12a
0957
(K12a
0957
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 11 3 1 12 2 7 5 8
Solving Sequence
3,7
6
2,11
5 12 10 4 1 9 8
c
6
c
2
c
5
c
11
c
10
c
3
c
1
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h6.01890 × 10
431
u
131
+ 1.67690 × 10
432
u
130
+ ··· + 1.63556 × 10
431
b − 3.45096 × 10
434
,
2.77517 × 10
434
u
131
+ 7.86280 × 10
434
u
130
+ ··· + 3.95805 × 10
433
a − 1.57625 × 10
437
,
u
132
+ 2u
131
+ ··· − 110u + 484i
I
u
2
= h−479758582336010u
30
− 1107917736884359u
29
+ ··· + 2241847239778b + 2757014414903866,
− 371686622838711u
30
− 869706396241666u
29
+ ··· + 2241847239778a + 2086493761025877,
u
31
+ 3u
30
+ ··· − 18u − 4i
* 2 irreducible components of dim
C
= 0, with total 163 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
= h6.02 × 10
431
u
131
+ 1.68 × 10
432
u
130
+ · · · + 1.64 × 10
431
b − 3.45 ×
10
434
, 2.78 × 10
434
u
131
+ 7.86 × 10
434
u
130
+ · · · + 3.96 × 10
433
a − 1.58 ×
10
437
, u
132
+ 2u
131
+ · · · − 110u + 484i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
2
=
−u
−u
3
+ u
a
11
=
−7.01147u
131
− 19.8654u
130
+ ··· + 3685.03u + 3982.40
−3.68003u
131
− 10.2528u
130
+ ··· + 1843.90u + 2109.96
a
5
=
−2.03352u
131
− 6.90245u
130
+ ··· − 18.6657u + 556.179
−0.450600u
131
− 1.95947u
130
+ ··· − 634.313u − 176.903
a
12
=
3.32732u
131
+ 14.7189u
130
+ ··· + 4001.59u + 1097.20
0.428259u
131
+ 1.23170u
130
+ ··· − 81.7935u − 202.244
a
10
=
−3.33144u
131
− 9.61255u
130
+ ··· + 1841.13u + 1872.44
−3.68003u
131
− 10.2528u
130
+ ··· + 1843.90u + 2109.96
a
4
=
−1.62545u
131
− 4.95251u
130
+ ··· + 818.930u + 842.032
−0.304230u
131
− 0.850231u
130
+ ··· + 163.230u + 174.466
a
1
=
51.7438u
131
+ 153.988u
130
+ ··· − 20436.0u − 25629.4
−0.942105u
131
− 2.64416u
130
+ ··· + 481.774u + 533.851
a
9
=
−5.61696u
131
− 15.5581u
130
+ ··· + 3561.67u + 3459.46
−1.96769u
131
− 5.37684u
130
+ ··· + 1078.36u + 1188.19
a
8
=
−85.5423u
131
− 248.486u
130
+ ··· + 39558.0u + 45553.8
−1.25261u
131
− 3.59742u
130
+ ··· + 593.297u + 683.193
(ii) Obstruction class = −1
(iii) Cusp Shapes = 164.847u
131
+ 466.596u
130
+ ··· − 94982.5u − 96460.8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
132
− 5u
131
+ ··· + 319u − 1
c
2
, c
6
u
132
+ 2u
131
+ ··· − 110u + 484
c
3
u
132
− u
131
+ ··· − 150284u − 19367
c
4
u
132
+ 3u
131
+ ··· + 1603714647u − 570362249
c
5
, c
11
u
132
− u
131
+ ··· − 3944517u − 299011
c
7
, c
8
, c
12
u
132
+ 68u
130
+ ··· + 19u + 1
c
9
u
132
− 2u
131
+ ··· + 11993u − 4467
c
10
u
132
+ u
131
+ ··· − 5047u + 321
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
132
− 9y
131
+ ··· − 100571y + 1
c
2
, c
6
y
132
− 72y
131
+ ··· − 2771868y + 234256
c
3
y
132
+ 23y
131
+ ··· + 8515836038y + 375080689
c
4
y
132
+ 59y
131
+ ··· + 3.67 × 10
18
y + 3.25 × 10
17
c
5
, c
11
y
132
+ 109y
131
+ ··· + 89028169385y + 89407578121
c
7
, c
8
, c
12
y
132
+ 136y
131
+ ··· − 145y + 1
c
9
y
132
+ 14y
131
+ ··· − 1024697647y + 19954089
c
10
y
132
+ 7y
131
+ ··· + 22512797y + 103041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.884816 + 0.474905I
a = 1.66252 − 0.11441I
b = 0.650392 − 0.231643I
−3.27259 − 2.47976I 0
u = −0.884816 − 0.474905I
a = 1.66252 + 0.11441I
b = 0.650392 + 0.231643I
−3.27259 + 2.47976I 0
u = 0.915765 + 0.340582I
a = −2.80388 − 1.06421I
b = −1.58944 − 1.35988I
−9.50542 − 4.87494I 0
u = 0.915765 − 0.340582I
a = −2.80388 + 1.06421I
b = −1.58944 + 1.35988I
−9.50542 + 4.87494I 0
u = −0.942190 + 0.424662I
a = −2.01410 + 0.52332I
b = −0.487234 + 0.684826I
−3.41617 − 6.49521I 0
u = −0.942190 − 0.424662I
a = −2.01410 − 0.52332I
b = −0.487234 − 0.684826I
−3.41617 + 6.49521I 0
u = −0.386658 + 0.884802I
a = −0.045284 + 0.449711I
b = 0.756898 + 0.730603I
−3.48885 + 1.37931I 0
u = −0.386658 − 0.884802I
a = −0.045284 − 0.449711I
b = 0.756898 − 0.730603I
−3.48885 − 1.37931I 0
u = −0.967695 + 0.409732I
a = 2.12999 − 0.80994I
b = 0.296010 − 0.830334I
−9.89787 − 9.67184I 0
u = −0.967695 − 0.409732I
a = 2.12999 + 0.80994I
b = 0.296010 + 0.830334I
−9.89787 + 9.67184I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789295 + 0.515215I
a = −1.19236 − 1.38844I
b = −1.32264 − 1.05992I
−8.63511 − 2.84252I 0
u = −0.789295 − 0.515215I
a = −1.19236 + 1.38844I
b = −1.32264 + 1.05992I
−8.63511 + 2.84252I 0
u = 0.938691 + 0.059442I
a = 4.15791 + 3.69908I
b = 0.191248 − 0.131579I
−5.07473 + 0.16829I 0
u = 0.938691 − 0.059442I
a = 4.15791 − 3.69908I
b = 0.191248 + 0.131579I
−5.07473 − 0.16829I 0
u = 0.989571 + 0.388105I
a = 1.45147 − 0.41211I
b = 1.06468 + 1.35709I
−1.11664 + 5.62858I 0
u = 0.989571 − 0.388105I
a = 1.45147 + 0.41211I
b = 1.06468 − 1.35709I
−1.11664 − 5.62858I 0
u = −0.775797 + 0.512353I
a = 1.35566 + 0.77126I
b = 1.056800 + 0.533841I
−3.35318 − 2.09628I 0
u = −0.775797 − 0.512353I
a = 1.35566 − 0.77126I
b = 1.056800 − 0.533841I
−3.35318 + 2.09628I 0
u = 0.246759 + 0.895153I
a = 0.086715 + 0.519405I
b = −0.290111 − 0.018909I
−1.15474 + 1.23049I 0
u = 0.246759 − 0.895153I
a = 0.086715 − 0.519405I
b = −0.290111 + 0.018909I
−1.15474 − 1.23049I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908416 + 0.190893I
a = −1.70213 − 0.54652I
b = −0.970588 + 0.555808I
−0.983366 + 0.894266I 0
u = 0.908416 − 0.190893I
a = −1.70213 + 0.54652I
b = −0.970588 − 0.555808I
−0.983366 − 0.894266I 0
u = 0.008635 + 0.928101I
a = −0.144296 + 0.342857I
b = −1.009900 − 0.536885I
−5.60921 + 7.00889I 0
u = 0.008635 − 0.928101I
a = −0.144296 − 0.342857I
b = −1.009900 + 0.536885I
−5.60921 − 7.00889I 0
u = 0.883314 + 0.281049I
a = 2.58613 + 0.89656I
b = 1.31484 + 0.80921I
−2.53291 − 2.22174I 0
u = 0.883314 − 0.281049I
a = 2.58613 − 0.89656I
b = 1.31484 − 0.80921I
−2.53291 + 2.22174I 0
u = −1.055710 + 0.263342I
a = 2.01783 + 0.09373I
b = 1.53656 − 0.78293I
−0.85765 − 5.45781I 0
u = −1.055710 − 0.263342I
a = 2.01783 − 0.09373I
b = 1.53656 + 0.78293I
−0.85765 + 5.45781I 0
u = 0.866590 + 0.210032I
a = 0.71853 − 1.34233I
b = 0.93448 − 2.06252I
−2.74406 + 4.51032I 0
u = 0.866590 − 0.210032I
a = 0.71853 + 1.34233I
b = 0.93448 + 2.06252I
−2.74406 − 4.51032I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.013820 + 0.888222I
a = −0.049782 − 0.384372I
b = 0.773005 + 0.387860I
0.32452 + 4.34292I 0
u = 0.013820 − 0.888222I
a = −0.049782 + 0.384372I
b = 0.773005 − 0.387860I
0.32452 − 4.34292I 0
u = 1.095560 + 0.190155I
a = −1.54685 + 0.71390I
b = −0.224526 − 0.518265I
−3.99476 + 0.29972I 0
u = 1.095560 − 0.190155I
a = −1.54685 − 0.71390I
b = −0.224526 + 0.518265I
−3.99476 − 0.29972I 0
u = 1.059130 + 0.375973I
a = −1.166780 + 0.693723I
b = −0.997325 − 0.841214I
3.18035 + 2.90322I 0
u = 1.059130 − 0.375973I
a = −1.166780 − 0.693723I
b = −0.997325 + 0.841214I
3.18035 − 2.90322I 0
u = −0.724711 + 0.487676I
a = −2.08125 − 0.81701I
b = −1.57151 − 0.05639I
−8.81589 − 1.30826I 0
u = −0.724711 − 0.487676I
a = −2.08125 + 0.81701I
b = −1.57151 + 0.05639I
−8.81589 + 1.30826I 0
u = −1.132960 + 0.135239I
a = −1.49657 + 0.19781I
b = −1.29493 + 0.87121I
4.49382 − 1.59161I 0
u = −1.132960 − 0.135239I
a = −1.49657 − 0.19781I
b = −1.29493 − 0.87121I
4.49382 + 1.59161I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851977
a = −3.75966
b = −0.269385
−0.410229 0
u = 1.097330 + 0.351337I
a = −0.284882 − 0.826418I
b = 0.564404 − 0.176494I
−2.48106 − 0.05788I 0
u = 1.097330 − 0.351337I
a = −0.284882 + 0.826418I
b = 0.564404 + 0.176494I
−2.48106 + 0.05788I 0
u = 0.247341 + 1.128890I
a = 0.116446 + 0.457801I
b = −0.866422 + 0.994465I
−11.1165 − 12.7107I 0
u = 0.247341 − 1.128890I
a = 0.116446 − 0.457801I
b = −0.866422 − 0.994465I
−11.1165 + 12.7107I 0
u = −0.803523 + 0.833951I
a = 0.440111 + 0.803172I
b = 1.193060 + 0.417998I
−3.01450 + 1.23639I 0
u = −0.803523 − 0.833951I
a = 0.440111 − 0.803172I
b = 1.193060 − 0.417998I
−3.01450 − 1.23639I 0
u = 1.127780 + 0.271409I
a = 1.028370 − 0.542660I
b = 0.496725 + 0.498862I
1.75805 + 1.07231I 0
u = 1.127780 − 0.271409I
a = 1.028370 + 0.542660I
b = 0.496725 − 0.498862I
1.75805 − 1.07231I 0
u = −1.103060 + 0.367632I
a = 0.573973 − 0.933648I
b = 0.17795 − 1.57989I
−5.07414 − 5.28950I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.103060 − 0.367632I
a = 0.573973 + 0.933648I
b = 0.17795 + 1.57989I
−5.07414 + 5.28950I 0
u = −1.015100 + 0.573103I
a = −0.964303 + 0.590903I
b = −0.0171108 + 0.0735246I
−8.63379 + 1.07483I 0
u = −1.015100 − 0.573103I
a = −0.964303 − 0.590903I
b = −0.0171108 − 0.0735246I
−8.63379 − 1.07483I 0
u = 0.787789 + 0.210688I
a = −0.05832 + 2.35922I
b = −0.61444 + 2.74989I
−10.14810 + 7.50183I 0
u = 0.787789 − 0.210688I
a = −0.05832 − 2.35922I
b = −0.61444 − 2.74989I
−10.14810 − 7.50183I 0
u = 1.128850 + 0.404643I
a = 0.93270 − 1.09980I
b = 1.194680 + 0.318888I
−0.445813 + 1.114960I 0
u = 1.128850 − 0.404643I
a = 0.93270 + 1.09980I
b = 1.194680 − 0.318888I
−0.445813 − 1.114960I 0
u = 0.282513 + 1.169350I
a = −0.116569 − 0.443418I
b = 0.770994 − 0.837968I
−4.14351 − 8.21803I 0
u = 0.282513 − 1.169350I
a = −0.116569 + 0.443418I
b = 0.770994 + 0.837968I
−4.14351 + 8.21803I 0
u = 1.138750 + 0.399109I
a = −0.378575 + 0.658815I
b = −0.722084 − 0.146977I
2.77717 + 1.00054I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.138750 − 0.399109I
a = −0.378575 − 0.658815I
b = −0.722084 + 0.146977I
2.77717 − 1.00054I 0
u = −0.526152 + 0.576468I
a = 0.558429 + 0.122035I
b = 0.045335 + 1.035590I
−4.20850 − 1.73518I 0
u = −0.526152 − 0.576468I
a = 0.558429 − 0.122035I
b = 0.045335 − 1.035590I
−4.20850 + 1.73518I 0
u = −1.126290 + 0.537145I
a = 1.84916 + 0.33181I
b = 1.61023 − 0.93755I
−1.29258 − 6.51091I 0
u = −1.126290 − 0.537145I
a = 1.84916 − 0.33181I
b = 1.61023 + 0.93755I
−1.29258 + 6.51091I 0
u = −0.164749 + 0.733190I
a = 0.643439 − 0.216613I
b = −0.601698 − 1.000480I
−0.90911 + 2.58269I 0
u = −0.164749 − 0.733190I
a = 0.643439 + 0.216613I
b = −0.601698 + 1.000480I
−0.90911 − 2.58269I 0
u = 1.208830 + 0.326446I
a = 2.08876 + 0.89815I
b = 1.85882 + 1.43889I
−6.31828 + 8.77435I 0
u = 1.208830 − 0.326446I
a = 2.08876 − 0.89815I
b = 1.85882 − 1.43889I
−6.31828 − 8.77435I 0
u = −0.179678 + 0.722554I
a = −0.929904 + 0.391490I
b = 0.60150 + 1.35100I
−6.22703 + 3.42085I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179678 − 0.722554I
a = −0.929904 − 0.391490I
b = 0.60150 − 1.35100I
−6.22703 − 3.42085I 0
u = −1.157780 + 0.499932I
a = 2.05361 − 0.46284I
b = 1.50176 − 1.67005I
−3.39124 − 8.01755I 0
u = −1.157780 − 0.499932I
a = 2.05361 + 0.46284I
b = 1.50176 + 1.67005I
−3.39124 + 8.01755I 0
u = −1.020200 + 0.752092I
a = −1.030420 − 0.695273I
b = −1.400400 + 0.146934I
1.07326 − 3.01270I 0
u = −1.020200 − 0.752092I
a = −1.030420 + 0.695273I
b = −1.400400 − 0.146934I
1.07326 + 3.01270I 0
u = −1.166740 + 0.501144I
a = −1.84066 + 0.18303I
b = −1.40640 + 1.36274I
2.00072 − 7.20882I 0
u = −1.166740 − 0.501144I
a = −1.84066 − 0.18303I
b = −1.40640 − 1.36274I
2.00072 + 7.20882I 0
u = −1.268970 + 0.048065I
a = 0.499876 + 0.218152I
b = 0.522206 + 0.829263I
3.21693 − 3.39726I 0
u = −1.268970 − 0.048065I
a = 0.499876 − 0.218152I
b = 0.522206 − 0.829263I
3.21693 + 3.39726I 0
u = 0.274668 + 1.257710I
a = 0.116896 + 0.411868I
b = −0.561626 + 0.711698I
−4.51046 − 2.07669I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274668 − 1.257710I
a = 0.116896 − 0.411868I
b = −0.561626 − 0.711698I
−4.51046 + 2.07669I 0
u = 0.589575 + 0.386588I
a = −1.57748 − 0.89380I
b = 0.455789 − 0.714399I
−2.32018 − 2.26770I 0
u = 0.589575 − 0.386588I
a = −1.57748 + 0.89380I
b = 0.455789 + 0.714399I
−2.32018 + 2.26770I 0
u = −0.550035 + 0.436106I
a = −0.103224 + 0.164424I
b = −0.188068 − 1.347500I
−4.53992 + 2.81085I 0
u = −0.550035 − 0.436106I
a = −0.103224 − 0.164424I
b = −0.188068 + 1.347500I
−4.53992 − 2.81085I 0
u = −0.323208 + 0.619235I
a = −0.887634 − 0.224841I
b = 0.342063 − 1.105550I
−10.47340 − 5.69331I 0
u = −0.323208 − 0.619235I
a = −0.887634 + 0.224841I
b = 0.342063 + 1.105550I
−10.47340 + 5.69331I 0
u = −1.238340 + 0.440198I
a = −0.898733 − 0.063698I
b = −0.711498 + 0.948497I
2.94539 − 5.54607I 0
u = −1.238340 − 0.440198I
a = −0.898733 + 0.063698I
b = −0.711498 − 0.948497I
2.94539 + 5.54607I 0
u = 0.144776 + 1.326740I
a = −0.162276 − 0.360508I
b = 0.150959 − 0.753969I
−12.87830 + 2.12922I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144776 − 1.326740I
a = −0.162276 + 0.360508I
b = 0.150959 + 0.753969I
−12.87830 − 2.12922I 0
u = −1.250160 + 0.474407I
a = 1.263590 + 0.359909I
b = 1.010330 − 0.836469I
4.11592 − 9.15779I 0
u = −1.250160 − 0.474407I
a = 1.263590 − 0.359909I
b = 1.010330 + 0.836469I
4.11592 + 9.15779I 0
u = −0.546041 + 0.360490I
a = −0.095680 − 0.643072I
b = 0.13621 + 1.50477I
−11.16580 + 6.20485I 0
u = −0.546041 − 0.360490I
a = −0.095680 + 0.643072I
b = 0.13621 − 1.50477I
−11.16580 − 6.20485I 0
u = −1.266490 + 0.484120I
a = −1.50902 − 0.46555I
b = −1.15695 + 0.81499I
−1.73795 − 11.98760I 0
u = −1.266490 − 0.484120I
a = −1.50902 + 0.46555I
b = −1.15695 − 0.81499I
−1.73795 + 11.98760I 0
u = −1.190310 + 0.667724I
a = 1.360860 + 0.257878I
b = 1.235540 − 0.643906I
−1.32829 − 7.15022I 0
u = −1.190310 − 0.667724I
a = 1.360860 − 0.257878I
b = 1.235540 + 0.643906I
−1.32829 + 7.15022I 0
u = 1.296540 + 0.446713I
a = 0.974729 − 0.284396I
b = 0.987903 + 0.232577I
4.26868 + 0.61252I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.296540 − 0.446713I
a = 0.974729 + 0.284396I
b = 0.987903 − 0.232577I
4.26868 − 0.61252I 0
u = 1.364210 + 0.170896I
a = −0.87983 − 1.51138I
b = −0.81179 − 1.93774I
1.50304 + 3.78464I 0
u = 1.364210 − 0.170896I
a = −0.87983 + 1.51138I
b = −0.81179 + 1.93774I
1.50304 − 3.78464I 0
u = 0.615040
a = 1.23931
b = −0.150084
0.986986 12.0140
u = 1.313880 + 0.471463I
a = −1.001950 − 0.183902I
b = −0.964616 − 0.717334I
2.54855 + 4.26966I 0
u = 1.313880 − 0.471463I
a = −1.001950 + 0.183902I
b = −0.964616 + 0.717334I
2.54855 − 4.26966I 0
u = 1.34776 + 0.47205I
a = −0.872535 + 0.571039I
b = −0.959679 + 0.155122I
−1.55609 − 1.83793I 0
u = 1.34776 − 0.47205I
a = −0.872535 − 0.571039I
b = −0.959679 − 0.155122I
−1.55609 + 1.83793I 0
u = 1.28250 + 0.63254I
a = −1.66972 − 0.06091I
b = −1.43305 − 1.21167I
−7.8525 + 18.9295I 0
u = 1.28250 − 0.63254I
a = −1.66972 + 0.06091I
b = −1.43305 + 1.21167I
−7.8525 − 18.9295I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230142 + 0.514693I
a = −1.80324 − 0.62819I
b = −0.525425 + 0.965595I
−7.51172 + 1.70362I −2.52590 − 0.81074I
u = −0.230142 − 0.514693I
a = −1.80324 + 0.62819I
b = −0.525425 − 0.965595I
−7.51172 − 1.70362I −2.52590 + 0.81074I
u = 1.28579 + 0.64812I
a = 1.49651 + 0.02872I
b = 1.34336 + 1.10923I
−0.9374 + 14.6050I 0
u = 1.28579 − 0.64812I
a = 1.49651 − 0.02872I
b = 1.34336 − 1.10923I
−0.9374 − 14.6050I 0
u = −0.019436 + 0.555259I
a = −0.747654 + 0.473871I
b = 0.950790 + 0.435099I
−3.54507 + 2.46772I 3.18286 − 2.50114I
u = −0.019436 − 0.555259I
a = −0.747654 − 0.473871I
b = 0.950790 − 0.435099I
−3.54507 − 2.46772I 3.18286 + 2.50114I
u = 1.31063 + 0.66241I
a = −1.275920 − 0.108001I
b = −1.17009 − 1.04443I
−1.15683 + 8.73043I 0
u = 1.31063 − 0.66241I
a = −1.275920 + 0.108001I
b = −1.17009 + 1.04443I
−1.15683 − 8.73043I 0
u = −1.31497 + 0.66175I
a = −1.341100 + 0.076982I
b = −0.975945 + 0.791344I
−9.10565 − 9.16843I 0
u = −1.31497 − 0.66175I
a = −1.341100 − 0.076982I
b = −0.975945 − 0.791344I
−9.10565 + 9.16843I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33416 + 0.62742I
a = 1.136730 + 0.402348I
b = 0.92069 + 1.15107I
−9.11709 + 4.43415I 0
u = 1.33416 − 0.62742I
a = 1.136730 − 0.402348I
b = 0.92069 − 1.15107I
−9.11709 − 4.43415I 0
u = 0.076842 + 0.510785I
a = 0.480728 + 1.151400I
b = 0.096934 − 0.406394I
−1.05502 + 1.51906I 1.40195 − 2.73250I
u = 0.076842 − 0.510785I
a = 0.480728 − 1.151400I
b = 0.096934 + 0.406394I
−1.05502 − 1.51906I 1.40195 + 2.73250I
u = −1.53024 + 0.14323I
a = −0.286910 − 0.613153I
b = −0.441171 − 0.056653I
−4.65323 + 7.64543I 0
u = −1.53024 − 0.14323I
a = −0.286910 + 0.613153I
b = −0.441171 + 0.056653I
−4.65323 − 7.64543I 0
u = −1.53807 + 0.01567I
a = 0.145407 − 0.288526I
b = 0.174898 + 0.285105I
3.00071 − 3.30970I 0
u = −1.53807 − 0.01567I
a = 0.145407 + 0.288526I
b = 0.174898 − 0.285105I
3.00071 + 3.30970I 0
u = −0.32651 + 1.52054I
a = −0.199800 − 0.277196I
b = −0.350961 − 0.465564I
−12.62660 + 2.18299I 0
u = −0.32651 − 1.52054I
a = −0.199800 + 0.277196I
b = −0.350961 + 0.465564I
−12.62660 − 2.18299I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215738 + 0.309658I
a = 1.56090 − 0.10275I
b = −0.570690 + 0.004455I
1.059320 + 0.231335I 10.25414 − 1.71431I
u = 0.215738 − 0.309658I
a = 1.56090 + 0.10275I
b = −0.570690 − 0.004455I
1.059320 − 0.231335I 10.25414 + 1.71431I
18
II. I
u
2
= h−4.80 × 10
14
u
30
− 1.11 × 10
15
u
29
+ · · · + 2.24 × 10
12
b + 2.76 ×
10
15
, −3.72 × 10
14
u
30
− 8.70 × 10
14
u
29
+ · · · + 2.24 × 10
12
a + 2.09 ×
10
15
, u
31
+ 3u
30
+ · · · − 18u − 4i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
2
=
−u
−u
3
+ u
a
11
=
165.795u
30
+ 387.942u
29
+ ··· − 2812.64u − 930.703
214.001u
30
+ 494.199u
29
+ ··· − 3767.72u − 1229.80
a
5
=
−191.651u
30
− 452.748u
29
+ ··· + 3179.22u + 1065.61
−u
30
− 2u
29
+ ··· + 15u + 3
a
12
=
−166.267u
30
− 407.875u
29
+ ··· + 2399.61u + 827.059
−170.610u
30
− 392.051u
29
+ ··· + 3000.56u + 975.239
a
10
=
−48.2067u
30
− 106.257u
29
+ ··· + 955.074u + 299.093
214.001u
30
+ 494.199u
29
+ ··· − 3767.72u − 1229.80
a
4
=
92.8593u
30
+ 204.761u
29
+ ··· − 1867.53u − 591.245
−149.846u
30
− 347.053u
29
+ ··· + 2659.17u + 877.272
a
1
=
11.0622u
30
+ 78.1211u
29
+ ··· + 1138.18u + 252.169
148.833u
30
+ 343.493u
29
+ ··· − 2644.73u − 867.355
a
9
=
42.2821u
30
+ 104.454u
29
+ ··· − 613.696u − 218.431
166.209u
30
+ 383.262u
29
+ ··· − 2930.59u − 955.294
a
8
=
93.0508u
30
+ 235.197u
29
+ ··· − 915.182u − 368.479
−73.7161u
30
− 173.108u
29
+ ··· + 1284.67u + 431.416
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
307335971617322
1120923619889
u
30
−
1661307222141219
2241847239778
u
29
+ ··· +
2093335817411432
1120923619889
u +
1021053253774145
1120923619889
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 10u
30
+ ··· − 8u − 1
c
2
u
31
− 3u
30
+ ··· − 18u + 4
c
3
u
31
− 2u
30
+ ··· + u + 1
c
4
u
31
− 4u
28
+ ··· + 2u + 1
c
5
u
31
− 2u
30
+ ··· + 4u + 1
c
6
u
31
+ 3u
30
+ ··· − 18u − 4
c
7
, c
8
u
31
− u
30
+ ··· + 14u + 1
c
9
u
31
− u
30
+ ··· − 10u
2
− 1
c
10
u
31
+ 4u
30
+ ··· − 2u + 1
c
11
u
31
+ 2u
30
+ ··· + 4u − 1
c
12
u
31
+ u
30
+ ··· + 14u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 4y
30
+ ··· + 12y −1
c
2
, c
6
y
31
− 15y
30
+ ··· + 236y −16
c
3
y
31
+ 198y
29
+ ··· − 41y −1
c
4
y
31
+ 16y
29
+ ··· − 14y −1
c
5
, c
11
y
31
+ 26y
30
+ ··· − 4y −1
c
7
, c
8
, c
12
y
31
+ 33y
30
+ ··· + 126y −1
c
9
y
31
+ 27y
30
+ ··· − 20y −1
c
10
y
31
+ 16y
30
+ ··· − 20y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.057307 + 0.973230I
a = 0.247039 − 0.169366I
b = −0.454732 − 0.714887I
−1.94780 + 1.84386I 1.45803 − 4.59325I
u = −0.057307 − 0.973230I
a = 0.247039 + 0.169366I
b = −0.454732 + 0.714887I
−1.94780 − 1.84386I 1.45803 + 4.59325I
u = 0.898610 + 0.350512I
a = 1.63164 − 0.54603I
b = 1.22810 + 0.90161I
−1.42861 + 4.54718I 3.68988 − 1.05273I
u = 0.898610 − 0.350512I
a = 1.63164 + 0.54603I
b = 1.22810 − 0.90161I
−1.42861 − 4.54718I 3.68988 + 1.05273I
u = 0.903896 + 0.092574I
a = −3.25175 − 2.58359I
b = −0.085902 + 0.124290I
−5.11343 + 0.22000I −16.4995 − 30.0570I
u = 0.903896 − 0.092574I
a = −3.25175 + 2.58359I
b = −0.085902 − 0.124290I
−5.11343 − 0.22000I −16.4995 + 30.0570I
u = −0.300086 + 0.831117I
a = −0.225560 − 1.008270I
b = −0.505222 − 0.530505I
−3.61006 − 0.33303I 1.48183 + 0.28332I
u = −0.300086 − 0.831117I
a = −0.225560 + 1.008270I
b = −0.505222 + 0.530505I
−3.61006 + 0.33303I 1.48183 − 0.28332I
u = 1.063730 + 0.384256I
a = −0.907360 + 0.596203I
b = −1.003190 − 0.387794I
3.15471 + 1.66264I 11.96669 − 2.85834I
u = 1.063730 − 0.384256I
a = −0.907360 − 0.596203I
b = −1.003190 + 0.387794I
3.15471 − 1.66264I 11.96669 + 2.85834I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834586
a = 3.51860
b = 0.247377
−0.429479 −157.470
u = 1.057770 + 0.581357I
a = 0.358699 − 0.930697I
b = 0.959263 − 0.297410I
−1.003480 − 0.632718I 9.72763 + 0.75640I
u = 1.057770 − 0.581357I
a = 0.358699 + 0.930697I
b = 0.959263 + 0.297410I
−1.003480 + 0.632718I 9.72763 − 0.75640I
u = −1.111060 + 0.506491I
a = 2.00178 + 0.03752I
b = 1.53151 − 1.42067I
−1.11219 − 7.62967I 6.00000 + 10.07351I
u = −1.111060 − 0.506491I
a = 2.00178 − 0.03752I
b = 1.53151 + 1.42067I
−1.11219 + 7.62967I 6.00000 − 10.07351I
u = −0.389079 + 0.652218I
a = −0.961979 + 0.621421I
b = 0.760965 + 1.122690I
−3.30951 + 3.11642I 0.69667 − 5.47819I
u = −0.389079 − 0.652218I
a = −0.961979 − 0.621421I
b = 0.760965 − 1.122690I
−3.30951 − 3.11642I 0.69667 + 5.47819I
u = −0.691646 + 0.005832I
a = −1.67697 − 1.53127I
b = −0.50600 − 2.15250I
−10.05550 − 6.75855I 2.79867 + 2.12113I
u = −0.691646 − 0.005832I
a = −1.67697 + 1.53127I
b = −0.50600 + 2.15250I
−10.05550 + 6.75855I 2.79867 − 2.12113I
u = −1.209820 + 0.504101I
a = −1.58579 + 0.22788I
b = −1.23990 + 1.24955I
1.53275 − 6.87011I 2.23968 + 3.95579I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.209820 − 0.504101I
a = −1.58579 − 0.22788I
b = −1.23990 − 1.24955I
1.53275 + 6.87011I 2.23968 − 3.95579I
u = −1.270400 + 0.346913I
a = 1.44096 − 0.92449I
b = 0.96722 − 1.29083I
−7.04927 − 8.05385I 0. + 5.30038I
u = −1.270400 − 0.346913I
a = 1.44096 + 0.92449I
b = 0.96722 + 1.29083I
−7.04927 + 8.05385I 0. − 5.30038I
u = 1.385820 + 0.214488I
a = −0.163353 + 0.147527I
b = −0.198598 − 0.530806I
3.46254 + 2.70014I 0
u = 1.385820 − 0.214488I
a = −0.163353 − 0.147527I
b = −0.198598 + 0.530806I
3.46254 − 2.70014I 0
u = −0.568046 + 0.149149I
a = 1.86516 + 1.82403I
b = 0.72455 + 1.52201I
−3.28222 − 3.84750I 2.24650 + 5.01378I
u = −0.568046 − 0.149149I
a = 1.86516 − 1.82403I
b = 0.72455 − 1.52201I
−3.28222 + 3.84750I 2.24650 − 5.01378I
u = −1.41218 + 0.17702I
a = −0.68326 + 1.32158I
b = −0.59409 + 1.70242I
1.32009 − 3.77713I −14.5756 + 0.I
u = −1.41218 − 0.17702I
a = −0.68326 − 1.32158I
b = −0.59409 − 1.70242I
1.32009 + 3.77713I −14.5756 + 0.I
u = −0.21750 + 1.62235I
a = 0.151437 + 0.311439I
b = 0.292335 + 0.308725I
−12.46670 + 2.12125I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21750 − 1.62235I
a = 0.151437 − 0.311439I
b = 0.292335 − 0.308725I
−12.46670 − 2.12125I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 10u
30
+ ··· − 8u − 1)(u
132
− 5u
131
+ ··· + 319u − 1)
c
2
(u
31
− 3u
30
+ ··· − 18u + 4)(u
132
+ 2u
131
+ ··· − 110u + 484)
c
3
(u
31
− 2u
30
+ ··· + u + 1)(u
132
− u
131
+ ··· − 150284u − 19367)
c
4
(u
31
− 4u
28
+ ··· + 2u + 1)
· (u
132
+ 3u
131
+ ··· + 1603714647u − 570362249)
c
5
(u
31
− 2u
30
+ ··· + 4u + 1)(u
132
− u
131
+ ··· − 3944517u − 299011)
c
6
(u
31
+ 3u
30
+ ··· − 18u − 4)(u
132
+ 2u
131
+ ··· − 110u + 484)
c
7
, c
8
(u
31
− u
30
+ ··· + 14u + 1)(u
132
+ 68u
130
+ ··· + 19u + 1)
c
9
(u
31
− u
30
+ ··· − 10u
2
− 1)(u
132
− 2u
131
+ ··· + 11993u − 4467)
c
10
(u
31
+ 4u
30
+ ··· − 2u + 1)(u
132
+ u
131
+ ··· − 5047u + 321)
c
11
(u
31
+ 2u
30
+ ··· + 4u − 1)(u
132
− u
131
+ ··· − 3944517u − 299011)
c
12
(u
31
+ u
30
+ ··· + 14u − 1)(u
132
+ 68u
130
+ ··· + 19u + 1)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
31
− 4y
30
+ ··· + 12y −1)(y
132
− 9y
131
+ ··· − 100571y + 1)
c
2
, c
6
(y
31
− 15y
30
+ ··· + 236y −16)
· (y
132
− 72y
131
+ ··· − 2771868y + 234256)
c
3
(y
31
+ 198y
29
+ ··· − 41y −1)
· (y
132
+ 23y
131
+ ··· + 8515836038y + 375080689)
c
4
(y
31
+ 16y
29
+ ··· − 14y −1)
· (y
132
+ 59y
131
+ ··· + 3.67 × 10
18
y + 3.25 × 10
17
)
c
5
, c
11
(y
31
+ 26y
30
+ ··· − 4y −1)
· (y
132
+ 109y
131
+ ··· + 89028169385y + 89407578121)
c
7
, c
8
, c
12
(y
31
+ 33y
30
+ ··· + 126y −1)(y
132
+ 136y
131
+ ··· − 145y + 1)
c
9
(y
31
+ 27y
30
+ ··· − 20y −1)
· (y
132
+ 14y
131
+ ··· − 1024697647y + 19954089)
c
10
(y
31
+ 16y
30
+ ··· − 20y −1)
· (y
132
+ 7y
131
+ ··· + 22512797y + 103041)
27
