12n
0367
(K12n
0367
)
A knot diagram
1
Linearized knot diagam
3 5 8 12 2 11 3 4 1 4 6 10
Solving Sequence
2,6
5 3
1,12
4 11 7 8 9 10
c
5
c
2
c
1
c
4
c
11
c
6
c
7
c
8
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.53963 × 10
157
u
87
+ 2.37834 × 10
157
u
86
+ ··· + 2.39381 × 10
157
b + 1.76070 × 10
157
,
2.34713 × 10
157
u
87
− 1.38197 × 10
157
u
86
+ ··· + 2.39381 × 10
157
a + 1.30597 × 10
158
, u
88
+ 22u
86
+ ··· + 2u + 1i
I
u
2
= h−104670u
25
+ 66491u
24
+ ··· + 54833b − 636383,
495202u
25
− 847689u
24
+ ··· + 54833a + 692536, u
26
− 3u
25
+ ··· − 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 114 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−1.54 × 10
157
u
87
+ 2.38 × 10
157
u
86
+ · · · + 2.39 × 10
157
b + 1.76 ×
10
157
, 2.35 × 10
157
u
87
− 1.38 × 10
157
u
86
+ · · · + 2.39 × 10
157
a + 1.31 ×
10
158
, u
88
+ 22u
86
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−0.980503u
87
+ 0.577312u
86
+ ··· − 5.19109u − 5.45563
0.643174u
87
− 0.993539u
86
+ ··· + 2.61924u − 0.735525
a
4
=
−1.71029u
87
+ 0.0126145u
86
+ ··· + 6.15889u − 0.333775
0.314661u
87
− 0.105993u
86
+ ··· + 1.28030u + 0.137825
a
11
=
−0.337329u
87
− 0.416227u
86
+ ··· − 2.57184u − 6.19116
0.643174u
87
− 0.993539u
86
+ ··· + 2.61924u − 0.735525
a
7
=
1.33512u
87
+ 0.213674u
86
+ ··· − 8.43237u + 2.51339
−0.537763u
87
+ 0.298042u
86
+ ··· − 2.98445u − 0.0534571
a
8
=
1.40782u
87
+ 0.124868u
86
+ ··· − 7.03532u + 2.37329
−0.415885u
87
+ 0.204932u
86
+ ··· − 1.48248u − 0.104746
a
9
=
−0.297558u
87
+ 0.610697u
86
+ ··· − 1.00875u + 4.31265
−0.434217u
87
+ 0.436621u
86
+ ··· − 1.53241u + 0.242672
a
10
=
0.195621u
87
− 0.814050u
86
+ ··· + 0.450308u − 4.69598
0.281328u
87
− 0.153582u
86
+ ··· + 2.43945u + 0.00833811
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.98512u
87
+ 0.111068u
86
+ ··· + 1.77043u − 2.63654
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 44u
87
+ ··· − 14u + 1
c
2
, c
5
u
88
+ 22u
86
+ ··· + 2u + 1
c
3
, c
7
, c
8
u
88
+ u
87
+ ··· + 4537u + 653
c
4
u
88
+ u
87
+ ··· − 6282u + 3780
c
6
, c
11
u
88
− 3u
87
+ ··· − 34779u + 4553
c
9
, c
12
u
88
− 3u
87
+ ··· − 5791u + 1003
c
10
u
88
− u
87
+ ··· + 33861u + 11617
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 16y
87
+ ··· + 38y + 1
c
2
, c
5
y
88
+ 44y
87
+ ··· − 14y + 1
c
3
, c
7
, c
8
y
88
− 39y
87
+ ··· − 16718609y + 426409
c
4
y
88
+ 47y
87
+ ··· + 424002276y + 14288400
c
6
, c
11
y
88
+ 47y
87
+ ··· + 457119657y + 20729809
c
9
, c
12
y
88
+ 37y
87
+ ··· + 28963255y + 1006009
c
10
y
88
− 13y
87
+ ··· − 5986209521y + 134954689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.950994 + 0.225023I
a = −0.0042485 + 0.1234880I
b = −0.494741 − 1.159590I
2.20661 − 4.50051I 0
u = 0.950994 − 0.225023I
a = −0.0042485 − 0.1234880I
b = −0.494741 + 1.159590I
2.20661 + 4.50051I 0
u = 0.285666 + 0.999025I
a = −1.271540 − 0.078839I
b = 0.527665 + 0.001231I
−0.94739 + 2.27872I 0
u = 0.285666 − 0.999025I
a = −1.271540 + 0.078839I
b = 0.527665 − 0.001231I
−0.94739 − 2.27872I 0
u = −0.925529 + 0.492184I
a = −0.0605045 + 0.0712789I
b = −0.599977 + 1.165180I
1.40800 + 4.49923I 0
u = −0.925529 − 0.492184I
a = −0.0605045 − 0.0712789I
b = −0.599977 − 1.165180I
1.40800 − 4.49923I 0
u = −0.432052 + 0.965201I
a = 2.14505 + 0.62032I
b = −0.210712 − 1.326370I
4.71577 − 4.97810I 0
u = −0.432052 − 0.965201I
a = 2.14505 − 0.62032I
b = −0.210712 + 1.326370I
4.71577 + 4.97810I 0
u = 0.403742 + 0.986207I
a = 1.42705 + 0.78190I
b = −1.24697 − 0.68296I
−2.68120 + 2.73860I 0
u = 0.403742 − 0.986207I
a = 1.42705 − 0.78190I
b = −1.24697 + 0.68296I
−2.68120 − 2.73860I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.495500 + 0.945563I
a = −1.87127 − 0.61725I
b = 0.44695 + 1.42224I
5.23357 − 0.17704I 0
u = −0.495500 − 0.945563I
a = −1.87127 + 0.61725I
b = 0.44695 − 1.42224I
5.23357 + 0.17704I 0
u = 0.916402 + 0.070900I
a = −0.293096 − 0.421980I
b = 0.038009 − 1.374640I
6.89951 + 0.18727I 7.38962 + 0.I
u = 0.916402 − 0.070900I
a = −0.293096 + 0.421980I
b = 0.038009 + 1.374640I
6.89951 − 0.18727I 7.38962 + 0.I
u = −0.362440 + 1.049730I
a = 1.47595 − 0.54699I
b = −0.685813 − 0.954186I
−4.05142 − 3.40776I 0
u = −0.362440 − 1.049730I
a = 1.47595 + 0.54699I
b = −0.685813 + 0.954186I
−4.05142 + 3.40776I 0
u = 0.830410 + 0.267292I
a = −0.154904 − 0.043619I
b = 0.434261 + 0.771534I
1.041510 + 0.827983I 1.47393 − 1.48857I
u = 0.830410 − 0.267292I
a = −0.154904 + 0.043619I
b = 0.434261 − 0.771534I
1.041510 − 0.827983I 1.47393 + 1.48857I
u = −0.482044 + 0.714046I
a = 0.501977 + 0.389736I
b = 0.18713 − 1.65749I
5.99785 − 3.85058I 2.05614 + 7.78115I
u = −0.482044 − 0.714046I
a = 0.501977 − 0.389736I
b = 0.18713 + 1.65749I
5.99785 + 3.85058I 2.05614 − 7.78115I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530443 + 1.007740I
a = 0.833164 + 0.920449I
b = −0.421505 + 1.042970I
−1.79639 + 3.12241I 0
u = 0.530443 − 1.007740I
a = 0.833164 − 0.920449I
b = −0.421505 − 1.042970I
−1.79639 − 3.12241I 0
u = −0.289666 + 1.102280I
a = −1.158050 + 0.650210I
b = 0.606326 + 0.743837I
−3.08768 + 2.63543I 0
u = −0.289666 − 1.102280I
a = −1.158050 − 0.650210I
b = 0.606326 − 0.743837I
−3.08768 − 2.63543I 0
u = −1.070320 + 0.410063I
a = −0.0461963 − 0.0452036I
b = 0.560313 − 1.284340I
4.31681 + 10.86790I 0
u = −1.070320 − 0.410063I
a = −0.0461963 + 0.0452036I
b = 0.560313 + 1.284340I
4.31681 − 10.86790I 0
u = −0.443590 + 1.065640I
a = 1.65905 + 1.05131I
b = −0.161908 − 0.797457I
6.47178 − 2.16309I 0
u = −0.443590 − 1.065640I
a = 1.65905 − 1.05131I
b = −0.161908 + 0.797457I
6.47178 + 2.16309I 0
u = 0.382878 + 1.090750I
a = −1.010260 − 0.717946I
b = 0.944931 + 0.886998I
−2.05368 − 1.85448I 0
u = 0.382878 − 1.090750I
a = −1.010260 + 0.717946I
b = 0.944931 − 0.886998I
−2.05368 + 1.85448I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.260391 + 0.792542I
a = 2.02389 + 0.11691I
b = −1.214820 − 0.002643I
−1.73937 + 0.22136I 1.85602 + 1.46273I
u = 0.260391 − 0.792542I
a = 2.02389 − 0.11691I
b = −1.214820 + 0.002643I
−1.73937 − 0.22136I 1.85602 − 1.46273I
u = −0.528314 + 1.040610I
a = 0.932239 − 0.854300I
b = −1.269650 + 0.553169I
−2.98847 − 3.16275I 0
u = −0.528314 − 1.040610I
a = 0.932239 + 0.854300I
b = −1.269650 − 0.553169I
−2.98847 + 3.16275I 0
u = −0.396057 + 0.732711I
a = −0.617862 + 0.433950I
b = −0.07362 + 1.57635I
5.53692 + 1.45907I 2.09471 + 3.45616I
u = −0.396057 − 0.732711I
a = −0.617862 − 0.433950I
b = −0.07362 − 1.57635I
5.53692 − 1.45907I 2.09471 − 3.45616I
u = 0.510718 + 0.654379I
a = −1.76586 − 0.92046I
b = −0.131347 − 0.554336I
−0.621825 + 1.176960I 1.91177 − 2.19037I
u = 0.510718 − 0.654379I
a = −1.76586 + 0.92046I
b = −0.131347 + 0.554336I
−0.621825 − 1.176960I 1.91177 + 2.19037I
u = −0.518141 + 1.051120I
a = −1.72372 − 0.55922I
b = 0.701048 + 0.820542I
7.07769 − 4.63089I 0
u = −0.518141 − 1.051120I
a = −1.72372 + 0.55922I
b = 0.701048 − 0.820542I
7.07769 + 4.63089I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501882 + 1.071530I
a = −1.31410 − 0.80647I
b = 0.467396 − 1.172060I
−1.27822 + 8.90820I 0
u = 0.501882 − 1.071530I
a = −1.31410 + 0.80647I
b = 0.467396 + 1.172060I
−1.27822 − 8.90820I 0
u = −0.482338 + 0.637957I
a = 1.44483 − 1.47393I
b = −1.153420 − 0.226060I
−1.56364 − 1.06781I 6.03726 − 6.31171I
u = −0.482338 − 0.637957I
a = 1.44483 + 1.47393I
b = −1.153420 + 0.226060I
−1.56364 + 1.06781I 6.03726 + 6.31171I
u = −0.536856 + 1.087540I
a = −1.24526 + 0.71064I
b = 1.350980 − 0.346633I
−1.50727 − 9.89367I 0
u = −0.536856 − 1.087540I
a = −1.24526 − 0.71064I
b = 1.350980 + 0.346633I
−1.50727 + 9.89367I 0
u = −0.883478 + 0.861213I
a = −0.009652 + 0.170471I
b = 0.556256 − 1.001050I
7.46659 − 0.54060I 0
u = −0.883478 − 0.861213I
a = −0.009652 − 0.170471I
b = 0.556256 + 1.001050I
7.46659 + 0.54060I 0
u = −0.837273 + 0.948164I
a = −1.257530 + 0.545736I
b = 0.719500 + 0.965996I
7.18578 − 5.81942I 0
u = −0.837273 − 0.948164I
a = −1.257530 − 0.545736I
b = 0.719500 − 0.965996I
7.18578 + 5.81942I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.093394 + 1.287980I
a = 0.674153 − 0.800344I
b = −0.687759 + 0.678198I
−4.89915 + 1.81520I 0
u = −0.093394 − 1.287980I
a = 0.674153 + 0.800344I
b = −0.687759 − 0.678198I
−4.89915 − 1.81520I 0
u = −0.470843 + 0.518883I
a = −0.904417 + 0.769983I
b = 0.440872 − 1.243470I
8.74330 + 0.43774I 8.09934 − 2.16625I
u = −0.470843 − 0.518883I
a = −0.904417 − 0.769983I
b = 0.440872 + 1.243470I
8.74330 − 0.43774I 8.09934 + 2.16625I
u = 0.584887 + 1.181660I
a = −1.53011 + 0.00453I
b = 0.758108 − 0.967143I
−1.65727 + 4.47065I 0
u = 0.584887 − 1.181660I
a = −1.53011 − 0.00453I
b = 0.758108 + 0.967143I
−1.65727 − 4.47065I 0
u = 0.601233 + 0.293144I
a = −0.304130 − 0.031403I
b = 0.183401 + 0.517058I
1.13886 + 0.89704I 3.89050 − 2.59952I
u = 0.601233 − 0.293144I
a = −0.304130 + 0.031403I
b = 0.183401 − 0.517058I
1.13886 − 0.89704I 3.89050 + 2.59952I
u = −0.688717 + 1.143690I
a = 1.62676 − 0.18674I
b = −0.79192 − 1.26585I
−0.58678 − 10.44900I 0
u = −0.688717 − 1.143690I
a = 1.62676 + 0.18674I
b = −0.79192 + 1.26585I
−0.58678 + 10.44900I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568898 + 0.324756I
a = −0.92706 + 1.71911I
b = 0.982482 + 0.018370I
0.60435 + 5.38463I 2.42475 − 4.14005I
u = −0.568898 − 0.324756I
a = −0.92706 − 1.71911I
b = 0.982482 − 0.018370I
0.60435 − 5.38463I 2.42475 + 4.14005I
u = 0.317693 + 1.306880I
a = −0.443125 − 0.770098I
b = 0.577322 + 0.400301I
−3.73728 + 4.73037I 0
u = 0.317693 − 1.306880I
a = −0.443125 + 0.770098I
b = 0.577322 − 0.400301I
−3.73728 − 4.73037I 0
u = 0.558864 + 1.226700I
a = −1.329560 + 0.240552I
b = 0.269392 − 1.306580I
3.23539 + 5.35337I 0
u = 0.558864 − 1.226700I
a = −1.329560 − 0.240552I
b = 0.269392 + 1.306580I
3.23539 − 5.35337I 0
u = 0.595060 + 1.211340I
a = 1.61825 − 0.21648I
b = −0.81450 + 1.21464I
−0.76474 + 10.05920I 0
u = 0.595060 − 1.211340I
a = 1.61825 + 0.21648I
b = −0.81450 − 1.21464I
−0.76474 − 10.05920I 0
u = −0.294632 + 0.568517I
a = 1.51039 + 0.73610I
b = −0.028348 + 1.231060I
8.24712 − 1.28370I 4.65282 + 4.56414I
u = −0.294632 − 0.568517I
a = 1.51039 − 0.73610I
b = −0.028348 − 1.231060I
8.24712 + 1.28370I 4.65282 − 4.56414I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.623842 + 1.214480I
a = 1.075840 − 0.392993I
b = −0.30418 + 1.39046I
3.66108 + 5.36800I 0
u = 0.623842 − 1.214480I
a = 1.075840 + 0.392993I
b = −0.30418 − 1.39046I
3.66108 − 5.36800I 0
u = 1.123010 + 0.810467I
a = −0.0751096 − 0.1045390I
b = −0.024807 − 1.008540I
6.81941 + 3.42608I 0
u = 1.123010 − 0.810467I
a = −0.0751096 + 0.1045390I
b = −0.024807 + 1.008540I
6.81941 − 3.42608I 0
u = 0.970073 + 1.006650I
a = 0.823943 + 0.304573I
b = −0.125707 + 0.872027I
6.19117 + 3.97335I 0
u = 0.970073 − 1.006650I
a = 0.823943 − 0.304573I
b = −0.125707 − 0.872027I
6.19117 − 3.97335I 0
u = −0.694895 + 1.214520I
a = −1.62709 − 0.01434I
b = 0.73871 + 1.36337I
1.7998 − 17.1939I 0
u = −0.694895 − 1.214520I
a = −1.62709 + 0.01434I
b = 0.73871 − 1.36337I
1.7998 + 17.1939I 0
u = 0.31799 + 1.38757I
a = −0.057553 + 0.871947I
b = −0.319947 − 0.722892I
−3.04754 − 0.05132I 0
u = 0.31799 − 1.38757I
a = −0.057553 − 0.871947I
b = −0.319947 + 0.722892I
−3.04754 + 0.05132I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.367116 + 0.434526I
a = 2.30266 + 2.31278I
b = 0.317228 + 0.674134I
0.68475 − 4.86775I 4.54514 + 2.43592I
u = 0.367116 − 0.434526I
a = 2.30266 − 2.31278I
b = 0.317228 − 0.674134I
0.68475 + 4.86775I 4.54514 − 2.43592I
u = −0.08440 + 1.49734I
a = −0.343432 + 0.798912I
b = 0.422587 − 0.904167I
−2.72050 + 6.74128I 0
u = −0.08440 − 1.49734I
a = −0.343432 − 0.798912I
b = 0.422587 + 0.904167I
−2.72050 − 6.74128I 0
u = 0.214717 + 0.168571I
a = −5.72982 − 2.26422I
b = 0.710194 − 0.502307I
0.63011 + 5.03685I 5.17161 − 7.47590I
u = 0.214717 − 0.168571I
a = −5.72982 + 2.26422I
b = 0.710194 + 0.502307I
0.63011 − 5.03685I 5.17161 + 7.47590I
u = −0.268639 + 0.033317I
a = −0.99972 − 2.83584I
b = −0.679398 − 0.233762I
−1.43149 − 0.62686I −4.31332 − 0.35363I
u = −0.268639 − 0.033317I
a = −0.99972 + 2.83584I
b = −0.679398 + 0.233762I
−1.43149 + 0.62686I −4.31332 + 0.35363I
13
II.
I
u
2
= h−1.05 × 10
5
u
25
+ 6.65 × 10
4
u
24
+ · · · + 5.48 × 10
4
b − 6.36 × 10
5
, 4.95 ×
10
5
u
25
−8.48×10
5
u
24
+· · · +5.48×10
4
a+6.93×10
5
, u
26
−3u
25
+· · · −3u +1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−9.03109u
25
+ 15.4595u
24
+ ··· + 28.9086u − 12.6299
1.90889u
25
− 1.21261u
24
+ ··· − 18.5745u + 11.6058
a
4
=
−1.97202u
25
+ 5.04526u
24
+ ··· − 31.6703u + 3.21190
−5.06120u
25
+ 13.9701u
24
+ ··· − 19.3107u + 2.08271
a
11
=
−7.12221u
25
+ 14.2469u
24
+ ··· + 10.3341u − 1.02407
1.90889u
25
− 1.21261u
24
+ ··· − 18.5745u + 11.6058
a
7
=
6.85087u
25
− 13.8176u
24
+ ··· − 7.50338u + 14.9467
6.73507u
25
− 18.2383u
24
+ ··· + 33.4994u − 6.85087
a
8
=
5.63734u
25
− 10.5724u
24
+ ··· − 18.6043u + 19.0080
5.90889u
25
− 15.2126u
24
+ ··· + 22.4255u − 2.39416
a
9
=
4.33626u
25
− 13.9840u
24
+ ··· + 32.1079u − 2.15582
3.54135u
25
− 8.59346u
24
+ ··· + 4.17579u + 0.0312768
a
10
=
4.60609u
25
− 15.9724u
24
+ ··· + 36.0640u − 3.30234
2.65220u
25
− 5.39325u
24
+ ··· − 0.997556u − 0.303850
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2984097
54833
u
25
+
8864634
54833
u
24
+ ··· −
12116723
54833
u +
2482104
54833
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 15u
25
+ ··· − 19u + 1
c
2
u
26
+ 3u
25
+ ··· + 3u + 1
c
3
u
26
− 10u
24
+ ··· + 2u + 1
c
4
u
26
+ 11u
24
+ ··· + 2u + 1
c
5
u
26
− 3u
25
+ ··· − 3u + 1
c
6
u
26
− 2u
25
+ ··· − 2u + 1
c
7
, c
8
u
26
− 10u
24
+ ··· − 2u + 1
c
9
u
26
− 4u
25
+ ··· − 4u + 1
c
10
u
26
+ 3u
24
+ ··· − 116u + 73
c
11
u
26
+ 2u
25
+ ··· + 2u + 1
c
12
u
26
+ 4u
25
+ ··· + 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 7y
25
+ ··· − y + 1
c
2
, c
5
y
26
+ 15y
25
+ ··· + 19y + 1
c
3
, c
7
, c
8
y
26
− 20y
25
+ ··· − 16y + 1
c
4
y
26
+ 22y
25
+ ··· + 2y + 1
c
6
, c
11
y
26
+ 18y
25
+ ··· − 2y + 1
c
9
, c
12
y
26
+ 16y
25
+ ··· + 12y + 1
c
10
y
26
+ 6y
25
+ ··· − 16376y + 5329
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.744693 + 0.730481I
a = −0.326891 − 0.049826I
b = 0.158314 − 1.174790I
9.92859 − 1.94515I 8.05557 + 3.20063I
u = −0.744693 − 0.730481I
a = −0.326891 + 0.049826I
b = 0.158314 + 1.174790I
9.92859 + 1.94515I 8.05557 − 3.20063I
u = 0.281526 + 0.879742I
a = −1.78119 − 0.53161I
b = 1.052870 + 0.243603I
−2.07048 + 1.35786I −2.25789 − 3.84059I
u = 0.281526 − 0.879742I
a = −1.78119 + 0.53161I
b = 1.052870 − 0.243603I
−2.07048 − 1.35786I −2.25789 + 3.84059I
u = −0.396708 + 1.055220I
a = 1.84102 + 1.11968I
b = −0.381175 − 1.017610I
6.60029 − 3.05480I 3.39325 + 5.25796I
u = −0.396708 − 1.055220I
a = 1.84102 − 1.11968I
b = −0.381175 + 1.017610I
6.60029 + 3.05480I 3.39325 − 5.25796I
u = 0.976532 + 0.651379I
a = −0.332917 − 0.030871I
b = −0.213369 − 1.266720I
7.24258 + 2.16991I 7.60959 − 1.89210I
u = 0.976532 − 0.651379I
a = −0.332917 + 0.030871I
b = −0.213369 + 1.266720I
7.24258 − 2.16991I 7.60959 + 1.89210I
u = 0.367690 + 0.692493I
a = −1.84886 − 1.52160I
b = 0.937404 − 0.046899I
−1.83720 + 1.38527I −8.37699 − 7.73251I
u = 0.367690 − 0.692493I
a = −1.84886 + 1.52160I
b = 0.937404 + 0.046899I
−1.83720 − 1.38527I −8.37699 + 7.73251I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309700 + 0.709984I
a = 0.864898 + 0.466942I
b = −0.253810 + 1.324560I
7.93378 + 0.00198I 0.780962 + 1.140220I
u = −0.309700 − 0.709984I
a = 0.864898 − 0.466942I
b = −0.253810 − 1.324560I
7.93378 − 0.00198I 0.780962 − 1.140220I
u = 0.201539 + 1.209020I
a = −0.172083 + 0.281633I
b = 0.525636 − 0.000472I
−3.65287 + 0.80825I −3.25539 − 1.80542I
u = 0.201539 − 1.209020I
a = −0.172083 − 0.281633I
b = 0.525636 + 0.000472I
−3.65287 − 0.80825I −3.25539 + 1.80542I
u = −0.713163 + 1.046300I
a = −1.40284 − 0.23800I
b = 0.239899 + 0.945977I
8.94234 − 3.65478I 7.25673 + 2.93988I
u = −0.713163 − 1.046300I
a = −1.40284 + 0.23800I
b = 0.239899 − 0.945977I
8.94234 + 3.65478I 7.25673 − 2.93988I
u = 0.112828 + 1.306440I
a = −0.149253 − 0.175433I
b = −0.339482 + 0.365880I
−2.89775 + 5.49517I 0.43892 − 4.19420I
u = 0.112828 − 1.306440I
a = −0.149253 + 0.175433I
b = −0.339482 − 0.365880I
−2.89775 − 5.49517I 0.43892 + 4.19420I
u = 0.513856 + 1.211170I
a = −1.268680 + 0.379339I
b = 0.257070 − 1.360450I
2.56406 + 5.90942I −3.25373 − 8.58917I
u = 0.513856 − 1.211170I
a = −1.268680 − 0.379339I
b = 0.257070 + 1.360450I
2.56406 − 5.90942I −3.25373 + 8.58917I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.013005 + 0.609915I
a = 4.12090 + 1.41971I
b = −0.630059 − 0.411133I
0.06562 − 5.01443I −9.64012 + 7.22969I
u = −0.013005 − 0.609915I
a = 4.12090 − 1.41971I
b = −0.630059 + 0.411133I
0.06562 + 5.01443I −9.64012 − 7.22969I
u = 0.94693 + 1.05296I
a = 0.840758 + 0.282706I
b = −0.340360 + 1.021250I
6.11694 + 4.83294I 3.37203 − 8.20308I
u = 0.94693 − 1.05296I
a = 0.840758 − 0.282706I
b = −0.340360 − 1.021250I
6.11694 − 4.83294I 3.37203 + 8.20308I
u = 0.276373 + 0.485038I
a = 1.61514 + 0.62744I
b = −0.01293 + 1.53881I
5.47733 − 2.25001I 1.37708 + 5.89841I
u = 0.276373 − 0.485038I
a = 1.61514 − 0.62744I
b = −0.01293 − 1.53881I
5.47733 + 2.25001I 1.37708 − 5.89841I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 15u
25
+ ··· − 19u + 1)(u
88
+ 44u
87
+ ··· − 14u + 1)
c
2
(u
26
+ 3u
25
+ ··· + 3u + 1)(u
88
+ 22u
86
+ ··· + 2u + 1)
c
3
(u
26
− 10u
24
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· + 4537u + 653)
c
4
(u
26
+ 11u
24
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· − 6282u + 3780)
c
5
(u
26
− 3u
25
+ ··· − 3u + 1)(u
88
+ 22u
86
+ ··· + 2u + 1)
c
6
(u
26
− 2u
25
+ ··· − 2u + 1)(u
88
− 3u
87
+ ··· − 34779u + 4553)
c
7
, c
8
(u
26
− 10u
24
+ ··· − 2u + 1)(u
88
+ u
87
+ ··· + 4537u + 653)
c
9
(u
26
− 4u
25
+ ··· − 4u + 1)(u
88
− 3u
87
+ ··· − 5791u + 1003)
c
10
(u
26
+ 3u
24
+ ··· − 116u + 73)(u
88
− u
87
+ ··· + 33861u + 11617)
c
11
(u
26
+ 2u
25
+ ··· + 2u + 1)(u
88
− 3u
87
+ ··· − 34779u + 4553)
c
12
(u
26
+ 4u
25
+ ··· + 4u + 1)(u
88
− 3u
87
+ ··· − 5791u + 1003)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 7y
25
+ ··· − y + 1)(y
88
+ 16y
87
+ ··· + 38y + 1)
c
2
, c
5
(y
26
+ 15y
25
+ ··· + 19y + 1)(y
88
+ 44y
87
+ ··· − 14y + 1)
c
3
, c
7
, c
8
(y
26
− 20y
25
+ ··· − 16y + 1)
· (y
88
− 39y
87
+ ··· − 16718609y + 426409)
c
4
(y
26
+ 22y
25
+ ··· + 2y + 1)
· (y
88
+ 47y
87
+ ··· + 424002276y + 14288400)
c
6
, c
11
(y
26
+ 18y
25
+ ··· − 2y + 1)
· (y
88
+ 47y
87
+ ··· + 457119657y + 20729809)
c
9
, c
12
(y
26
+ 16y
25
+ ··· + 12y + 1)
· (y
88
+ 37y
87
+ ··· + 28963255y + 1006009)
c
10
(y
26
+ 6y
25
+ ··· − 16376y + 5329)
· (y
88
− 13y
87
+ ··· − 5986209521y + 134954689)
21
