12a
1207
(K12a
1207
)
A knot diagram
1
Linearized knot diagam
4 11 10 9 2 3 12 5 1 6 7 8
Solving Sequence
7,11
12 8
1,3
2 6 5 10 4 9
c
11
c
7
c
12
c
2
c
6
c
5
c
10
c
3
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h9.69782 × 10
536
u
139
− 2.25657 × 10
536
u
138
+ ··· + 6.06990 × 10
539
b + 5.03879 × 10
539
,
2.09110 × 10
539
u
139
− 1.68892 × 10
539
u
138
+ ··· + 5.15941 × 10
541
a − 1.14839 × 10
541
,
u
140
− u
139
+ ··· + 1003u − 289i
I
u
2
= h−186986226u
33
+ 327109657u
32
+ ··· + 86350699b − 1171458903,
1805845965u
33
− 920160738u
32
+ ··· + 86350699a + 6335297871, u
34
− 22u
32
+ ··· + 10u + 1i
* 2 irreducible components of dim
C
= 0, with total 174 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
= h9.70 × 10
536
u
139
− 2.26 × 10
536
u
138
+ · · · + 6.07 × 10
539
b + 5.04 ×
10
539
, 2.09 × 10
539
u
139
− 1.69 × 10
539
u
138
+ · · · + 5.16 × 10
541
a − 1.15 ×
10
541
, u
140
− u
139
+ · · · + 1003u − 289i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−0.00405297u
139
+ 0.00327347u
138
+ ··· + 3.21409u + 0.222581
−0.00159769u
139
+ 0.000371764u
138
+ ··· + 2.12271u − 0.830128
a
2
=
−0.00565066u
139
+ 0.00364523u
138
+ ··· + 5.33680u − 0.607546
−0.00159769u
139
+ 0.000371764u
138
+ ··· + 2.12271u − 0.830128
a
6
=
0.00200581u
139
+ 0.00496507u
138
+ ··· − 6.08461u + 3.72627
−0.000810012u
139
+ 0.000938180u
138
+ ··· + 0.913658u + 0.556043
a
5
=
0.00402005u
139
− 0.00217381u
138
+ ··· − 5.07444u + 0.659975
0.000571152u
139
− 0.00100493u
138
+ ··· − 0.805524u + 0.766408
a
10
=
0.00270227u
139
− 0.00279415u
138
+ ··· − 1.21625u + 4.64222
−0.00228002u
139
+ 0.00212213u
138
+ ··· + 3.56568u − 0.996732
a
4
=
0.00489730u
139
− 0.00549964u
138
+ ··· − 8.88933u + 3.90747
0.0000696783u
139
− 0.00146228u
138
+ ··· + 1.57653u + 0.256233
a
9
=
0.00261727u
139
− 0.00177802u
138
+ ··· − 0.497087u + 4.05204
−0.00181158u
139
+ 0.00219701u
138
+ ··· + 2.86224u − 0.820622
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0120913u
139
+ 0.00925037u
138
+ ··· − 5.95755u − 14.8088
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 4u
139
+ ··· − 9u + 1
c
2
u
140
− 2u
139
+ ··· + 333381u − 48473
c
3
u
140
− 2u
139
+ ··· − 41435571198u − 5037373313
c
4
, c
8
u
140
+ 41u
138
+ ··· − 3278u − 326
c
5
u
140
− 36u
138
+ ··· + 1736923383u + 361950067
c
6
u
140
− 8u
139
+ ··· + 106962u + 10082
c
7
, c
11
, c
12
u
140
− u
139
+ ··· + 1003u − 289
c
9
u
140
− u
139
+ ··· + 31u − 211
c
10
u
140
+ 3u
139
+ ··· + 14u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ 10y
139
+ ··· + 27y + 1
c
2
y
140
− 40y
139
+ ··· − 91720535629y + 2349631729
c
3
y
140
+ 84y
139
+ ··· + 9.52 × 10
20
y + 2.54 × 10
19
c
4
, c
8
y
140
+ 82y
139
+ ··· + 3039300y + 106276
c
5
y
140
− 72y
139
+ ··· − 3.85 × 10
18
y + 1.31 × 10
17
c
6
y
140
+ 50y
139
+ ··· − 13461745852y + 101646724
c
7
, c
11
, c
12
y
140
− 159y
139
+ ··· − 199121y + 83521
c
9
y
140
− 17y
139
+ ··· − 3596401y + 44521
c
10
y
140
+ 11y
139
+ ··· + 18y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.664700 + 0.764460I
a = 0.786549 − 0.391919I
b = −0.777311 − 0.272732I
−4.21163 + 0.44946I 0
u = −0.664700 − 0.764460I
a = 0.786549 + 0.391919I
b = −0.777311 + 0.272732I
−4.21163 − 0.44946I 0
u = 0.723613 + 0.663890I
a = 0.100235 + 1.407650I
b = −1.098430 − 0.770465I
−4.29384 − 9.41106I 0
u = 0.723613 − 0.663890I
a = 0.100235 − 1.407650I
b = −1.098430 + 0.770465I
−4.29384 + 9.41106I 0
u = −0.875504 + 0.391347I
a = −0.694523 + 0.387506I
b = 0.785277 + 0.019643I
−1.105740 − 0.505263I 0
u = −0.875504 − 0.391347I
a = −0.694523 − 0.387506I
b = 0.785277 − 0.019643I
−1.105740 + 0.505263I 0
u = −0.733482 + 0.494442I
a = 1.337570 − 0.211604I
b = −0.097656 − 0.212794I
1.98403 − 3.21396I 0
u = −0.733482 − 0.494442I
a = 1.337570 + 0.211604I
b = −0.097656 + 0.212794I
1.98403 + 3.21396I 0
u = 1.061780 + 0.419066I
a = −0.466473 − 0.043502I
b = 0.186946 − 0.630288I
2.41235 − 5.18322I 0
u = 1.061780 − 0.419066I
a = −0.466473 + 0.043502I
b = 0.186946 + 0.630288I
2.41235 + 5.18322I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.842849 + 0.091369I
a = −0.389431 − 0.059980I
b = 0.589549 + 0.329056I
−0.971976 + 0.163551I 0
u = −0.842849 − 0.091369I
a = −0.389431 + 0.059980I
b = 0.589549 − 0.329056I
−0.971976 − 0.163551I 0
u = 0.797009 + 0.237221I
a = 0.61591 − 1.60801I
b = 0.841277 + 0.591255I
−1.00052 − 4.05079I 0
u = 0.797009 − 0.237221I
a = 0.61591 + 1.60801I
b = 0.841277 − 0.591255I
−1.00052 + 4.05079I 0
u = −0.695414 + 0.416816I
a = 0.415690 − 1.231430I
b = 0.747231 + 1.026780I
−0.84448 − 4.06575I 0
u = −0.695414 − 0.416816I
a = 0.415690 + 1.231430I
b = 0.747231 − 1.026780I
−0.84448 + 4.06575I 0
u = −0.784025 + 0.909426I
a = 0.199354 − 1.141200I
b = −1.039980 + 0.900244I
−0.7502 + 14.8929I 0
u = −0.784025 − 0.909426I
a = 0.199354 + 1.141200I
b = −1.039980 − 0.900244I
−0.7502 − 14.8929I 0
u = −0.427709 + 1.129230I
a = −0.486121 + 0.803738I
b = 0.917993 − 0.745761I
−2.94428 + 5.11499I 0
u = −0.427709 − 1.129230I
a = −0.486121 − 0.803738I
b = 0.917993 + 0.745761I
−2.94428 − 5.11499I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.110880 + 0.770452I
a = −1.176030 + 0.513815I
b = 0.959095 − 0.550578I
−2.67355 + 4.62927I 0
u = 0.110880 − 0.770452I
a = −1.176030 − 0.513815I
b = 0.959095 + 0.550578I
−2.67355 − 4.62927I 0
u = 0.579144 + 0.513632I
a = −0.502537 − 0.140677I
b = 0.652717 − 0.875480I
3.12611 + 4.01064I 0
u = 0.579144 − 0.513632I
a = −0.502537 + 0.140677I
b = 0.652717 + 0.875480I
3.12611 − 4.01064I 0
u = 0.662666 + 0.391153I
a = −0.14133 − 1.72463I
b = 0.994817 + 0.972515I
−1.03835 − 6.46385I 0
u = 0.662666 − 0.391153I
a = −0.14133 + 1.72463I
b = 0.994817 − 0.972515I
−1.03835 + 6.46385I 0
u = 0.703698 + 0.296351I
a = 1.69296 + 0.67637I
b = 1.023900 − 0.024241I
−1.23542 + 4.69462I 0
u = 0.703698 − 0.296351I
a = 1.69296 − 0.67637I
b = 1.023900 + 0.024241I
−1.23542 − 4.69462I 0
u = −1.169030 + 0.406222I
a = 0.374439 + 0.919876I
b = 1.01034 − 0.99123I
1.69637 + 3.05376I 0
u = −1.169030 − 0.406222I
a = 0.374439 − 0.919876I
b = 1.01034 + 0.99123I
1.69637 − 3.05376I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.055131 + 0.760060I
a = 0.654166 + 1.059530I
b = −0.564034 − 0.881275I
5.41822 + 1.05469I 0
u = 0.055131 − 0.760060I
a = 0.654166 − 1.059530I
b = −0.564034 + 0.881275I
5.41822 − 1.05469I 0
u = 0.512374 + 0.531816I
a = −0.124478 + 1.229360I
b = −1.19410 − 0.93878I
3.24255 − 7.63630I 0
u = 0.512374 − 0.531816I
a = −0.124478 − 1.229360I
b = −1.19410 + 0.93878I
3.24255 + 7.63630I 0
u = −0.668082 + 0.296672I
a = −0.319331 + 0.795469I
b = 0.962171 − 0.600319I
−1.87716 + 0.12463I 0
u = −0.668082 − 0.296672I
a = −0.319331 − 0.795469I
b = 0.962171 + 0.600319I
−1.87716 − 0.12463I 0
u = 0.574185 + 0.440435I
a = 0.971814 − 0.681398I
b = 0.036914 + 0.599146I
2.57035 − 1.43023I 0
u = 0.574185 − 0.440435I
a = 0.971814 + 0.681398I
b = 0.036914 − 0.599146I
2.57035 + 1.43023I 0
u = 0.462670 + 0.554740I
a = 0.28947 − 1.44217I
b = 0.268987 + 0.813665I
2.90772 − 2.18120I 0
u = 0.462670 − 0.554740I
a = 0.28947 + 1.44217I
b = 0.268987 − 0.813665I
2.90772 + 2.18120I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325781 + 0.637531I
a = 0.73161 − 1.30044I
b = −0.646866 + 0.111992I
−0.28044 + 3.17028I 0
u = −0.325781 − 0.637531I
a = 0.73161 + 1.30044I
b = −0.646866 − 0.111992I
−0.28044 − 3.17028I 0
u = 0.633748 + 1.166710I
a = 0.586035 + 0.085599I
b = −0.750696 + 0.232676I
−0.87696 − 5.20914I 0
u = 0.633748 − 1.166710I
a = 0.586035 − 0.085599I
b = −0.750696 − 0.232676I
−0.87696 + 5.20914I 0
u = 0.915236 + 0.974210I
a = −0.129646 − 0.943460I
b = 0.966530 + 0.747208I
−1.83283 − 2.03560I 0
u = 0.915236 − 0.974210I
a = −0.129646 + 0.943460I
b = 0.966530 − 0.747208I
−1.83283 + 2.03560I 0
u = −0.397448 + 0.491112I
a = −2.64127 − 0.55813I
b = −0.472527 + 0.413037I
0.04254 + 7.33492I −9.9382 − 14.3032I
u = −0.397448 − 0.491112I
a = −2.64127 + 0.55813I
b = −0.472527 − 0.413037I
0.04254 − 7.33492I −9.9382 + 14.3032I
u = −0.459772 + 1.299100I
a = −0.634517 − 0.229659I
b = 0.684407 + 0.575593I
0.44709 − 7.98394I 0
u = −0.459772 − 1.299100I
a = −0.634517 + 0.229659I
b = 0.684407 − 0.575593I
0.44709 + 7.98394I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.439314 + 0.438525I
a = −0.260113 − 1.107590I
b = −1.19873 + 1.08257I
−0.48464 − 7.47319I −11.6774 + 11.9215I
u = 0.439314 − 0.438525I
a = −0.260113 + 1.107590I
b = −1.19873 − 1.08257I
−0.48464 + 7.47319I −11.6774 − 11.9215I
u = −0.396768 + 0.443070I
a = −0.89644 + 2.45471I
b = 0.375721 − 0.782823I
2.98407 + 6.46449I 0.34509 − 10.66849I
u = −0.396768 − 0.443070I
a = −0.89644 − 2.45471I
b = 0.375721 + 0.782823I
2.98407 − 6.46449I 0.34509 + 10.66849I
u = −0.191276 + 0.560807I
a = 1.38693 − 1.88511I
b = −0.847157 + 0.495383I
0.99488 + 4.11864I 6.68742 − 8.04172I
u = −0.191276 − 0.560807I
a = 1.38693 + 1.88511I
b = −0.847157 − 0.495383I
0.99488 − 4.11864I 6.68742 + 8.04172I
u = −0.512094 + 0.288469I
a = 0.201018 + 0.891256I
b = −0.70226 − 1.39420I
−2.57763 + 2.49455I −13.1614 − 11.8667I
u = −0.512094 − 0.288469I
a = 0.201018 − 0.891256I
b = −0.70226 + 1.39420I
−2.57763 − 2.49455I −13.1614 + 11.8667I
u = 0.312147 + 0.473730I
a = −0.851897 − 0.627104I
b = 0.992979 + 0.845993I
−1.64722 − 2.64192I −6.75968 + 7.82828I
u = 0.312147 − 0.473730I
a = −0.851897 + 0.627104I
b = 0.992979 − 0.845993I
−1.64722 + 2.64192I −6.75968 − 7.82828I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564449
a = 0.133288
b = 0.672795
−0.962744 −10.1490
u = −1.43044 + 0.15138I
a = −0.115764 + 0.526391I
b = 0.782330 − 0.869276I
−3.57102 − 0.35621I 0
u = −1.43044 − 0.15138I
a = −0.115764 − 0.526391I
b = 0.782330 + 0.869276I
−3.57102 + 0.35621I 0
u = 1.45865 + 0.11674I
a = 0.64936 − 1.26547I
b = 1.006320 + 0.697960I
−4.44443 − 6.18107I 0
u = 1.45865 − 0.11674I
a = 0.64936 + 1.26547I
b = 1.006320 − 0.697960I
−4.44443 + 6.18107I 0
u = 1.46459 + 0.13353I
a = −1.213010 − 0.673295I
b = −0.792738 + 0.117029I
−7.91264 − 1.67664I 0
u = 1.46459 − 0.13353I
a = −1.213010 + 0.673295I
b = −0.792738 − 0.117029I
−7.91264 + 1.67664I 0
u = −1.47219 + 0.12110I
a = −0.231901 + 0.522863I
b = −1.54570 − 1.57835I
−8.19313 + 0.75936I 0
u = −1.47219 − 0.12110I
a = −0.231901 − 0.522863I
b = −1.54570 + 1.57835I
−8.19313 − 0.75936I 0
u = −1.48733 + 0.03501I
a = 0.322703 + 0.980063I
b = 0.724917 − 0.201965I
−5.89372 − 3.44747I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48733 − 0.03501I
a = 0.322703 − 0.980063I
b = 0.724917 + 0.201965I
−5.89372 + 3.44747I 0
u = 1.48781 + 0.05381I
a = 0.752448 − 0.618143I
b = 1.59477 + 0.64458I
−4.93916 − 2.78367I 0
u = 1.48781 − 0.05381I
a = 0.752448 + 0.618143I
b = 1.59477 − 0.64458I
−4.93916 + 2.78367I 0
u = 0.503828 + 0.073523I
a = −2.44089 − 2.01714I
b = −0.545407 − 0.128755I
−3.64336 − 1.92912I −22.2195 + 4.5913I
u = 0.503828 − 0.073523I
a = −2.44089 + 2.01714I
b = −0.545407 + 0.128755I
−3.64336 + 1.92912I −22.2195 − 4.5913I
u = −1.48908 + 0.12089I
a = −0.060076 − 0.562281I
b = −1.302230 + 0.127007I
−8.02860 − 2.49175I 0
u = −1.48908 − 0.12089I
a = −0.060076 + 0.562281I
b = −1.302230 − 0.127007I
−8.02860 + 2.49175I 0
u = 1.47894 + 0.21321I
a = −0.658120 + 0.409281I
b = −0.755694 + 0.115306I
−5.65381 − 0.48158I 0
u = 1.47894 − 0.21321I
a = −0.658120 − 0.409281I
b = −0.755694 − 0.115306I
−5.65381 + 0.48158I 0
u = 1.49203 + 0.08952I
a = −0.427255 + 0.881362I
b = −1.48446 − 1.13266I
−8.45812 − 5.96609I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49203 − 0.08952I
a = −0.427255 − 0.881362I
b = −1.48446 + 1.13266I
−8.45812 + 5.96609I 0
u = 1.48826 + 0.17864I
a = 0.535093 − 1.113330I
b = 0.823116 + 0.394357I
−6.31084 − 5.99967I 0
u = 1.48826 − 0.17864I
a = 0.535093 + 1.113330I
b = 0.823116 − 0.394357I
−6.31084 + 5.99967I 0
u = −0.335044 + 0.367577I
a = 2.03708 + 0.63434I
b = 0.726011 − 0.525189I
−2.09120 − 0.13055I −11.23045 − 3.27237I
u = −0.335044 − 0.367577I
a = 2.03708 − 0.63434I
b = 0.726011 + 0.525189I
−2.09120 + 0.13055I −11.23045 + 3.27237I
u = 1.50933 + 0.13545I
a = 1.61865 + 0.68437I
b = 0.541875 − 0.007146I
−6.33975 − 9.50478I 0
u = 1.50933 − 0.13545I
a = 1.61865 − 0.68437I
b = 0.541875 + 0.007146I
−6.33975 + 9.50478I 0
u = −1.51497 + 0.13006I
a = −0.185483 − 0.538002I
b = −1.68824 + 1.32651I
−7.94331 + 4.70663I 0
u = −1.51497 − 0.13006I
a = −0.185483 + 0.538002I
b = −1.68824 − 1.32651I
−7.94331 − 4.70663I 0
u = 1.52067 + 0.11940I
a = −0.289867 + 1.292590I
b = −0.475269 − 1.136580I
−3.51038 − 8.39205I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52067 − 0.11940I
a = −0.289867 − 1.292590I
b = −0.475269 + 1.136580I
−3.51038 + 8.39205I 0
u = −1.51859 + 0.15663I
a = −0.527020 − 0.806732I
b = −0.554889 + 0.927513I
−3.66738 + 4.69280I 0
u = −1.51859 − 0.15663I
a = −0.527020 + 0.806732I
b = −0.554889 − 0.927513I
−3.66738 − 4.69280I 0
u = 1.52841
a = −0.713515
b = −1.27813
−7.81776 0
u = −1.53279 + 0.01394I
a = 1.14809 − 1.21363I
b = 0.620121 + 0.251284I
−10.52960 + 2.20106I 0
u = −1.53279 − 0.01394I
a = 1.14809 + 1.21363I
b = 0.620121 − 0.251284I
−10.52960 − 2.20106I 0
u = −1.52839 + 0.12828I
a = 0.081023 − 0.416786I
b = 1.48690 + 1.88540I
−7.13324 + 9.48597I 0
u = −1.52839 − 0.12828I
a = 0.081023 + 0.416786I
b = 1.48690 − 1.88540I
−7.13324 − 9.48597I 0
u = 1.54665 + 0.05449I
a = 0.009875 + 0.380881I
b = 0.95023 − 2.11525I
−9.57912 − 3.58725I 0
u = 1.54665 − 0.05449I
a = 0.009875 − 0.380881I
b = 0.95023 + 2.11525I
−9.57912 + 3.58725I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54101 + 0.15944I
a = 0.564425 + 0.524302I
b = 1.75708 − 0.92401I
−3.63309 + 10.12680I 0
u = −1.54101 − 0.15944I
a = 0.564425 − 0.524302I
b = 1.75708 + 0.92401I
−3.63309 − 10.12680I 0
u = −1.56856 + 0.00769I
a = −0.87398 + 1.15965I
b = −0.719647 − 0.558022I
−9.07794 − 4.17420I 0
u = −1.56856 − 0.00769I
a = −0.87398 − 1.15965I
b = −0.719647 + 0.558022I
−9.07794 + 4.17420I 0
u = −1.57737 + 0.02561I
a = −0.621805 − 0.176074I
b = −0.638593 − 0.178351I
−5.01387 − 2.33379I 0
u = −1.57737 − 0.02561I
a = −0.621805 + 0.176074I
b = −0.638593 + 0.178351I
−5.01387 + 2.33379I 0
u = −0.108930 + 0.404335I
a = −1.95782 + 1.65702I
b = 1.168180 − 0.645412I
−2.66601 + 4.44912I −15.4555 − 3.5906I
u = −0.108930 − 0.404335I
a = −1.95782 − 1.65702I
b = 1.168180 + 0.645412I
−2.66601 − 4.44912I −15.4555 + 3.5906I
u = 1.59026 + 0.06498I
a = −0.177485 + 0.499893I
b = −1.46257 − 1.12144I
−9.55332 − 1.37380I 0
u = 1.59026 − 0.06498I
a = −0.177485 − 0.499893I
b = −1.46257 + 1.12144I
−9.55332 + 1.37380I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59423 + 0.11837I
a = −0.352989 − 0.889997I
b = −1.32213 + 1.32352I
−8.72906 + 8.38051I 0
u = −1.59423 − 0.11837I
a = −0.352989 + 0.889997I
b = −1.32213 − 1.32352I
−8.72906 − 8.38051I 0
u = −1.60372 + 0.21478I
a = 0.513235 + 0.943608I
b = 1.32832 − 0.91986I
−12.0451 + 12.7341I 0
u = −1.60372 − 0.21478I
a = 0.513235 − 0.943608I
b = 1.32832 + 0.91986I
−12.0451 − 12.7341I 0
u = 1.61829 + 0.08905I
a = −0.115496 + 0.480212I
b = −1.201190 − 0.645880I
−9.46916 − 1.00537I 0
u = 1.61829 − 0.08905I
a = −0.115496 − 0.480212I
b = −1.201190 + 0.645880I
−9.46916 + 1.00537I 0
u = 1.62968 + 0.05452I
a = −0.230254 − 0.511771I
b = −1.31338 + 1.55457I
−9.05093 + 2.51533I 0
u = 1.62968 − 0.05452I
a = −0.230254 + 0.511771I
b = −1.31338 − 1.55457I
−9.05093 − 2.51533I 0
u = 1.61209 + 0.25281I
a = 0.008322 − 0.664491I
b = 0.931965 + 0.237653I
−11.78290 − 4.33530I 0
u = 1.61209 − 0.25281I
a = 0.008322 + 0.664491I
b = 0.931965 − 0.237653I
−11.78290 + 4.33530I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.300912 + 0.205547I
a = 2.41558 + 2.51152I
b = −0.669129 + 0.407572I
0.23225 + 4.08304I −16.4105 − 4.0590I
u = 0.300912 − 0.205547I
a = 2.41558 − 2.51152I
b = −0.669129 − 0.407572I
0.23225 − 4.08304I −16.4105 + 4.0590I
u = 0.199111 + 0.298771I
a = 1.22881 + 1.87046I
b = 0.890082 − 0.895262I
−2.54694 + 0.86537I −12.46402 + 5.98089I
u = 0.199111 − 0.298771I
a = 1.22881 − 1.87046I
b = 0.890082 + 0.895262I
−2.54694 − 0.86537I −12.46402 − 5.98089I
u = 1.61375 + 0.36334I
a = −0.368619 + 0.873433I
b = −1.33880 − 0.95632I
−9.8237 − 10.4986I 0
u = 1.61375 − 0.36334I
a = −0.368619 − 0.873433I
b = −1.33880 + 0.95632I
−9.8237 + 10.4986I 0
u = 1.64173 + 0.29194I
a = 0.429051 − 0.914569I
b = 1.34940 + 1.02524I
−8.7098 − 19.4012I 0
u = 1.64173 − 0.29194I
a = 0.429051 + 0.914569I
b = 1.34940 − 1.02524I
−8.7098 + 19.4012I 0
u = −0.187115 + 0.267019I
a = 0.21996 − 3.10938I
b = −1.014640 + 0.389268I
0.93632 + 1.85529I 1.08312 − 2.65422I
u = −0.187115 − 0.267019I
a = 0.21996 + 3.10938I
b = −1.014640 − 0.389268I
0.93632 − 1.85529I 1.08312 + 2.65422I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.076035 + 0.309971I
a = 2.55660 − 1.68509I
b = −0.708724 + 0.256940I
1.01016 + 1.78617I −0.59593 − 2.45671I
u = 0.076035 − 0.309971I
a = 2.55660 + 1.68509I
b = −0.708724 − 0.256940I
1.01016 − 1.78617I −0.59593 + 2.45671I
u = −1.67758 + 0.21213I
a = −0.447388 − 0.880625I
b = −1.23909 + 0.92102I
−10.76140 + 6.29072I 0
u = −1.67758 − 0.21213I
a = −0.447388 + 0.880625I
b = −1.23909 − 0.92102I
−10.76140 − 6.29072I 0
u = −1.66320 + 0.34428I
a = 0.002532 + 0.582245I
b = 1.022320 − 0.244740I
−8.53641 + 10.73160I 0
u = −1.66320 − 0.34428I
a = 0.002532 − 0.582245I
b = 1.022320 + 0.244740I
−8.53641 − 10.73160I 0
u = −1.82968 + 0.54136I
a = 0.063321 − 0.344650I
b = −0.723983 + 0.035174I
−7.56867 + 2.29891I 0
u = −1.82968 − 0.54136I
a = 0.063321 + 0.344650I
b = −0.723983 − 0.035174I
−7.56867 − 2.29891I 0
u = 2.04595 + 0.16785I
a = −0.053376 + 0.312098I
b = −0.511875 − 0.170646I
−8.05626 + 0.26551I 0
u = 2.04595 − 0.16785I
a = −0.053376 − 0.312098I
b = −0.511875 + 0.170646I
−8.05626 − 0.26551I 0
18
II.
I
u
2
= h−1.87 × 10
8
u
33
+ 3.27 × 10
8
u
32
+ · · · + 8.64 × 10
7
b − 1.17 × 10
9
, 1.81 ×
10
9
u
33
−9.20×10
8
u
32
+· · ·+8.64×10
7
a+6.34×10
9
, u
34
−22u
32
+· · ·+10u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−20.9129u
33
+ 10.6561u
32
+ ··· − 457.670u − 73.3671
2.16543u
33
− 3.78815u
32
+ ··· + 81.8945u + 13.5663
a
2
=
−18.7475u
33
+ 6.86794u
32
+ ··· − 375.776u − 59.8008
2.16543u
33
− 3.78815u
32
+ ··· + 81.8945u + 13.5663
a
6
=
5.06829u
33
− 6.67284u
32
+ ··· + 17.1786u − 2.50160
0.180126u
33
− 3.86825u
32
+ ··· − 97.1453u − 16.8136
a
5
=
−8.79495u
33
+ 2.09806u
32
+ ··· − 264.937u − 46.2246
2.94152u
33
− 5.16362u
32
+ ··· − 51.1550u − 8.71002
a
10
=
10.9766u
33
+ 2.51680u
32
+ ··· + 310.285u + 52.7726
−7.26168u
33
+ 9.08502u
32
+ ··· − 79.8501u − 11.7365
a
4
=
−16.9016u
33
+ 7.90644u
32
+ ··· − 339.054u − 55.2055
−0.163445u
33
− 1.31578u
32
+ ··· + 22.9550u + 4.29848
a
9
=
0.910329u
33
+ 11.9905u
32
+ ··· + 194.865u + 35.1480
−9.87884u
33
+ 11.0194u
32
+ ··· − 95.8747u − 14.1151
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2794613904
86350699
u
33
−
2574155598
86350699
u
32
+ ··· +
37461769996
86350699
u +
4272649106
86350699
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 11u
33
+ ··· − 2u + 1
c
2
u
34
− 3u
33
+ ··· − 8u + 1
c
3
u
34
− u
33
+ ··· + 7u + 1
c
4
u
34
+ u
33
+ ··· + 21u
2
+ 2
c
5
u
34
− 3u
33
+ ··· + 18u + 1
c
6
u
34
− 3u
33
+ ··· − 4u + 2
c
7
u
34
− 22u
32
+ ··· − 10u + 1
c
8
u
34
− u
33
+ ··· + 21u
2
+ 2
c
9
u
34
+ 2u
33
+ ··· + 4u + 1
c
10
u
34
− u
32
+ ··· + u + 1
c
11
, c
12
u
34
− 22u
32
+ ··· + 10u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 5y
33
+ ··· + 6y + 1
c
2
y
34
− 9y
33
+ ··· − 10y + 1
c
3
y
34
+ 23y
33
+ ··· + 31y + 1
c
4
, c
8
y
34
+ 25y
33
+ ··· + 84y + 4
c
5
y
34
− 17y
33
+ ··· − 26y + 1
c
6
y
34
+ 17y
33
+ ··· + 44y + 4
c
7
, c
11
, c
12
y
34
− 44y
33
+ ··· − 34y + 1
c
9
y
34
− 10y
33
+ ··· − 2y + 1
c
10
y
34
− 2y
33
+ ··· + 25y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.989279 + 0.203665I
a = 0.734686 − 0.351984I
b = −0.612336 + 0.017182I
−0.768130 − 0.646243I 4.55850 + 11.73565I
u = −0.989279 − 0.203665I
a = 0.734686 + 0.351984I
b = −0.612336 − 0.017182I
−0.768130 + 0.646243I 4.55850 − 11.73565I
u = 0.937641 + 0.055659I
a = 0.76662 + 1.30586I
b = 0.952695 − 0.837177I
0.80858 + 5.24365I −5.52201 − 7.49048I
u = 0.937641 − 0.055659I
a = 0.76662 − 1.30586I
b = 0.952695 + 0.837177I
0.80858 − 5.24365I −5.52201 + 7.49048I
u = −0.840695 + 0.352056I
a = 0.476619 + 1.233590I
b = 1.128380 − 0.531768I
−0.07404 + 2.79039I −7.16144 − 3.77932I
u = −0.840695 − 0.352056I
a = 0.476619 − 1.233590I
b = 1.128380 + 0.531768I
−0.07404 − 2.79039I −7.16144 + 3.77932I
u = 0.307755 + 0.803304I
a = −0.761474 − 0.991730I
b = 1.046430 + 0.758500I
−1.91553 − 4.83286I −4.81123 + 6.61635I
u = 0.307755 − 0.803304I
a = −0.761474 + 0.991730I
b = 1.046430 − 0.758500I
−1.91553 + 4.83286I −4.81123 − 6.61635I
u = 0.757447 + 0.152912I
a = 0.078985 − 1.049000I
b = −0.496303 − 0.391394I
1.48015 − 5.95377I −7.86042 + 7.92767I
u = 0.757447 − 0.152912I
a = 0.078985 + 1.049000I
b = −0.496303 + 0.391394I
1.48015 + 5.95377I −7.86042 − 7.92767I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117754 + 0.755803I
a = −0.254223 + 0.805048I
b = −0.276335 + 0.438138I
0.02355 − 6.24126I −8.21423 + 5.84475I
u = 0.117754 − 0.755803I
a = −0.254223 − 0.805048I
b = −0.276335 − 0.438138I
0.02355 + 6.24126I −8.21423 − 5.84475I
u = −1.45892 + 0.00202I
a = −0.467200 − 0.594925I
b = −1.002530 + 0.141984I
−6.65687 − 2.02827I 0
u = −1.45892 − 0.00202I
a = −0.467200 + 0.594925I
b = −1.002530 − 0.141984I
−6.65687 + 2.02827I 0
u = 1.47127 + 0.12256I
a = −0.55365 + 1.30221I
b = −0.872420 − 0.726831I
−4.84652 − 6.29791I 0
u = 1.47127 − 0.12256I
a = −0.55365 − 1.30221I
b = −0.872420 + 0.726831I
−4.84652 + 6.29791I 0
u = −1.51061 + 0.14842I
a = 0.880143 − 0.339347I
b = 0.790066 + 0.560236I
−5.96983 + 8.96814I 0
u = −1.51061 − 0.14842I
a = 0.880143 + 0.339347I
b = 0.790066 − 0.560236I
−5.96983 − 8.96814I 0
u = −0.055421 + 0.471133I
a = −2.45158 + 1.46306I
b = 0.743456 − 0.481939I
0.61118 + 4.38332I −5.0601 − 16.0624I
u = −0.055421 − 0.471133I
a = −2.45158 − 1.46306I
b = 0.743456 + 0.481939I
0.61118 − 4.38332I −5.0601 + 16.0624I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362471 + 0.293998I
a = −1.234700 + 0.347680I
b = 0.223830 − 0.867827I
−2.69779 + 1.69937I −13.14521 − 2.88968I
u = −0.362471 − 0.293998I
a = −1.234700 − 0.347680I
b = 0.223830 + 0.867827I
−2.69779 − 1.69937I −13.14521 + 2.88968I
u = 1.55029 + 0.04466I
a = 0.148100 + 0.731735I
b = −0.041462 − 1.189880I
−9.47670 − 2.74180I 0
u = 1.55029 − 0.04466I
a = 0.148100 − 0.731735I
b = −0.041462 + 1.189880I
−9.47670 + 2.74180I 0
u = 1.59021 + 0.00218I
a = −0.256671 + 0.520415I
b = −1.45056 − 1.15797I
−9.04202 − 1.90270I 0
u = 1.59021 − 0.00218I
a = −0.256671 − 0.520415I
b = −1.45056 + 1.15797I
−9.04202 + 1.90270I 0
u = −1.58709 + 0.15483I
a = −0.357886 − 0.861043I
b = −1.38538 + 1.22934I
−8.86158 + 7.90479I 0
u = −1.58709 − 0.15483I
a = −0.357886 + 0.861043I
b = −1.38538 − 1.22934I
−8.86158 − 7.90479I 0
u = −1.61457 + 0.18278I
a = −0.426045 + 0.244454I
b = −0.669300 − 0.364931I
−6.67896 + 1.57798I 0
u = −1.61457 − 0.18278I
a = −0.426045 − 0.244454I
b = −0.669300 + 0.364931I
−6.67896 − 1.57798I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.251994 + 0.021132I
a = 0.23982 − 3.40414I
b = 1.078590 + 0.516054I
−2.15043 − 2.00413I −13.9856 + 2.3495I
u = −0.251994 − 0.021132I
a = 0.23982 + 3.40414I
b = 1.078590 − 0.516054I
−2.15043 + 2.00413I −13.9856 − 2.3495I
u = 1.93868 + 0.15000I
a = −0.061543 + 0.305664I
b = −0.656821 − 0.339100I
−7.93749 − 1.05206I 0
u = 1.93868 − 0.15000I
a = −0.061543 − 0.305664I
b = −0.656821 + 0.339100I
−7.93749 + 1.05206I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
34
− 11u
33
+ ··· − 2u + 1)(u
140
+ 4u
139
+ ··· − 9u + 1)
c
2
(u
34
− 3u
33
+ ··· − 8u + 1)(u
140
− 2u
139
+ ··· + 333381u − 48473)
c
3
(u
34
− u
33
+ ··· + 7u + 1)
· (u
140
− 2u
139
+ ··· − 41435571198u − 5037373313)
c
4
(u
34
+ u
33
+ ··· + 21u
2
+ 2)(u
140
+ 41u
138
+ ··· − 3278u − 326)
c
5
(u
34
− 3u
33
+ ··· + 18u + 1)
· (u
140
− 36u
138
+ ··· + 1736923383u + 361950067)
c
6
(u
34
− 3u
33
+ ··· − 4u + 2)(u
140
− 8u
139
+ ··· + 106962u + 10082)
c
7
(u
34
− 22u
32
+ ··· − 10u + 1)(u
140
− u
139
+ ··· + 1003u − 289)
c
8
(u
34
− u
33
+ ··· + 21u
2
+ 2)(u
140
+ 41u
138
+ ··· − 3278u − 326)
c
9
(u
34
+ 2u
33
+ ··· + 4u + 1)(u
140
− u
139
+ ··· + 31u − 211)
c
10
(u
34
− u
32
+ ··· + u + 1)(u
140
+ 3u
139
+ ··· + 14u − 1)
c
11
, c
12
(u
34
− 22u
32
+ ··· + 10u + 1)(u
140
− u
139
+ ··· + 1003u − 289)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
34
+ 5y
33
+ ··· + 6y + 1)(y
140
+ 10y
139
+ ··· + 27y + 1)
c
2
(y
34
− 9y
33
+ ··· − 10y + 1)
· (y
140
− 40y
139
+ ··· − 91720535629y + 2349631729)
c
3
(y
34
+ 23y
33
+ ··· + 31y + 1)
· (y
140
+ 84y
139
+ ··· + 9.52 × 10
20
y + 2.54 × 10
19
)
c
4
, c
8
(y
34
+ 25y
33
+ ··· + 84y + 4)
· (y
140
+ 82y
139
+ ··· + 3039300y + 106276)
c
5
(y
34
− 17y
33
+ ··· − 26y + 1)
· (y
140
− 72y
139
+ ··· − 3.85 × 10
18
y + 1.31 × 10
17
)
c
6
(y
34
+ 17y
33
+ ··· + 44y + 4)
· (y
140
+ 50y
139
+ ··· − 13461745852y + 101646724)
c
7
, c
11
, c
12
(y
34
− 44y
33
+ ··· − 34y + 1)
· (y
140
− 159y
139
+ ··· − 199121y + 83521)
c
9
(y
34
− 10y
33
+ ··· − 2y + 1)(y
140
− 17y
139
+ ··· − 3596401y + 44521)
c
10
(y
34
− 2y
33
+ ··· + 25y + 1)(y
140
+ 11y
139
+ ··· + 18y + 1)
27
