98424 0
u = −0.589174 + 0.319764I
a = 1.203050 − 0.015067I
b = −0.385004 − 0.457325I
2.11743 − 0.36396I 3.49832 − 0.87137I
u = −0.589174 − 0.319764I
a = 1.203050 + 0.015067I
b = −0.385004 + 0.457325I
2.11743 + 0.36396I 3.49832 + 0.87137I
u = 1.324120 + 0.139120I
a = −0.266451 + 0.394339I
b = −0.876107 − 0.467778I
−3.33632 − 0.52697I 0
u = 1.324120 − 0.139120I
a = −0.266451 − 0.394339I
b = −0.876107 + 0.467778I
−3.33632 + 0.52697I 0
u = −1.329680 + 0.196232I
a = 0.587300 + 0.598823I
b = 1.54345 − 1.27752I
−3.38231 + 2.55549I 0
u = −1.329680 − 0.196232I
a = 0.587300 − 0.598823I
b = 1.54345 + 1.27752I
−3.38231 − 2.55549I 0
u = 1.342810 + 0.078875I
a = −0.187174 − 0.754241I
b = −0.913573 + 0.753421I
−1.97670 − 0.12270I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.342810 − 0.078875I
a = −0.187174 + 0.754241I
b = −0.913573 − 0.753421I
−1.97670 + 0.12270I 0
u = −0.314553 + 0.571005I
a = 0.34198 − 1.91552I
b = −0.730849 + 0.865353I
3.10558 + 3.61737I 5.02209 − 6.95770I
u = −0.314553 − 0.571005I
a = 0.34198 + 1.91552I
b = −0.730849 − 0.865353I
3.10558 − 3.61737I 5.02209 + 6.95770I
u = −1.374090 + 0.059413I
a = −1.25490 + 0.74710I
b = −1.094480 − 0.250638I
−1.94268 + 2.09451I 0
u = −1.374090 − 0.059413I
a = −1.25490 − 0.74710I
b = −1.094480 + 0.250638I
−1.94268 − 2.09451I 0
u = 0.132610 + 0.570783I
a = −0.50919 − 1.37405I
b = 0.68277 + 1.29422I
1.178210 + 0.222024I 4.09639 + 0.81351I
u = 0.132610 − 0.570783I
a = −0.50919 + 1.37405I
b = 0.68277 − 1.29422I
1.178210 − 0.222024I 4.09639 − 0.81351I
u = −1.40897 + 0.12756I
a = 0.309238 + 0.806431I
b = 0.720029 − 0.800960I
−5.23918 + 2.82523I 0
u = −1.40897 − 0.12756I
a = 0.309238 − 0.806431I
b = 0.720029 + 0.800960I
−5.23918 − 2.82523I 0
u = 1.38798 + 0.30000I
a = −0.362647 + 0.963676I
b = −0.89457 − 1.13107I
−1.14649 − 6.58052I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38798 − 0.30000I
a = −0.362647 − 0.963676I
b = −0.89457 + 1.13107I
−1.14649 + 6.58052I 0
u = −1.40581 + 0.21716I
a = −0.0848306 − 0.0957051I
b = 0.831029 + 1.020710I
4.00655 + 2.36985I 0
u = −1.40581 − 0.21716I
a = −0.0848306 + 0.0957051I
b = 0.831029 − 1.020710I
4.00655 − 2.36985I 0
u = 1.42021 + 0.11685I
a = 0.53593 + 1.37207I
b = 0.376787 − 0.204202I
−1.80362 − 6.92361I 0
u = 1.42021 − 0.11685I
a = 0.53593 − 1.37207I
b = 0.376787 + 0.204202I
−1.80362 + 6.92361I 0
u = −1.43035 + 0.14032I
a = −0.765440 − 0.605974I
b = −1.78067 + 0.94085I
−4.46694 + 5.12991I 0
u = −1.43035 − 0.14032I
a = −0.765440 + 0.605974I
b = −1.78067 − 0.94085I
−4.46694 − 5.12991I 0
u = 1.42057 + 0.24111I
a = −0.320890 + 0.937987I
b = −0.443208 − 0.993210I
−0.88819 − 6.41567I 0
u = 1.42057 − 0.24111I
a = −0.320890 − 0.937987I
b = −0.443208 + 0.993210I
−0.88819 + 6.41567I 0
u = 0.532037 + 0.171780I
a = −1.25986 − 1.38703I
b = −0.221282 − 0.570042I
−0.60605 − 2.64565I −4.49649 + 6.49734I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532037 − 0.171780I
a = −1.25986 + 1.38703I
b = −0.221282 + 0.570042I
−0.60605 + 2.64565I −4.49649 − 6.49734I
u = 1.43699 + 0.18185I
a = −0.743374 + 0.995991I
b = −1.05676 − 0.94158I
−2.54175 − 6.29202I 0
u = 1.43699 − 0.18185I
a = −0.743374 − 0.995991I
b = −1.05676 + 0.94158I
−2.54175 + 6.29202I 0
u = −1.33720 + 0.57739I
a = −0.039250 + 0.490500I
b = 0.809011 − 0.511517I
−1.03852 + 1.09123I 0
u = −1.33720 − 0.57739I
a = −0.039250 − 0.490500I
b = 0.809011 + 0.511517I
−1.03852 − 1.09123I 0
u = −0.529233 + 0.072478I
a = 0.601191 + 0.531110I
b = 1.134370 − 0.143375I
−2.45286 + 0.05284I −5.63964 + 1.73847I
u = −0.529233 − 0.072478I
a = 0.601191 − 0.531110I
b = 1.134370 + 0.143375I
−2.45286 − 0.05284I −5.63964 − 1.73847I
u = −1.49390 + 0.01527I
a = −0.608509 + 0.989132I
b = −0.391289 − 0.128041I
−7.22577 + 3.21947I 0
u = −1.49390 − 0.01527I
a = −0.608509 − 0.989132I
b = −0.391289 + 0.128041I
−7.22577 − 3.21947I 0
u = −0.495392
a = 1.86962
b = 1.12220
−2.29548 −12.9840
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50591 + 0.08560I
a = 0.680720 − 0.597516I
b = 1.259100 + 0.380183I
−9.29517 − 0.94784I 0
u = 1.50591 − 0.08560I
a = 0.680720 + 0.597516I
b = 1.259100 − 0.380183I
−9.29517 + 0.94784I 0
u = 1.50512 + 0.24468I
a = 0.672410 − 0.815869I
b = 1.45385 + 1.03810I
−6.12726 − 11.90180I 0
u = 1.50512 − 0.24468I
a = 0.672410 + 0.815869I
b = 1.45385 − 1.03810I
−6.12726 + 11.90180I 0
u = 0.220734 + 0.403612I
a = −0.435314 − 1.126120I
b = 0.252796 + 0.437167I
0.025892 − 0.911298I 0.62892 + 7.31065I
u = 0.220734 − 0.403612I
a = −0.435314 + 1.126120I
b = 0.252796 − 0.437167I
0.025892 + 0.911298I 0.62892 − 7.31065I
u = −1.53491 + 0.23090I
a = −0.425740 − 0.784087I
b = −1.156090 + 0.526124I
−10.40670 + 6.21904I 0
u = −1.53491 − 0.23090I
a = −0.425740 + 0.784087I
b = −1.156090 − 0.526124I
−10.40670 − 6.21904I 0
u = −1.46348 + 0.53879I
a = 0.245647 − 0.459594I
b = −0.520196 − 0.000046I
0.09944 + 3.14108I 0
u = −1.46348 − 0.53879I
a = 0.245647 + 0.459594I
b = −0.520196 + 0.000046I
0.09944 − 3.14108I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52285 + 0.36735I
a = 0.286966 − 0.888749I
b = 1.063900 + 0.566426I
−4.37424 − 10.64490I 0
u = 1.52285 − 0.36735I
a = 0.286966 + 0.888749I
b = 1.063900 − 0.566426I
−4.37424 + 10.64490I 0
u = 1.56699
a = 1.16899
b = 1.19872
−9.43280 0
u = 0.246141 + 0.356204I
a = 0.22173 + 2.08454I
b = −1.24916 − 1.09515I
1.07143 − 3.25313I 2.48691 + 9.00005I
u = 0.246141 − 0.356204I
a = 0.22173 − 2.08454I
b = −1.24916 + 1.09515I
1.07143 + 3.25313I 2.48691 − 9.00005I
u = −1.54762 + 0.26412I
a = 0.857409 + 0.971079I
b = 1.084390 − 0.836561I
3.09097 + 9.12831I 0
u = −1.54762 − 0.26412I
a = 0.857409 − 0.971079I
b = 1.084390 + 0.836561I
3.09097 − 9.12831I 0
u = −1.53890 + 0.34716I
a = −0.644387 − 0.922484I
b = −1.31977 + 1.00529I
−0.0472 + 17.1279I 0
u = −1.53890 − 0.34716I
a = −0.644387 + 0.922484I
b = −1.31977 − 1.00529I
−0.0472 − 17.1279I 0
u = 1.62586 + 0.20972I
a = 0.182206 − 0.440937I
b = 0.451653 + 0.037173I
−6.11301 − 0.51432I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62586 − 0.20972I
a = 0.182206 + 0.440937I
b = 0.451653 − 0.037173I
−6.11301 + 0.51432I 0
u = 0.356284
a = −2.91113
b = 1.21929
10.5861 26.2890
u = 1.64481
a = 0.865174
b = 0.368194
−5.76238 0
u = −1.67324
a = −1.44838
b = −1.08626
−6.27557 0
u = −0.179458 + 0.253158I
a = 4.28566 − 3.03405I
b = 0.442602 − 0.472115I
3.56599 + 5.45286I −1.25190 − 10.82442I
u = −0.179458 − 0.253158I
a = 4.28566 + 3.03405I
b = 0.442602 + 0.472115I
3.56599 − 5.45286I −1.25190 + 10.82442I
u = −0.044517 + 0.238637I
a = −2.58596 + 4.06517I
b = −0.839573 − 0.212992I
2.54998 − 1.15743I 1.31085 + 1.86464I
u = −0.044517 − 0.238637I
a = −2.58596 − 4.06517I
b = −0.839573 + 0.212992I
2.54998 + 1.15743I 1.31085 − 1.86464I
u = −2.09450
a = −0.0187236
b = −0.432020
−3.71793 0
14
II.
I
u
2
= hu
20
+u
19
+· · ·+b+1, 11u
20
+6u
19
+· · ·+2a+23, u
21
−14u
19
+· · ·+u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−
11
2
u
20
− 3u
19
+ ··· −
23
2
u −
23
2
−u
20
− u
19
+ ··· − 2u − 1
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−
11
2
u
20
− 4u
19
+ ··· − 9u − 10
−
1
2
u
17
+ 6u
15
+ ··· − u +
1
2
a
2
=
−
13
2
u
20
− 4u
19
+ ··· −
27
2
u −
25
2
−u
20
− u
19
+ ··· − 2u − 1
a
11
=
−u
20
−
3
2
u
19
+ ··· +
5
2
u
2
−
5
2
u
−4u
20
−
5
2
u
19
+ ··· −
11
2
u − 7
a
6
=
13
2
u
20
+ 5u
19
+ ··· + 14u +
27
2
−u
20
+ u
19
+ ··· − 8u −
7
2
a
5
=
7
2
u
20
+
9
2
u
19
+ ··· + u + 3
−3u
20
+
1
2
u
19
+ ··· −
31
2
u − 9
a
10
=
−
1
2
u
20
+
3
2
u
19
+ ··· − 9u − 3
4u
20
+
5
2
u
19
+ ··· +
11
2
u +
13
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 48u
20
+
53
2
u
19
− 652u
18
− 355u
17
+
7445
2
u
16
+ 2041u
15
−
23209
2
u
14
−
12835
2
u
13
+ 21257u
12
+
23307
2
u
11
−
44969
2
u
10
−
23279
2
u
9
+
23709
2
u
8
+
9515
2
u
7
−
2437
2
u
6
+ 1171u
5
− 889u
4
− 1380u
3
−
269
2
u
2
+ 109u + 95
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 3u
20
+ ··· − 3u − 1
c
2
u
21
− u
20
+ ··· + 10u
2
− 1
c
3
, c
4
u
21
− 12u
19
+ ··· − u + 1
c
5
u
21
− 3u
20
+ ··· − 3u + 1
c
6
u
21
+ u
20
+ ··· + 3u − 1
c
7
, c
8
u
21
− 14u
19
+ ··· + u − 1
c
9
u
21
− 12u
19
+ ··· − u − 1
c
10
u
21
− u
20
+ ··· + 3u + 1
c
11
u
21
− 4u
19
+ ··· + 3u + 1
c
12
u
21
− 14u
19
+ ··· + u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
21
− 21y
20
+ ··· + 21y −1
c
2
y
21
− 9y
20
+ ··· + 20y −1
c
3
, c
4
, c
9
y
21
− 24y
20
+ ··· + 9y −1
c
6
, c
10
y
21
− 21y
20
+ ··· + 15y −1
c
7
, c
8
, c
12
y
21
− 28y
20
+ ··· + 9y −1
c
11
y
21
− 8y
20
+ ··· + 5y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881099 + 0.195365I
a = 1.43500 + 0.46001I
b = 0.846170 − 0.040778I
1.49501 − 0.09295I −4.02271 − 0.89982I
u = −0.881099 − 0.195365I
a = 1.43500 − 0.46001I
b = 0.846170 + 0.040778I
1.49501 + 0.09295I −4.02271 + 0.89982I
u = 1.26209
a = −1.13394
b = −1.94619
7.53887 8.47890
u = 1.257190 + 0.177710I
a = −0.119622 + 0.372206I
b = −0.994792 − 0.741082I
−4.09060 − 0.90910I −8.18162 + 0.25711I
u = 1.257190 − 0.177710I
a = −0.119622 − 0.372206I
b = −0.994792 + 0.741082I
−4.09060 + 0.90910I −8.18162 − 0.25711I
u = −1.323230 + 0.110086I
a = 0.567557 + 0.767122I
b = 1.39924 − 1.32178I
−2.79185 + 3.86713I −1.43690 − 4.63715I
u = −1.323230 − 0.110086I
a = 0.567557 − 0.767122I
b = 1.39924 + 1.32178I
−2.79185 − 3.86713I −1.43690 + 4.63715I
u = −1.283850 + 0.429554I
a = −0.363241 + 0.416469I
b = 0.421606 − 0.430118I
0.68309 + 3.44414I 2.65757 − 5.08852I
u = −1.283850 − 0.429554I
a = −0.363241 − 0.416469I
b = 0.421606 + 0.430118I
0.68309 − 3.44414I 2.65757 + 5.08852I
u = 1.375930 + 0.201231I
a = −0.242144 + 1.260580I
b = −0.494720 − 1.153360I
−0.31421 − 7.51279I 2.51674 + 9.19321I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.375930 − 0.201231I
a = −0.242144 − 1.260580I
b = −0.494720 + 1.153360I
−0.31421 + 7.51279I 2.51674 − 9.19321I
u = 0.104336 + 0.589212I
a = 1.92730 − 0.17150I
b = −0.161347 + 0.695868I
4.07643 + 4.88190I 5.40318 − 3.69735I
u = 0.104336 − 0.589212I
a = 1.92730 + 0.17150I
b = −0.161347 − 0.695868I
4.07643 − 4.88190I 5.40318 + 3.69735I
u = 0.467261
a = 2.13481
b = −1.20120
10.4200 −22.1910
u = −1.57234
a = −1.11050
b = −1.34671
−9.00212 4.81910
u = 0.416567
a = −1.93080
b = −1.31432
−1.96719 13.2570
u = −0.225246 + 0.324822I
a = −1.93832 + 0.00613I
b = 0.769744 + 0.956939I
1.01492 − 2.41280I 1.186685 + 0.269194I
u = −0.225246 − 0.324822I
a = −1.93832 − 0.00613I
b = 0.769744 − 0.956939I
1.01492 + 2.41280I 1.186685 − 0.269194I
u = 1.63120
a = 1.55820
b = 0.927719
−7.02740 −9.07960
u = 1.73739
a = 0.211044
b = 0.565115
−6.45731 −15.2050
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.99023
a = −0.261891
b = −0.256225
−3.52004 15.6760
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
99
− 2u
98
+ ··· − 168u + 49)
c
2
(u
21
− u
20
+ ··· + 10u
2
− 1)(u
99
− 2u
98
+ ··· + 163u + 17)
c
3
, c
4
(u
21
− 12u
19
+ ··· − u + 1)(u
99
− u
98
+ ··· − 634u − 23)
c
5
(u
21
− 3u
20
+ ··· − 3u + 1)(u
99
− 2u
98
+ ··· − 168u + 49)
c
6
(u
21
+ u
20
+ ··· + 3u − 1)(u
99
− 36u
97
+ ··· + 52u − 7)
c
7
, c
8
(u
21
− 14u
19
+ ··· + u − 1)(u
99
− 3u
98
+ ··· + 74u − 19)
c
9
(u
21
− 12u
19
+ ··· − u − 1)(u
99
− u
98
+ ··· − 634u − 23)
c
10
(u
21
− u
20
+ ··· + 3u + 1)(u
99
− 36u
97
+ ··· + 52u − 7)
c
11
(u
21
− 4u
19
+ ··· + 3u + 1)(u
99
− 5u
98
+ ··· + 465u
2
− 1)
c
12
(u
21
− 14u
19
+ ··· + u + 1)(u
99
− 3u
98
+ ··· + 74u − 19)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
21
− 21y
20
+ ··· + 21y −1)(y
99
− 60y
98
+ ··· + 121030y −2401)
c
2
(y
21
− 9y
20
+ ··· + 20y −1)(y
99
− 20y
98
+ ··· + 25889y −289)
c
3
, c
4
, c
9
(y
21
− 24y
20
+ ··· + 9y −1)(y
99
− 95y
98
+ ··· + 306322y −529)
c
6
, c
10
(y
21
− 21y
20
+ ··· + 15y −1)(y
99
− 72y
98
+ ··· + 660y −49)
c
7
, c
8
, c
12
(y
21
− 28y
20
+ ··· + 9y −1)(y
99
− 103y
98
+ ··· − 6038y −361)
c
11
(y
21
− 8y
20
+ ··· + 5y −1)(y
99
− 7y
98
+ ··· + 930y −1)
22
