11a
328
(K11a
328
)
A knot diagram
1
Linearized knot diagam
9 6 1 8 10 2 11 4 3 7 5
Solving Sequence
5,8
4
1,9
2 3 11 7 6 10
c
4
c
8
c
1
c
3
c
11
c
7
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.23921 × 10
242
u
86
− 7.92450 × 10
242
u
85
+ ··· + 2.99360 × 10
243
b + 1.15001 × 10
243
,
2.69979 × 10
242
u
86
+ 1.06399 × 10
243
u
85
+ ··· + 5.98721 × 10
243
a − 3.98514 × 10
244
,
u
87
+ 4u
86
+ ··· + 343u − 49i
I
u
2
= h491u
12
− 351u
11
+ ··· + 2441b + 3926, 3175u
12
+ 6674u
11
+ ··· + 4882a − 4765,
u
13
+ u
12
+ 5u
11
+ 5u
10
+ 15u
9
+ 6u
8
+ 26u
7
− 3u
6
+ 25u
5
− 10u
4
+ 13u
3
− 5u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 100 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−2.24 × 10
242
u
86
− 7.92 × 10
242
u
85
+ · · · + 2.99 × 10
243
b + 1.15 ×
10
243
, 2.70 × 10
242
u
86
+ 1.06 × 10
243
u
85
+ · · · + 5.99 × 10
243
a − 3.99 ×
10
244
, u
87
+ 4u
86
+ · · · + 343u − 49i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
−0.0450926u
86
− 0.177711u
85
+ ··· − 17.8452u + 6.65609
0.0747999u
86
+ 0.264715u
85
+ ··· − 0.552281u − 0.384156
a
9
=
u
u
3
+ u
a
2
=
0.0402372u
86
+ 0.122380u
85
+ ··· − 33.7223u + 8.81924
0.0372983u
86
+ 0.116784u
85
+ ··· + 1.89332u − 0.241227
a
3
=
−0.0493242u
86
− 0.246384u
85
+ ··· − 11.7605u − 0.960720
0.0348186u
86
+ 0.139522u
85
+ ··· − 21.6142u + 4.39832
a
11
=
0.0297073u
86
+ 0.0870039u
85
+ ··· − 18.3975u + 6.27193
0.0747999u
86
+ 0.264715u
85
+ ··· − 0.552281u − 0.384156
a
7
=
0.0601123u
86
+ 0.192499u
85
+ ··· − 42.5585u + 12.4589
−0.0878581u
86
− 0.355305u
85
+ ··· + 15.9562u − 1.44904
a
6
=
0.0993724u
86
+ 0.357805u
85
+ ··· − 25.6649u + 5.15445
0.0206546u
86
+ 0.131560u
85
+ ··· + 0.640094u + 1.53755
a
10
=
−0.106056u
86
− 0.436946u
85
+ ··· + 36.4451u − 8.52379
−0.0235474u
86
− 0.0851142u
85
+ ··· + 9.34856u − 2.37135
a
10
=
−0.106056u
86
− 0.436946u
85
+ ··· + 36.4451u − 8.52379
−0.0235474u
86
− 0.0851142u
85
+ ··· + 9.34856u − 2.37135
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.108591u
86
+ 0.627995u
85
+ ··· − 113.643u + 28.5257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
87
+ 3u
86
+ ··· − 5484u + 667
c
2
, c
6
u
87
+ u
86
+ ··· − 140u + 23
c
3
2(2u
87
− 17u
86
+ ··· − 8u + 1)
c
4
, c
8
u
87
− 4u
86
+ ··· + 343u + 49
c
5
u
87
− 3u
86
+ ··· + 11633u + 2362
c
7
, c
10
2(2u
87
+ 5u
86
+ ··· + 9624u + 539)
c
9
2(2u
87
− 5u
86
+ ··· + 1311u + 349)
c
11
u
87
+ 2u
86
+ ··· + 2885u + 538
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
87
− 13y
86
+ ··· + 17748096y −444889
c
2
, c
6
y
87
+ 45y
86
+ ··· + 11504y −529
c
3
4(4y
87
− 13y
86
+ ··· − 4y −1)
c
4
, c
8
y
87
+ 66y
86
+ ··· + 43561y −2401
c
5
y
87
+ 9y
86
+ ··· − 55400087y −5579044
c
7
, c
10
4(4y
87
− 285y
86
+ ··· + 1.28127 × 10
7
y −290521)
c
9
4(4y
87
+ 103y
86
+ ··· − 1.77548 × 10
7
y −121801)
c
11
y
87
− 38y
86
+ ··· + 7135321y −289444
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776879 + 0.541054I
a = 0.188536 + 1.157520I
b = 1.026510 − 0.627724I
1.01962 + 3.49300I 0
u = −0.776879 − 0.541054I
a = 0.188536 − 1.157520I
b = 1.026510 + 0.627724I
1.01962 − 3.49300I 0
u = 1.007580 + 0.327641I
a = 0.183992 + 0.069606I
b = 0.789772 − 0.734118I
−1.60864 + 6.07731I 0
u = 1.007580 − 0.327641I
a = 0.183992 − 0.069606I
b = 0.789772 + 0.734118I
−1.60864 − 6.07731I 0
u = 0.245817 + 0.897592I
a = 1.80503 − 0.59455I
b = −0.938277 + 0.817700I
3.46748 + 3.58811I 0
u = 0.245817 − 0.897592I
a = 1.80503 + 0.59455I
b = −0.938277 − 0.817700I
3.46748 − 3.58811I 0
u = 0.908219 + 0.099499I
a = 0.364543 − 0.135798I
b = −0.390262 − 0.953575I
5.02660 − 6.57361I 0
u = 0.908219 − 0.099499I
a = 0.364543 + 0.135798I
b = −0.390262 + 0.953575I
5.02660 + 6.57361I 0
u = −0.374562 + 1.029910I
a = 1.97132 − 0.41269I
b = −2.04798 − 0.80570I
−0.50770 − 7.93768I 0
u = −0.374562 − 1.029910I
a = 1.97132 + 0.41269I
b = −2.04798 + 0.80570I
−0.50770 + 7.93768I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217099 + 1.081390I
a = −1.90936 + 0.88490I
b = 0.529903 + 0.247555I
−0.703925 − 0.037215I 0
u = −0.217099 − 1.081390I
a = −1.90936 − 0.88490I
b = 0.529903 − 0.247555I
−0.703925 + 0.037215I 0
u = −0.220013 + 1.097370I
a = −0.953091 − 0.049330I
b = 0.613788 + 0.509488I
−0.94053 − 1.58665I 0
u = −0.220013 − 1.097370I
a = −0.953091 + 0.049330I
b = 0.613788 − 0.509488I
−0.94053 + 1.58665I 0
u = −0.027487 + 1.147150I
a = −0.068691 − 0.603804I
b = 0.109168 − 1.084490I
−2.95518 − 0.92414I 0
u = −0.027487 − 1.147150I
a = −0.068691 + 0.603804I
b = 0.109168 + 1.084490I
−2.95518 + 0.92414I 0
u = −0.834059 + 0.034209I
a = −0.225565 − 0.290060I
b = −0.822239 + 0.737364I
3.93560 + 2.19338I −1.92699 − 3.84180I
u = −0.834059 − 0.034209I
a = −0.225565 + 0.290060I
b = −0.822239 − 0.737364I
3.93560 − 2.19338I −1.92699 + 3.84180I
u = 0.202235 + 1.161160I
a = −1.79634 + 0.72293I
b = 0.802586 − 0.468686I
2.03222 + 0.78901I 0
u = 0.202235 − 1.161160I
a = −1.79634 − 0.72293I
b = 0.802586 + 0.468686I
2.03222 − 0.78901I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012862 + 1.192010I
a = −1.90807 − 0.84701I
b = 1.94746 + 1.83329I
−3.17906 + 6.66017I 0
u = 0.012862 − 1.192010I
a = −1.90807 + 0.84701I
b = 1.94746 − 1.83329I
−3.17906 − 6.66017I 0
u = 0.235984 + 1.200170I
a = 1.48127 + 0.13165I
b = −0.951440 − 0.148069I
−4.06130 + 2.44977I 0
u = 0.235984 − 1.200170I
a = 1.48127 − 0.13165I
b = −0.951440 + 0.148069I
−4.06130 − 2.44977I 0
u = 0.761682 + 0.143291I
a = −0.976859 + 0.023521I
b = −0.563074 + 0.406965I
−1.92081 + 0.61884I −7.87734 − 1.96780I
u = 0.761682 − 0.143291I
a = −0.976859 − 0.023521I
b = −0.563074 − 0.406965I
−1.92081 − 0.61884I −7.87734 + 1.96780I
u = 0.112847 + 1.223690I
a = 2.47523 − 0.15334I
b = −2.44222 + 1.06035I
−7.01048 + 0.84605I 0
u = 0.112847 − 1.223690I
a = 2.47523 + 0.15334I
b = −2.44222 − 1.06035I
−7.01048 − 0.84605I 0
u = −0.755476 + 0.104993I
a = −0.419450 − 0.027979I
b = 0.223634 + 0.914975I
1.83703 − 2.21620I −3.51529 + 3.55324I
u = −0.755476 − 0.104993I
a = −0.419450 + 0.027979I
b = 0.223634 − 0.914975I
1.83703 + 2.21620I −3.51529 − 3.55324I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.210730 + 0.265007I
a = −0.113980 + 0.093687I
b = −0.811339 − 0.684971I
1.28183 − 11.73510I 0
u = −1.210730 − 0.265007I
a = −0.113980 − 0.093687I
b = −0.811339 + 0.684971I
1.28183 + 11.73510I 0
u = −0.370860 + 1.187910I
a = −1.44787 + 0.53047I
b = 1.49725 − 0.21594I
−0.72894 − 6.29842I 0
u = −0.370860 − 1.187910I
a = −1.44787 − 0.53047I
b = 1.49725 + 0.21594I
−0.72894 + 6.29842I 0
u = 0.082178 + 1.267230I
a = 1.81882 + 0.60579I
b = −1.43238 + 0.41505I
−7.65344 + 1.93513I 0
u = 0.082178 − 1.267230I
a = 1.81882 − 0.60579I
b = −1.43238 − 0.41505I
−7.65344 − 1.93513I 0
u = 0.154767 + 1.267260I
a = −1.123800 + 0.806234I
b = 1.16362 − 1.85704I
−6.42084 + 3.25398I 0
u = 0.154767 − 1.267260I
a = −1.123800 − 0.806234I
b = 1.16362 + 1.85704I
−6.42084 − 3.25398I 0
u = 0.315271 + 0.626744I
a = 0.014758 − 0.894661I
b = 0.34862 + 1.39642I
4.42600 − 0.87222I −1.33257 − 4.60840I
u = 0.315271 − 0.626744I
a = 0.014758 + 0.894661I
b = 0.34862 − 1.39642I
4.42600 + 0.87222I −1.33257 + 4.60840I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138100 + 1.293420I
a = −1.55432 + 0.54367I
b = 1.168620 + 0.682207I
−4.91824 − 8.48201I 0
u = −0.138100 − 1.293420I
a = −1.55432 − 0.54367I
b = 1.168620 − 0.682207I
−4.91824 + 8.48201I 0
u = 0.428306 + 1.245240I
a = −1.62246 + 0.15416I
b = 0.755026 − 0.694879I
1.44453 + 11.33890I 0
u = 0.428306 − 1.245240I
a = −1.62246 − 0.15416I
b = 0.755026 + 0.694879I
1.44453 − 11.33890I 0
u = 0.181300 + 1.304480I
a = −0.363009 − 0.100801I
b = 0.459339 − 0.988301I
−6.35047 + 2.80896I 0
u = 0.181300 − 1.304480I
a = −0.363009 + 0.100801I
b = 0.459339 + 0.988301I
−6.35047 − 2.80896I 0
u = −0.388024 + 1.265100I
a = −1.80417 + 0.04080I
b = 1.63904 + 0.82465I
0.10297 − 6.59252I 0
u = −0.388024 − 1.265100I
a = −1.80417 − 0.04080I
b = 1.63904 − 0.82465I
0.10297 + 6.59252I 0
u = −0.328530 + 1.294480I
a = 1.49353 + 0.38820I
b = −0.815892 − 0.631455I
−2.48697 − 6.11850I 0
u = −0.328530 − 1.294480I
a = 1.49353 − 0.38820I
b = −0.815892 + 0.631455I
−2.48697 + 6.11850I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012517 + 1.341530I
a = 0.877313 − 0.120821I
b = −0.758450 − 0.797102I
−6.25662 + 2.11272I 0
u = 0.012517 − 1.341530I
a = 0.877313 + 0.120821I
b = −0.758450 + 0.797102I
−6.25662 − 2.11272I 0
u = 1.354960 + 0.065636I
a = −0.249415 − 0.140378I
b = −0.659999 + 0.151798I
−2.16816 + 0.86837I 0
u = 1.354960 − 0.065636I
a = −0.249415 + 0.140378I
b = −0.659999 − 0.151798I
−2.16816 − 0.86837I 0
u = 0.100175 + 0.612166I
a = 0.37206 + 2.60657I
b = −0.273208 + 0.157111I
−1.084890 + 0.871384I −15.6106 − 3.4978I
u = 0.100175 − 0.612166I
a = 0.37206 − 2.60657I
b = −0.273208 − 0.157111I
−1.084890 − 0.871384I −15.6106 + 3.4978I
u = −0.67656 + 1.24255I
a = 0.0242517 − 0.0831628I
b = 0.012280 + 0.372469I
−0.78893 − 2.23324I 0
u = −0.67656 − 1.24255I
a = 0.0242517 + 0.0831628I
b = 0.012280 − 0.372469I
−0.78893 + 2.23324I 0
u = −0.543318 + 0.090886I
a = 0.411855 − 1.155200I
b = −0.757344 − 0.051881I
2.36842 + 2.62824I −3.63497 − 2.44788I
u = −0.543318 − 0.090886I
a = 0.411855 + 1.155200I
b = −0.757344 + 0.051881I
2.36842 − 2.62824I −3.63497 + 2.44788I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.42905 + 1.44683I
a = 1.54404 − 0.21136I
b = −1.51558 + 1.17301I
−7.14017 + 11.20710I 0
u = 0.42905 − 1.44683I
a = 1.54404 + 0.21136I
b = −1.51558 − 1.17301I
−7.14017 − 11.20710I 0
u = 0.43735 + 1.45185I
a = −1.149860 − 0.022344I
b = 1.21403 − 0.98521I
−7.95756 + 5.21172I 0
u = 0.43735 − 1.45185I
a = −1.149860 + 0.022344I
b = 1.21403 + 0.98521I
−7.95756 − 5.21172I 0
u = −0.12280 + 1.51626I
a = −0.377043 + 0.062903I
b = 0.441833 + 0.292673I
−0.68412 − 1.98002I 0
u = −0.12280 − 1.51626I
a = −0.377043 − 0.062903I
b = 0.441833 − 0.292673I
−0.68412 + 1.98002I 0
u = 0.403739 + 0.208025I
a = 0.804446 − 0.453238I
b = −0.259208 − 1.215850I
4.93158 + 1.73284I 1.22516 − 5.83487I
u = 0.403739 − 0.208025I
a = 0.804446 + 0.453238I
b = −0.259208 + 1.215850I
4.93158 − 1.73284I 1.22516 + 5.83487I
u = −0.50070 + 1.46622I
a = −1.44297 − 0.11937I
b = 1.43093 + 1.14290I
−4.1159 − 17.6919I 0
u = −0.50070 − 1.46622I
a = −1.44297 + 0.11937I
b = 1.43093 − 1.14290I
−4.1159 + 17.6919I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.60050 + 1.43503I
a = −1.090220 − 0.150328I
b = 1.36060 − 0.72302I
−6.65882 + 7.54335I 0
u = 0.60050 − 1.43503I
a = −1.090220 + 0.150328I
b = 1.36060 + 0.72302I
−6.65882 − 7.54335I 0
u = −0.49169 + 1.48005I
a = 1.152940 − 0.055999I
b = −1.09293 − 0.91892I
−6.98154 − 8.93541I 0
u = −0.49169 − 1.48005I
a = 1.152940 + 0.055999I
b = −1.09293 + 0.91892I
−6.98154 + 8.93541I 0
u = 0.283569 + 0.325822I
a = −0.86667 + 2.61101I
b = 0.219477 + 0.269391I
−1.04332 + 1.10567I −9.46807 + 3.92768I
u = 0.283569 − 0.325822I
a = −0.86667 − 2.61101I
b = 0.219477 − 0.269391I
−1.04332 − 1.10567I −9.46807 − 3.92768I
u = −0.52905 + 1.51463I
a = 1.050270 − 0.039593I
b = −1.218100 − 0.659542I
−6.59608 − 4.70222I 0
u = −0.52905 − 1.51463I
a = 1.050270 + 0.039593I
b = −1.218100 + 0.659542I
−6.59608 + 4.70222I 0
u = 0.354922
a = −1.12692
b = 0.380191
−0.829400 −12.4500
u = 0.294507 + 0.068923I
a = 1.91812 − 1.72593I
b = 1.327900 + 0.309964I
−3.55911 + 0.66256I −6.82987 − 9.28934I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294507 − 0.068923I
a = 1.91812 + 1.72593I
b = 1.327900 − 0.309964I
−3.55911 − 0.66256I −6.82987 + 9.28934I
u = −0.206735 + 0.210541I
a = −0.51301 − 4.12782I
b = −1.264930 + 0.200555I
−0.32476 − 6.96628I −7.63597 + 5.26059I
u = −0.206735 − 0.210541I
a = −0.51301 + 4.12782I
b = −1.264930 − 0.200555I
−0.32476 + 6.96628I −7.63597 − 5.26059I
u = −1.88839 + 0.16543I
a = 0.0280191 + 0.0598057I
b = 0.473251 + 0.100354I
−1.16868 − 2.46445I 0
u = −1.88839 − 0.16543I
a = 0.0280191 − 0.0598057I
b = 0.473251 − 0.100354I
−1.16868 + 2.46445I 0
u = −0.14180 + 1.98107I
a = −0.190656 − 0.343084I
b = 0.270083 + 0.903599I
−2.44085 + 2.75616I 0
u = −0.14180 − 1.98107I
a = −0.190656 + 0.343084I
b = 0.270083 − 0.903599I
−2.44085 − 2.75616I 0
13
II. I
u
2
= h491u
12
− 351u
11
+ · · · + 2441b + 3926, 3175u
12
+ 6674u
11
+ · · · +
4882a − 4765, u
13
+ u
12
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
−0.650348u
12
− 1.36706u
11
+ ··· − 1.98382u + 0.976034
−0.201147u
12
+ 0.143794u
11
+ ··· + 3.64154u − 1.60836
a
9
=
u
u
3
+ u
a
2
=
−0.495494u
12
− 0.779189u
11
+ ··· − 0.591766u + 0.104261
−0.261368u
12
+ 0.192954u
11
+ ··· + 4.32241u − 2.04711
a
3
=
0.880479u
12
+ 1.39349u
11
+ ··· − 3.72522u + 0.700635
−0.612864u
12
− 1.03032u
11
+ ··· − 0.519869u + 0.820565
a
11
=
−0.851495u
12
− 1.22327u
11
+ ··· + 1.65772u − 0.632323
−0.201147u
12
+ 0.143794u
11
+ ··· + 3.64154u − 1.60836
a
7
=
0.744879u
12
+ 1.74908u
11
+ ··· + 1.39973u − 0.573023
0.798853u
12
+ 1.14379u
11
+ ··· − 0.358460u + 0.391643
a
6
=
0.0437321u
12
+ 0.892872u
11
+ ··· + 3.54127u − 1.68138
1.35190u
12
+ 1.24334u
11
+ ··· − 4.52970u + 0.278165
a
10
=
−0.978748u
12
− 0.0836747u
11
+ ··· + 5.32861u − 2.05945
0.196641u
12
+ 0.635395u
11
+ ··· + 3.45023u − 0.995903
a
10
=
−0.978748u
12
− 0.0836747u
11
+ ··· + 5.32861u − 2.05945
0.196641u
12
+ 0.635395u
11
+ ··· + 3.45023u − 0.995903
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
33641
39056
u
12
−
24777
19528
u
11
+ ··· −
452231
39056
u −
213017
39056
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 2u
12
+ ··· + 7u + 1
c
2
u
13
+ 2u
12
+ ··· + u − 1
c
3
2(2u
13
+ 5u
12
+ ··· + 7u + 1)
c
4
u
13
+ u
12
+ ··· + 2u − 1
c
5
u
13
+ 2u
12
+ ··· − u − 2
c
6
u
13
− 2u
12
+ ··· + u + 1
c
7
2(2u
13
+ u
12
+ ··· + 13u − 5)
c
8
u
13
− u
12
+ ··· + 2u + 1
c
9
2(2u
13
− u
12
+ ··· + 6u + 1)
c
10
2(2u
13
− u
12
+ ··· + 13u + 5)
c
11
u
13
+ u
12
+ ··· − 5u − 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 2y
12
+ ··· + 25y −1
c
2
, c
6
y
13
+ 4y
12
+ ··· − 11y −1
c
3
4(4y
13
− y
12
+ ··· + 21y −1)
c
4
, c
8
y
13
+ 9y
12
+ ··· − 6y −1
c
5
y
13
− 4y
12
+ ··· + 21y −4
c
7
, c
10
4(4y
13
− 65y
12
+ ··· + 189y −25)
c
9
4(4y
13
+ 19y
12
+ ··· + 16y −1)
c
11
y
13
− 15y
12
+ ··· + 21y −4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325948 + 1.074870I
a = 2.13139 − 0.98959I
b = −2.08257 − 0.08658I
−1.43580 − 8.24449I −11.3041 + 10.0681I
u = −0.325948 − 1.074870I
a = 2.13139 + 0.98959I
b = −2.08257 + 0.08658I
−1.43580 + 8.24449I −11.3041 − 10.0681I
u = 0.360305 + 0.702792I
a = −0.23551 + 1.84462I
b = −0.270408 + 0.367997I
−0.852875 − 0.473363I −10.87019 − 3.13875I
u = 0.360305 − 0.702792I
a = −0.23551 − 1.84462I
b = −0.270408 − 0.367997I
−0.852875 + 0.473363I −10.87019 + 3.13875I
u = 0.089681 + 1.215230I
a = −2.25917 − 0.12722I
b = 2.05969 − 0.84594I
−6.78588 + 1.52935I −8.62170 − 4.17456I
u = 0.089681 − 1.215230I
a = −2.25917 + 0.12722I
b = 2.05969 + 0.84594I
−6.78588 − 1.52935I −8.62170 + 4.17456I
u = −0.097116 + 0.522146I
a = 0.897260 − 0.736167I
b = −0.095808 + 1.315800I
4.14699 + 1.46163I −8.28713 − 5.07807I
u = −0.097116 − 0.522146I
a = 0.897260 + 0.736167I
b = −0.095808 − 1.315800I
4.14699 − 1.46163I −8.28713 + 5.07807I
u = 0.55292 + 1.47705I
a = −1.027900 − 0.056511I
b = 1.17981 − 0.80934I
−7.07568 + 6.46295I −10.78671 − 4.43761I
u = 0.55292 − 1.47705I
a = −1.027900 + 0.056511I
b = 1.17981 + 0.80934I
−7.07568 − 6.46295I −10.78671 + 4.43761I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420998
a = −1.44871
b = −1.13723
−3.49272 −9.11080
u = −1.29035 + 1.11018I
a = −0.031716 + 0.214422I
b = 0.277898 + 0.180723I
−1.05481 − 2.28411I −28.6060 − 9.4367I
u = −1.29035 − 1.11018I
a = −0.031716 − 0.214422I
b = 0.277898 − 0.180723I
−1.05481 + 2.28411I −28.6060 + 9.4367I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 2u
12
+ ··· + 7u + 1)(u
87
+ 3u
86
+ ··· − 5484u + 667)
c
2
(u
13
+ 2u
12
+ ··· + u − 1)(u
87
+ u
86
+ ··· − 140u + 23)
c
3
4(2u
13
+ 5u
12
+ ··· + 7u + 1)(2u
87
− 17u
86
+ ··· − 8u + 1)
c
4
(u
13
+ u
12
+ ··· + 2u − 1)(u
87
− 4u
86
+ ··· + 343u + 49)
c
5
(u
13
+ 2u
12
+ ··· − u − 2)(u
87
− 3u
86
+ ··· + 11633u + 2362)
c
6
(u
13
− 2u
12
+ ··· + u + 1)(u
87
+ u
86
+ ··· − 140u + 23)
c
7
4(2u
13
+ u
12
+ ··· + 13u − 5)(2u
87
+ 5u
86
+ ··· + 9624u + 539)
c
8
(u
13
− u
12
+ ··· + 2u + 1)(u
87
− 4u
86
+ ··· + 343u + 49)
c
9
4(2u
13
− u
12
+ ··· + 6u + 1)(2u
87
− 5u
86
+ ··· + 1311u + 349)
c
10
4(2u
13
− u
12
+ ··· + 13u + 5)(2u
87
+ 5u
86
+ ··· + 9624u + 539)
c
11
(u
13
+ u
12
+ ··· − 5u − 2)(u
87
+ 2u
86
+ ··· + 2885u + 538)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 2y
12
+ ··· + 25y −1)
· (y
87
− 13y
86
+ ··· + 17748096y −444889)
c
2
, c
6
(y
13
+ 4y
12
+ ··· − 11y −1)(y
87
+ 45y
86
+ ··· + 11504y −529)
c
3
16(4y
13
− y
12
+ ··· + 21y −1)(4y
87
− 13y
86
+ ··· − 4y −1)
c
4
, c
8
(y
13
+ 9y
12
+ ··· − 6y −1)(y
87
+ 66y
86
+ ··· + 43561y −2401)
c
5
(y
13
− 4y
12
+ ··· + 21y −4)
· (y
87
+ 9y
86
+ ··· − 55400087y −5579044)
c
7
, c
10
16(4y
13
− 65y
12
+ ··· + 189y −25)
· (4y
87
− 285y
86
+ ··· + 12812724y −290521)
c
9
16(4y
13
+ 19y
12
+ ··· + 16y −1)
· (4y
87
+ 103y
86
+ ··· − 17754781y −121801)
c
11
(y
13
− 15y
12
+ ··· + 21y −4)
· (y
87
− 38y
86
+ ··· + 7135321y −289444)
20
