12a
0317
(K12a
0317
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 12 5 1 7 4 10
Solving Sequence
2,6 3,9
7 1 10 11 5 4 8 12
c
2
c
6
c
1
c
9
c
10
c
5
c
4
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.32563 × 10
433
u
170
+ 1.21640 × 10
434
u
169
+ ··· + 1.40890 × 10
433
b − 1.01659 × 10
434
,
1.54855 × 10
434
u
170
− 5.21699 × 10
434
u
169
+ ··· + 1.40890 × 10
433
a − 1.21190 × 10
435
,
u
171
− 4u
170
+ ··· − 15u + 1i
I
u
2
= h32195546u
41
+ 78988862u
40
+ ··· + 764339b + 140677369,
90471926u
41
+ 220915467u
40
+ ··· + 2293017a + 394515903, u
42
+ 3u
41
+ ··· − 26u
2
+ 3i
* 2 irreducible components of dim
C
= 0, with total 213 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−2.33 × 10
433
u
170
+ 1.22 × 10
434
u
169
+ · · · + 1.41 × 10
433
b − 1.02 ×
10
434
, 1.55 × 10
434
u
170
− 5.22 × 10
434
u
169
+ · · · + 1.41 × 10
433
a − 1.21 ×
10
435
, u
171
− 4u
170
+ · · · − 15u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−10.9912u
170
+ 37.0289u
169
+ ··· − 657.898u + 86.0181
1.65068u
170
− 8.63368u
169
+ ··· − 35.5431u + 7.21549
a
7
=
4.08126u
170
+ 16.4331u
169
+ ··· − 1390.19u + 180.144
30.3070u
170
− 84.4218u
169
+ ··· + 157.355u − 4.90611
a
1
=
−u
2
+ 1
−u
4
a
10
=
−23.2483u
170
+ 71.0398u
169
+ ··· − 834.056u + 102.538
−9.46748u
170
+ 18.0078u
169
+ ··· − 87.8514u + 10.3668
a
11
=
55.3657u
170
− 186.121u
169
+ ··· + 1834.04u − 189.057
26.3127u
170
− 71.7091u
169
+ ··· + 227.304u − 15.1206
a
5
=
u
u
a
4
=
42.9698u
170
− 160.816u
169
+ ··· + 1415.01u − 125.166
15.3205u
170
− 65.5905u
169
+ ··· + 387.277u − 26.3923
a
8
=
−14.8780u
170
+ 50.2409u
169
+ ··· − 718.830u + 90.9230
−2.23607u
170
+ 4.57829u
169
+ ··· − 96.4751u + 12.1204
a
12
=
8.25459u
170
− 7.08653u
169
+ ··· − 609.543u + 67.1361
35.9201u
170
− 121.227u
169
+ ··· + 606.030u − 45.7176
(ii) Obstruction class = −1
(iii) Cusp Shapes = −73.4828u
170
+ 198.083u
169
+ ··· − 1119.20u + 108.206
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
171
+ 82u
170
+ ··· + 109u + 1
c
2
, c
5
u
171
+ 4u
170
+ ··· − 15u − 1
c
3
u
171
+ u
170
+ ··· + 426385251u − 251071867
c
4
, c
11
u
171
− 2u
170
+ ··· + 3950u − 1849
c
6
u
171
− 3u
170
+ ··· − 148u − 1496
c
7
u
171
+ 2u
170
+ ··· − 2755517934u − 204636559
c
8
u
171
− 15u
169
+ ··· − 541710u − 228281
c
9
, c
12
u
171
+ 11u
170
+ ··· − 15988u − 3784
c
10
u
171
+ 4u
170
+ ··· − 974881u − 49723
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
171
+ 26y
170
+ ··· + 2329y −1
c
2
, c
5
y
171
− 82y
170
+ ··· + 109y −1
c
3
y
171
+ 39y
170
+ ··· − 1949406148708587857y −63037082398865689
c
4
, c
11
y
171
+ 106y
170
+ ··· − 87630868y −3418801
c
6
y
171
+ 7y
170
+ ··· + 82092464y −2238016
c
7
y
171
+ 60y
170
+ ··· − 3089300280968879260y −41876121279360481
c
8
y
171
− 30y
170
+ ··· + 167534946682y −52112214961
c
9
, c
12
y
171
+ 131y
170
+ ··· − 270117680y −14318656
c
10
y
171
+ 50y
170
+ ··· − 24962763117y −2472376729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380674 + 0.927822I
a = −1.44104 + 0.75185I
b = −0.0853248 − 0.0837685I
−4.1236 + 14.6388I 0
u = 0.380674 − 0.927822I
a = −1.44104 − 0.75185I
b = −0.0853248 + 0.0837685I
−4.1236 − 14.6388I 0
u = −0.366931 + 0.917472I
a = 1.24732 + 0.78228I
b = 0.0952655 + 0.0515088I
−0.53997 − 8.66240I 0
u = −0.366931 − 0.917472I
a = 1.24732 − 0.78228I
b = 0.0952655 − 0.0515088I
−0.53997 + 8.66240I 0
u = 0.342928 + 0.920390I
a = −1.043760 + 0.494653I
b = 0.066645 + 0.176467I
−6.04580 + 3.49754I 0
u = 0.342928 − 0.920390I
a = −1.043760 − 0.494653I
b = 0.066645 − 0.176467I
−6.04580 − 3.49754I 0
u = −0.457582 + 0.853117I
a = 0.495659 + 0.753146I
b = 0.062593 + 0.311303I
3.31452 − 0.97599I 0
u = −0.457582 − 0.853117I
a = 0.495659 − 0.753146I
b = 0.062593 − 0.311303I
3.31452 + 0.97599I 0
u = 0.513246 + 0.819161I
a = −0.400049 + 1.051320I
b = −0.250673 + 0.288197I
0.55062 − 5.32202I 0
u = 0.513246 − 0.819161I
a = −0.400049 − 1.051320I
b = −0.250673 − 0.288197I
0.55062 + 5.32202I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.963158 + 0.402921I
a = −0.200696 − 0.192810I
b = 1.95696 − 1.21862I
−6.54806 − 0.36272I 0
u = −0.963158 − 0.402921I
a = −0.200696 + 0.192810I
b = 1.95696 + 1.21862I
−6.54806 + 0.36272I 0
u = −0.902678 + 0.300350I
a = 0.169921 − 0.476034I
b = 0.31990 − 2.60195I
−6.00184 + 3.22017I 0
u = −0.902678 − 0.300350I
a = 0.169921 + 0.476034I
b = 0.31990 + 2.60195I
−6.00184 − 3.22017I 0
u = −0.524370 + 0.789822I
a = 0.952807 + 0.482256I
b = −0.327914 − 0.000260I
3.81793 − 2.46825I 0
u = −0.524370 − 0.789822I
a = 0.952807 − 0.482256I
b = −0.327914 + 0.000260I
3.81793 + 2.46825I 0
u = 0.619006 + 0.717514I
a = 1.45978 − 0.38331I
b = 0.984183 − 0.260417I
−0.55947 + 2.06152I 0
u = 0.619006 − 0.717514I
a = 1.45978 + 0.38331I
b = 0.984183 + 0.260417I
−0.55947 − 2.06152I 0
u = −0.963099 + 0.428193I
a = −1.078290 + 0.719454I
b = 0.04140 + 1.50915I
−4.11245 − 0.56172I 0
u = −0.963099 − 0.428193I
a = −1.078290 − 0.719454I
b = 0.04140 − 1.50915I
−4.11245 + 0.56172I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983442 + 0.380664I
a = −0.088813 + 0.216542I
b = 0.422686 + 0.496267I
−1.69986 − 1.28381I 0
u = 0.983442 − 0.380664I
a = −0.088813 − 0.216542I
b = 0.422686 − 0.496267I
−1.69986 + 1.28381I 0
u = −0.608840 + 0.864426I
a = −1.46352 − 0.29358I
b = −0.760839 + 0.330719I
−0.89924 − 4.15334I 0
u = −0.608840 − 0.864426I
a = −1.46352 + 0.29358I
b = −0.760839 − 0.330719I
−0.89924 + 4.15334I 0
u = −0.852708 + 0.633407I
a = −0.067536 + 0.409120I
b = 0.288912 + 1.118510I
1.80657 + 0.58573I 0
u = −0.852708 − 0.633407I
a = −0.067536 − 0.409120I
b = 0.288912 − 1.118510I
1.80657 − 0.58573I 0
u = 0.601646 + 0.717900I
a = 0.722399 + 0.676708I
b = −0.061865 + 0.750125I
−1.72699 + 3.31478I 0
u = 0.601646 − 0.717900I
a = 0.722399 − 0.676708I
b = −0.061865 − 0.750125I
−1.72699 − 3.31478I 0
u = 0.472074 + 0.807039I
a = −1.224110 + 0.555132I
b = 0.324520 − 0.201902I
0.35785 + 8.72561I 0
u = 0.472074 − 0.807039I
a = −1.224110 − 0.555132I
b = 0.324520 + 0.201902I
0.35785 − 8.72561I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.910458 + 0.553549I
a = 0.609592 − 1.005530I
b = 0.59333 − 1.73565I
2.17789 − 2.71349I 0
u = 0.910458 − 0.553549I
a = 0.609592 + 1.005530I
b = 0.59333 + 1.73565I
2.17789 + 2.71349I 0
u = 0.737359 + 0.574044I
a = 1.24787 − 0.67806I
b = 0.387336 − 0.505592I
2.70711 − 1.80349I 0
u = 0.737359 − 0.574044I
a = 1.24787 + 0.67806I
b = 0.387336 + 0.505592I
2.70711 + 1.80349I 0
u = −0.996064 + 0.412530I
a = 1.23619 − 1.36760I
b = 0.83346 − 1.99349I
−4.94892 + 4.79852I 0
u = −0.996064 − 0.412530I
a = 1.23619 + 1.36760I
b = 0.83346 + 1.99349I
−4.94892 − 4.79852I 0
u = −1.027420 + 0.328668I
a = −0.534851 + 0.323176I
b = −1.63930 + 1.42441I
−1.98076 + 0.78863I 0
u = −1.027420 − 0.328668I
a = −0.534851 − 0.323176I
b = −1.63930 − 1.42441I
−1.98076 − 0.78863I 0
u = −0.652142 + 0.649935I
a = −1.54760 − 0.45381I
b = −0.480196 + 0.209602I
2.49581 − 1.32359I 0
u = −0.652142 − 0.649935I
a = −1.54760 + 0.45381I
b = −0.480196 − 0.209602I
2.49581 + 1.32359I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906002 + 0.159736I
a = 0.689025 + 0.974067I
b = −0.03277 + 2.18678I
−6.22172 − 2.61465I 0
u = −0.906002 − 0.159736I
a = 0.689025 − 0.974067I
b = −0.03277 − 2.18678I
−6.22172 + 2.61465I 0
u = −0.869676 + 0.299010I
a = −1.04273 + 1.82876I
b = −0.67765 + 2.07453I
−4.15612 − 1.96479I 0
u = −0.869676 − 0.299010I
a = −1.04273 − 1.82876I
b = −0.67765 − 2.07453I
−4.15612 + 1.96479I 0
u = −1.064860 + 0.185668I
a = −0.629574 + 1.258680I
b = −1.21135 + 2.25302I
−5.13287 − 3.61597I 0
u = −1.064860 − 0.185668I
a = −0.629574 − 1.258680I
b = −1.21135 − 2.25302I
−5.13287 + 3.61597I 0
u = 1.077930 + 0.132381I
a = −0.464354 + 0.339009I
b = −0.465901 + 1.022110I
−2.06028 − 1.44412I 0
u = 1.077930 − 0.132381I
a = −0.464354 − 0.339009I
b = −0.465901 − 1.022110I
−2.06028 + 1.44412I 0
u = −0.770478 + 0.767055I
a = 0.407056 + 0.408084I
b = −0.218278 − 0.150888I
2.06081 + 4.74559I 0
u = −0.770478 − 0.767055I
a = 0.407056 − 0.408084I
b = −0.218278 + 0.150888I
2.06081 − 4.74559I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993773 + 0.458962I
a = −1.99976 − 1.52669I
b = −1.85743 − 2.32894I
−7.53815 − 8.95364I 0
u = 0.993773 − 0.458962I
a = −1.99976 + 1.52669I
b = −1.85743 + 2.32894I
−7.53815 + 8.95364I 0
u = −0.832496 + 0.341495I
a = 0.22368 − 1.39703I
b = −0.68750 − 2.12663I
−3.47452 + 3.78054I 0
u = −0.832496 − 0.341495I
a = 0.22368 + 1.39703I
b = −0.68750 + 2.12663I
−3.47452 − 3.78054I 0
u = −1.004720 + 0.455046I
a = 0.95877 + 1.80347I
b = 0.13848 + 2.70177I
−7.53406 − 3.01774I 0
u = −1.004720 − 0.455046I
a = 0.95877 − 1.80347I
b = 0.13848 − 2.70177I
−7.53406 + 3.01774I 0
u = 0.997250 + 0.488051I
a = 0.503407 − 0.672180I
b = −0.87705 − 1.19948I
−3.62922 − 6.25773I 0
u = 0.997250 − 0.488051I
a = 0.503407 + 0.672180I
b = −0.87705 + 1.19948I
−3.62922 + 6.25773I 0
u = 0.877140 + 0.148952I
a = 0.319254 − 0.244380I
b = 1.383800 − 0.021803I
−1.94154 − 1.69217I 0
u = 0.877140 − 0.148952I
a = 0.319254 + 0.244380I
b = 1.383800 + 0.021803I
−1.94154 + 1.69217I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.551191 + 0.697646I
a = −0.718557 − 0.424698I
b = −0.000171 + 0.443670I
1.83304 − 0.04257I 0
u = −0.551191 − 0.697646I
a = −0.718557 + 0.424698I
b = −0.000171 − 0.443670I
1.83304 + 0.04257I 0
u = −1.113720 + 0.007895I
a = 0.696014 − 0.362883I
b = 1.28502 − 1.37620I
−5.25534 − 6.96011I 0
u = −1.113720 − 0.007895I
a = 0.696014 + 0.362883I
b = 1.28502 + 1.37620I
−5.25534 + 6.96011I 0
u = −0.397409 + 0.784388I
a = −1.61735 − 0.84389I
b = −0.346025 − 0.010243I
0.88603 − 2.61590I 0
u = −0.397409 − 0.784388I
a = −1.61735 + 0.84389I
b = −0.346025 + 0.010243I
0.88603 + 2.61590I 0
u = 1.001020 + 0.506622I
a = 0.362424 + 0.558521I
b = −1.11134 + 2.02291I
−5.78670 − 6.09009I 0
u = 1.001020 − 0.506622I
a = 0.362424 − 0.558521I
b = −1.11134 − 2.02291I
−5.78670 + 6.09009I 0
u = −0.070999 + 0.872170I
a = 0.222455 − 0.293730I
b = −0.079710 + 0.800694I
−4.04271 + 0.14105I 0
u = −0.070999 − 0.872170I
a = 0.222455 + 0.293730I
b = −0.079710 − 0.800694I
−4.04271 − 0.14105I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062620 + 0.373348I
a = 0.669379 + 1.159990I
b = −0.00720 + 2.58624I
−9.42963 + 3.52313I 0
u = 1.062620 − 0.373348I
a = 0.669379 − 1.159990I
b = −0.00720 − 2.58624I
−9.42963 − 3.52313I 0
u = 1.029440 + 0.468018I
a = −0.679986 + 1.187760I
b = 0.03796 + 1.87433I
−4.50899 − 1.41426I 0
u = 1.029440 − 0.468018I
a = −0.679986 − 1.187760I
b = 0.03796 − 1.87433I
−4.50899 + 1.41426I 0
u = −1.055360 + 0.416777I
a = 1.41093 + 0.56066I
b = 1.10806 + 1.28031I
−7.87632 + 5.00657I 0
u = −1.055360 − 0.416777I
a = 1.41093 − 0.56066I
b = 1.10806 − 1.28031I
−7.87632 − 5.00657I 0
u = 1.128130 + 0.138441I
a = 0.490406 + 1.029600I
b = 1.21506 + 1.53210I
−4.14419 + 0.26617I 0
u = 1.128130 − 0.138441I
a = 0.490406 − 1.029600I
b = 1.21506 − 1.53210I
−4.14419 − 0.26617I 0
u = −0.974222 + 0.606012I
a = −0.362252 − 1.303630I
b = −0.89790 − 2.06897I
1.51676 + 6.24193I 0
u = −0.974222 − 0.606012I
a = −0.362252 + 1.303630I
b = −0.89790 + 2.06897I
1.51676 − 6.24193I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.411540 + 0.737500I
a = 1.98145 − 0.41932I
b = 0.198004 − 0.081694I
−0.52582 + 5.71309I 0
u = 0.411540 − 0.737500I
a = 1.98145 + 0.41932I
b = 0.198004 + 0.081694I
−0.52582 − 5.71309I 0
u = 1.041990 + 0.524020I
a = 0.188332 + 0.059206I
b = 0.858931 + 0.001148I
−1.60249 − 1.20863I 0
u = 1.041990 − 0.524020I
a = 0.188332 − 0.059206I
b = 0.858931 − 0.001148I
−1.60249 + 1.20863I 0
u = 0.504932 + 0.663071I
a = −0.029547 − 1.046380I
b = −0.144795 + 0.279639I
−0.01068 − 3.46818I 0
u = 0.504932 − 0.663071I
a = −0.029547 + 1.046380I
b = −0.144795 − 0.279639I
−0.01068 + 3.46818I 0
u = 1.030840 + 0.550584I
a = 0.081680 + 0.737119I
b = 0.07377 + 2.27695I
−4.12716 − 2.65231I 0
u = 1.030840 − 0.550584I
a = 0.081680 − 0.737119I
b = 0.07377 − 2.27695I
−4.12716 + 2.65231I 0
u = 1.077090 + 0.455377I
a = −1.59679 − 0.24739I
b = −1.63729 − 0.38978I
−7.57854 − 1.92005I 0
u = 1.077090 − 0.455377I
a = −1.59679 + 0.24739I
b = −1.63729 + 0.38978I
−7.57854 + 1.92005I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.065590 + 0.482857I
a = −0.032303 − 0.881627I
b = 1.24334 − 2.14322I
−8.70093 + 10.41120I 0
u = −1.065590 − 0.482857I
a = −0.032303 + 0.881627I
b = 1.24334 + 2.14322I
−8.70093 − 10.41120I 0
u = 0.447936 + 1.084730I
a = 0.793300 − 0.275904I
b = 0.106561 + 0.242441I
−4.09201 + 3.51596I 0
u = 0.447936 − 1.084730I
a = 0.793300 + 0.275904I
b = 0.106561 − 0.242441I
−4.09201 − 3.51596I 0
u = 0.774135 + 0.887136I
a = −0.285418 + 0.534779I
b = −0.025746 − 0.229887I
−1.76625 − 10.05830I 0
u = 0.774135 − 0.887136I
a = −0.285418 − 0.534779I
b = −0.025746 + 0.229887I
−1.76625 + 10.05830I 0
u = 1.057200 + 0.522195I
a = 0.319475 − 1.147410I
b = 1.15222 − 2.70949I
−0.68694 − 5.83662I 0
u = 1.057200 − 0.522195I
a = 0.319475 + 1.147410I
b = 1.15222 + 2.70949I
−0.68694 + 5.83662I 0
u = 1.014160 + 0.611681I
a = 0.49863 − 1.52419I
b = 0.42736 − 1.97683I
−1.77729 − 7.16397I 0
u = 1.014160 − 0.611681I
a = 0.49863 + 1.52419I
b = 0.42736 + 1.97683I
−1.77729 + 7.16397I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.490276 + 0.649949I
a = −1.25407 − 0.97607I
b = 0.044037 + 0.412853I
2.05585 + 0.51972I 0
u = −0.490276 − 0.649949I
a = −1.25407 + 0.97607I
b = 0.044037 − 0.412853I
2.05585 − 0.51972I 0
u = −1.046380 + 0.570637I
a = −0.472941 − 0.969669I
b = −1.49813 − 1.94744I
0.42171 + 4.26907I 0
u = −1.046380 − 0.570637I
a = −0.472941 + 0.969669I
b = −1.49813 + 1.94744I
0.42171 − 4.26907I 0
u = −1.042350 + 0.593238I
a = −0.023763 − 0.780552I
b = −0.60275 − 1.50249I
0.34557 + 5.01997I 0
u = −1.042350 − 0.593238I
a = −0.023763 + 0.780552I
b = −0.60275 + 1.50249I
0.34557 − 5.01997I 0
u = −0.201828 + 0.771335I
a = −0.90135 − 1.61437I
b = −0.191801 − 0.131891I
1.10724 − 2.01592I 0
u = −0.201828 − 0.771335I
a = −0.90135 + 1.61437I
b = −0.191801 + 0.131891I
1.10724 + 2.01592I 0
u = 1.167640 + 0.293720I
a = −0.192728 − 0.745197I
b = 0.783957 − 1.173730I
−8.30514 − 3.98448I 0
u = 1.167640 − 0.293720I
a = −0.192728 + 0.745197I
b = 0.783957 + 1.173730I
−8.30514 + 3.98448I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.045390 + 0.627865I
a = −0.549568 − 0.896469I
b = −0.26589 − 1.78659I
−3.10720 − 8.54200I 0
u = 1.045390 − 0.627865I
a = −0.549568 + 0.896469I
b = −0.26589 + 1.78659I
−3.10720 + 8.54200I 0
u = 0.709475 + 0.317529I
a = 0.70726 + 2.86628I
b = 0.40349 + 2.30893I
−6.41519 + 5.46475I 0
u = 0.709475 − 0.317529I
a = 0.70726 − 2.86628I
b = 0.40349 − 2.30893I
−6.41519 − 5.46475I 0
u = −1.149490 + 0.441407I
a = 0.329460 − 0.001479I
b = −0.553301 + 0.312929I
−7.43064 + 4.29698I 0
u = −1.149490 − 0.441407I
a = 0.329460 + 0.001479I
b = −0.553301 − 0.312929I
−7.43064 − 4.29698I 0
u = −1.061680 + 0.635110I
a = 0.273735 + 0.822058I
b = 0.60024 + 2.06447I
2.20474 + 7.83098I 0
u = −1.061680 − 0.635110I
a = 0.273735 − 0.822058I
b = 0.60024 − 2.06447I
2.20474 − 7.83098I 0
u = 1.093920 + 0.584750I
a = 0.27404 − 1.64466I
b = 0.44168 − 3.03809I
−2.53199 − 10.75090I 0
u = 1.093920 − 0.584750I
a = 0.27404 + 1.64466I
b = 0.44168 + 3.03809I
−2.53199 + 10.75090I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844461 + 0.909920I
a = −0.036134 + 0.171839I
b = −0.511082 + 0.464120I
−1.98553 + 3.69676I 0
u = 0.844461 − 0.909920I
a = −0.036134 − 0.171839I
b = −0.511082 − 0.464120I
−1.98553 − 3.69676I 0
u = −1.053720 + 0.677803I
a = −0.24880 − 1.57148I
b = −0.68846 − 2.15501I
−2.29942 + 9.87625I 0
u = −1.053720 − 0.677803I
a = −0.24880 + 1.57148I
b = −0.68846 + 2.15501I
−2.29942 − 9.87625I 0
u = 1.090210 + 0.627244I
a = −0.276428 + 1.000330I
b = −0.87343 + 2.39462I
−1.4939 − 14.1007I 0
u = 1.090210 − 0.627244I
a = −0.276428 − 1.000330I
b = −0.87343 − 2.39462I
−1.4939 + 14.1007I 0
u = −1.109810 + 0.595798I
a = −0.56579 − 1.52348I
b = −1.06136 − 2.59414I
−1.22390 + 7.80396I 0
u = −1.109810 − 0.595798I
a = −0.56579 + 1.52348I
b = −1.06136 + 2.59414I
−1.22390 − 7.80396I 0
u = 1.071680 + 0.675404I
a = −0.578131 + 0.433434I
b = −0.769959 + 0.563752I
−1.109680 − 0.239217I 0
u = 1.071680 − 0.675404I
a = −0.578131 − 0.433434I
b = −0.769959 − 0.563752I
−1.109680 + 0.239217I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576149 + 0.433704I
a = −0.967765 − 0.533623I
b = 0.98431 − 1.39957I
−4.48236 + 2.03856I 0
u = 0.576149 − 0.433704I
a = −0.967765 + 0.533623I
b = 0.98431 + 1.39957I
−4.48236 − 2.03856I 0
u = −1.100880 + 0.658866I
a = 0.440915 + 0.610542I
b = 0.438226 + 1.167770I
1.39954 + 6.58242I 0
u = −1.100880 − 0.658866I
a = 0.440915 − 0.610542I
b = 0.438226 − 1.167770I
1.39954 − 6.58242I 0
u = 0.438745 + 0.565194I
a = −0.922849 − 0.305989I
b = 0.636590 + 0.015216I
−2.50848 − 1.85627I 0
u = 0.438745 − 0.565194I
a = −0.922849 + 0.305989I
b = 0.636590 − 0.015216I
−2.50848 + 1.85627I 0
u = −1.186580 + 0.574880I
a = −0.759028 − 0.930199I
b = −1.40864 − 1.66478I
−1.71299 + 7.11811I 0
u = −1.186580 − 0.574880I
a = −0.759028 + 0.930199I
b = −1.40864 + 1.66478I
−1.71299 − 7.11811I 0
u = −1.315580 + 0.125248I
a = 0.627221 − 0.754303I
b = 1.39249 − 1.43802I
−10.0986 − 11.3443I 0
u = −1.315580 − 0.125248I
a = 0.627221 + 0.754303I
b = 1.39249 + 1.43802I
−10.0986 + 11.3443I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167420 + 0.624750I
a = −0.309489 + 0.995822I
b = −0.39917 + 2.08712I
−8.53381 − 9.12168I 0
u = 1.167420 − 0.624750I
a = −0.309489 − 0.995822I
b = −0.39917 − 2.08712I
−8.53381 + 9.12168I 0
u = −1.165530 + 0.633557I
a = 0.482070 + 1.193780I
b = 0.89158 + 2.27526I
−2.9570 + 14.3312I 0
u = −1.165530 − 0.633557I
a = 0.482070 − 1.193780I
b = 0.89158 − 2.27526I
−2.9570 − 14.3312I 0
u = 1.166340 + 0.639823I
a = −0.427733 + 1.343320I
b = −0.94877 + 2.57215I
−6.5136 − 20.3636I 0
u = 1.166340 − 0.639823I
a = −0.427733 − 1.343320I
b = −0.94877 − 2.57215I
−6.5136 + 20.3636I 0
u = 0.562527 + 0.360078I
a = 0.535055 + 0.250854I
b = 0.23212 − 1.47561I
−2.30551 + 2.41321I 0
u = 0.562527 − 0.360078I
a = 0.535055 − 0.250854I
b = 0.23212 + 1.47561I
−2.30551 − 2.41321I 0
u = 1.324030 + 0.149451I
a = −0.581312 − 0.633839I
b = −1.13471 − 1.13580I
−6.38377 + 5.27943I 0
u = 1.324030 − 0.149451I
a = −0.581312 + 0.633839I
b = −1.13471 + 1.13580I
−6.38377 − 5.27943I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.253400 + 0.461324I
a = 0.920744 − 0.218807I
b = 1.66177 − 0.56815I
−2.85340 − 2.22309I 0
u = 1.253400 − 0.461324I
a = 0.920744 + 0.218807I
b = 1.66177 + 0.56815I
−2.85340 + 2.22309I 0
u = −1.355450 + 0.122500I
a = 0.292938 − 0.662790I
b = 0.365990 − 1.319890I
−11.95100 + 0.03526I 0
u = −1.355450 − 0.122500I
a = 0.292938 + 0.662790I
b = 0.365990 + 1.319890I
−11.95100 − 0.03526I 0
u = −0.569278 + 0.268741I
a = 1.92621 − 0.68538I
b = 1.11269 + 1.26871I
−6.12285 + 6.51973I 0. − 6.19150I
u = −0.569278 − 0.268741I
a = 1.92621 + 0.68538I
b = 1.11269 − 1.26871I
−6.12285 − 6.51973I 0. + 6.19150I
u = 0.384605 + 0.488008I
a = 1.98026 − 0.76831I
b = −0.382636 + 0.345120I
1.18594 + 1.54456I 6.00000 + 0.I
u = 0.384605 − 0.488008I
a = 1.98026 + 0.76831I
b = −0.382636 − 0.345120I
1.18594 − 1.54456I 6.00000 + 0.I
u = 1.204570 + 0.697620I
a = 0.125886 − 0.921075I
b = 0.52355 − 1.73548I
−6.51030 − 9.89166I 0
u = 1.204570 − 0.697620I
a = 0.125886 + 0.921075I
b = 0.52355 + 1.73548I
−6.51030 + 9.89166I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165315 + 0.465261I
a = 0.39378 + 2.37313I
b = −0.089740 + 1.128560I
−5.18810 − 1.89288I 1.19982 + 2.47414I
u = 0.165315 − 0.465261I
a = 0.39378 − 2.37313I
b = −0.089740 − 1.128560I
−5.18810 + 1.89288I 1.19982 − 2.47414I
u = −0.194114 + 0.446095I
a = −1.98584 + 1.02772I
b = 0.312667 − 1.013280I
−6.50477 − 6.47522I 1.82966 + 5.52245I
u = −0.194114 − 0.446095I
a = −1.98584 − 1.02772I
b = 0.312667 + 1.013280I
−6.50477 + 6.47522I 1.82966 − 5.52245I
u = 0.283597 + 0.352278I
a = −1.83595 − 0.26178I
b = −0.456914 + 0.949294I
−2.63254 − 2.28841I 4.95456 + 3.86114I
u = 0.283597 − 0.352278I
a = −1.83595 + 0.26178I
b = −0.456914 − 0.949294I
−2.63254 + 2.28841I 4.95456 − 3.86114I
u = −1.65908 + 0.01030I
a = −0.038605 + 0.215099I
b = −0.218873 + 0.332343I
−11.93350 + 0.51771I 0
u = −1.65908 − 0.01030I
a = −0.038605 − 0.215099I
b = −0.218873 − 0.332343I
−11.93350 − 0.51771I 0
u = −0.232545
a = −1.56904
b = −0.441694
0.757026 13.4850
u = 0.172569 + 0.015223I
a = 6.99491 − 2.93176I
b = −0.270473 − 0.456161I
1.11614 − 1.37432I 3.73816 − 2.29235I
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172569 − 0.015223I
a = 6.99491 + 2.93176I
b = −0.270473 + 0.456161I
1.11614 + 1.37432I 3.73816 + 2.29235I
22
II. I
u
2
= h3.22 × 10
7
u
41
+ 7.90 × 10
7
u
40
+ · · · + 7.64 × 10
5
b + 1.41 × 10
8
, 9.05 ×
10
7
u
41
+2.21×10
8
u
40
+· · ·+2.29×10
6
a+3.95×10
8
, u
42
+3u
41
+· · ·−26u
2
+3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−39.4554u
41
− 96.3427u
40
+ ··· + 193.507u − 172.051
−42.1221u
41
− 103.343u
40
+ ··· + 196.841u − 184.051
a
7
=
151.040u
41
+ 332.264u
40
+ ··· − 470.103u + 473.697
205.034u
41
+ 429.544u
40
+ ··· − 515.716u + 602.451
a
1
=
−u
2
+ 1
−u
4
a
10
=
−61.4724u
41
− 140.672u
40
+ ··· + 242.420u − 238.195
−72.6820u
41
− 161.789u
40
+ ··· + 234.907u − 249.320
a
11
=
42.6390u
41
+ 123.914u
40
+ ··· − 312.347u + 206.513
58.2703u
41
+ 166.496u
40
+ ··· − 443.718u + 304.497
a
5
=
u
u
a
4
=
60.7798u
41
+ 98.9825u
40
+ ··· + 2.83355u + 110.653
41.9942u
41
+ 48.4683u
40
+ ··· + 155.753u − 10.3840
a
8
=
−40.4554u
41
− 96.3427u
40
+ ··· + 185.507u − 169.051
−43.1221u
41
− 103.343u
40
+ ··· + 188.841u − 181.051
a
12
=
−44.2697u
41
− 94.4060u
40
+ ··· + 113.630u − 155.305
−55.2775u
41
− 106.785u
40
+ ··· + 68.1978u − 121.661
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
118142947
764339
u
41
−
319492704
764339
u
40
+ ··· +
818560154
764339
u −
566660982
764339
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
42
− 25u
41
+ ··· − 156u + 9
c
2
u
42
+ 3u
41
+ ··· − 26u
2
+ 3
c
3
u
42
− 2u
40
+ ··· − 2u + 1
c
4
u
42
+ u
41
+ ··· + u + 1
c
5
u
42
− 3u
41
+ ··· − 26u
2
+ 3
c
6
u
42
+ 16u
41
+ ··· + 112u + 8
c
7
u
42
+ u
41
+ ··· − 15u + 3
c
8
u
42
+ 3u
41
+ ··· + 9u + 1
c
9
u
42
+ 2u
41
+ ··· + 7u + 1
c
10
u
42
+ 3u
41
+ ··· − 2u + 1
c
11
u
42
− u
41
+ ··· − u + 1
c
12
u
42
− 2u
41
+ ··· − 7u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− 5y
41
+ ··· + 1008y + 81
c
2
, c
5
y
42
− 25y
41
+ ··· − 156y + 9
c
3
y
42
− 4y
41
+ ··· + 46y + 1
c
4
, c
11
y
42
+ 27y
41
+ ··· + 29y + 1
c
6
y
42
+ 12y
41
+ ··· + 992y + 64
c
7
y
42
+ 9y
41
+ ··· + 321y + 9
c
8
y
42
− 13y
41
+ ··· − 25y + 1
c
9
, c
12
y
42
+ 40y
41
+ ··· + 57y + 1
c
10
y
42
+ 27y
41
+ ··· + 2y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950455 + 0.305739I
a = 1.46536 − 1.11570I
b = 0.900838 − 0.310788I
−7.47440 + 7.44321I −1.35817 − 7.45357I
u = −0.950455 − 0.305739I
a = 1.46536 + 1.11570I
b = 0.900838 + 0.310788I
−7.47440 − 7.44321I −1.35817 + 7.45357I
u = 0.978940 + 0.247424I
a = 0.85009 + 1.62491I
b = 1.18486 + 2.16175I
−4.79501 + 2.06027I −3.74268 − 1.03228I
u = 0.978940 − 0.247424I
a = 0.85009 − 1.62491I
b = 1.18486 − 2.16175I
−4.79501 − 2.06027I −3.74268 + 1.03228I
u = −0.952141 + 0.413492I
a = 0.691387 + 0.329126I
b = −1.10151 + 1.04083I
−6.17745 − 0.42747I 6.00000 + 1.53704I
u = −0.952141 − 0.413492I
a = 0.691387 − 0.329126I
b = −1.10151 − 1.04083I
−6.17745 + 0.42747I 6.00000 − 1.53704I
u = 0.994762 + 0.332933I
a = 0.511915 + 0.214663I
b = 1.29740 + 0.74563I
−0.803314 − 1.046230I 8.87158 + 0.64110I
u = 0.994762 − 0.332933I
a = 0.511915 − 0.214663I
b = 1.29740 − 0.74563I
−0.803314 + 1.046230I 8.87158 − 0.64110I
u = −0.894418 + 0.311210I
a = −0.06540 + 2.21926I
b = −0.41663 + 3.42169I
−7.28408 − 4.87526I −3.30424 + 3.66370I
u = −0.894418 − 0.311210I
a = −0.06540 − 2.21926I
b = −0.41663 − 3.42169I
−7.28408 + 4.87526I −3.30424 − 3.66370I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536116 + 0.762720I
a = −1.76248 − 0.46691I
b = −0.765475 + 0.017457I
−0.50936 − 3.17813I 5.46215 + 2.44478I
u = −0.536116 − 0.762720I
a = −1.76248 + 0.46691I
b = −0.765475 − 0.017457I
−0.50936 + 3.17813I 5.46215 − 2.44478I
u = −0.437139 + 0.817645I
a = −0.699117 − 0.717728I
b = 0.0575289 − 0.1221050I
3.33029 − 1.50340I 8.43166 + 5.43951I
u = −0.437139 − 0.817645I
a = −0.699117 + 0.717728I
b = 0.0575289 + 0.1221050I
3.33029 + 1.50340I 8.43166 − 5.43951I
u = 1.067150 + 0.193273I
a = −0.399628 − 1.005190I
b = −0.110132 − 0.777969I
−4.96584 − 3.41767I 2.55114 + 2.70113I
u = 1.067150 − 0.193273I
a = −0.399628 + 1.005190I
b = −0.110132 + 0.777969I
−4.96584 + 3.41767I 2.55114 − 2.70113I
u = −0.824147 + 0.349081I
a = 0.446059 + 0.589435I
b = 0.63553 + 2.47791I
−5.63369 + 3.63547I 2.06259 − 9.95411I
u = −0.824147 − 0.349081I
a = 0.446059 − 0.589435I
b = 0.63553 − 2.47791I
−5.63369 − 3.63547I 2.06259 + 9.95411I
u = 0.613680 + 0.948187I
a = 0.900161 + 0.082005I
b = 0.222985 + 0.263234I
−2.94042 + 4.12643I 0. − 6.84078I
u = 0.613680 − 0.948187I
a = 0.900161 − 0.082005I
b = 0.222985 − 0.263234I
−2.94042 − 4.12643I 0. + 6.84078I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016270 + 0.510467I
a = −0.570359 − 0.372196I
b = 0.61336 − 1.30916I
−5.31912 − 6.11142I 6.00000 + 8.63274I
u = 1.016270 − 0.510467I
a = −0.570359 + 0.372196I
b = 0.61336 + 1.30916I
−5.31912 + 6.11142I 6.00000 − 8.63274I
u = −1.024030 + 0.539879I
a = −0.512115 − 1.212970I
b = −1.39318 − 2.29964I
0.49914 + 5.10411I 0. − 6.82539I
u = −1.024030 − 0.539879I
a = −0.512115 + 1.212970I
b = −1.39318 + 2.29964I
0.49914 − 5.10411I 0. + 6.82539I
u = −0.598251 + 0.545469I
a = −1.79273 − 0.60929I
b = −0.195739 + 0.282322I
1.85564 − 0.68349I 6.64001 − 3.21154I
u = −0.598251 − 0.545469I
a = −1.79273 + 0.60929I
b = −0.195739 − 0.282322I
1.85564 + 0.68349I 6.64001 + 3.21154I
u = 0.397145 + 0.691883I
a = 0.433660 + 0.041184I
b = −0.463476 + 0.905266I
−3.59397 + 1.76380I 4.69246 − 1.87261I
u = 0.397145 − 0.691883I
a = 0.433660 − 0.041184I
b = −0.463476 − 0.905266I
−3.59397 − 1.76380I 4.69246 + 1.87261I
u = −1.069900 + 0.609641I
a = −0.47718 − 1.69608I
b = −0.79127 − 2.59435I
−2.15943 + 8.39551I 0
u = −1.069900 − 0.609641I
a = −0.47718 + 1.69608I
b = −0.79127 + 2.59435I
−2.15943 − 8.39551I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.058590 + 0.669027I
a = −0.244549 − 1.247240I
b = −0.20636 − 2.12537I
−4.39127 − 9.99269I 0
u = 1.058590 − 0.669027I
a = −0.244549 + 1.247240I
b = −0.20636 + 2.12537I
−4.39127 + 9.99269I 0
u = 1.171190 + 0.473424I
a = 0.538639 − 0.310474I
b = 1.061100 − 0.636919I
−0.95429 − 1.62282I 0
u = 1.171190 − 0.473424I
a = 0.538639 + 0.310474I
b = 1.061100 + 0.636919I
−0.95429 + 1.62282I 0
u = 0.703787 + 0.205389I
a = 0.674199 + 1.168430I
b = −0.26560 + 2.00903I
−3.50925 + 2.38598I 2.81211 − 4.43489I
u = 0.703787 − 0.205389I
a = 0.674199 − 1.168430I
b = −0.26560 − 2.00903I
−3.50925 − 2.38598I 2.81211 + 4.43489I
u = −1.104950 + 0.654924I
a = −0.358378 − 0.691276I
b = −0.50656 − 1.42701I
1.35727 + 7.01956I 0
u = −1.104950 − 0.654924I
a = −0.358378 + 0.691276I
b = −0.50656 + 1.42701I
1.35727 − 7.01956I 0
u = 0.567146 + 0.360348I
a = 1.46206 − 1.25083I
b = 0.0110741 − 0.0812385I
1.18767 − 1.94619I 5.18581 + 9.50954I
u = 0.567146 − 0.360348I
a = 1.46206 + 1.25083I
b = 0.0110741 + 0.0812385I
1.18767 + 1.94619I 5.18581 − 9.50954I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67712 + 0.03214I
a = −0.091602 + 0.162397I
b = −0.268741 + 0.155044I
−11.87150 − 0.63109I 0
u = −1.67712 − 0.03214I
a = −0.091602 − 0.162397I
b = −0.268741 − 0.155044I
−11.87150 + 0.63109I 0
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
42
− 25u
41
+ ··· − 156u + 9)(u
171
+ 82u
170
+ ··· + 109u + 1)
c
2
(u
42
+ 3u
41
+ ··· − 26u
2
+ 3)(u
171
+ 4u
170
+ ··· − 15u − 1)
c
3
(u
42
− 2u
40
+ ··· − 2u + 1)
· (u
171
+ u
170
+ ··· + 426385251u − 251071867)
c
4
(u
42
+ u
41
+ ··· + u + 1)(u
171
− 2u
170
+ ··· + 3950u − 1849)
c
5
(u
42
− 3u
41
+ ··· − 26u
2
+ 3)(u
171
+ 4u
170
+ ··· − 15u − 1)
c
6
(u
42
+ 16u
41
+ ··· + 112u + 8)(u
171
− 3u
170
+ ··· − 148u − 1496)
c
7
(u
42
+ u
41
+ ··· − 15u + 3)
· (u
171
+ 2u
170
+ ··· − 2755517934u − 204636559)
c
8
(u
42
+ 3u
41
+ ··· + 9u + 1)(u
171
− 15u
169
+ ··· − 541710u − 228281)
c
9
(u
42
+ 2u
41
+ ··· + 7u + 1)(u
171
+ 11u
170
+ ··· − 15988u − 3784)
c
10
(u
42
+ 3u
41
+ ··· − 2u + 1)(u
171
+ 4u
170
+ ··· − 974881u − 49723)
c
11
(u
42
− u
41
+ ··· − u + 1)(u
171
− 2u
170
+ ··· + 3950u − 1849)
c
12
(u
42
− 2u
41
+ ··· − 7u + 1)(u
171
+ 11u
170
+ ··· − 15988u − 3784)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
42
− 5y
41
+ ··· + 1008y + 81)(y
171
+ 26y
170
+ ··· + 2329y −1)
c
2
, c
5
(y
42
− 25y
41
+ ··· − 156y + 9)(y
171
− 82y
170
+ ··· + 109y −1)
c
3
(y
42
− 4y
41
+ ··· + 46y + 1)
· (y
171
+ 39y
170
+ ··· − 1949406148708587857y −63037082398865689)
c
4
, c
11
(y
42
+ 27y
41
+ ··· + 29y + 1)
· (y
171
+ 106y
170
+ ··· − 87630868y −3418801)
c
6
(y
42
+ 12y
41
+ ··· + 992y + 64)
· (y
171
+ 7y
170
+ ··· + 82092464y −2238016)
c
7
(y
42
+ 9y
41
+ ··· + 321y + 9)
· (y
171
+ 60y
170
+ ··· − 3089300280968879260y −41876121279360481)
c
8
(y
42
− 13y
41
+ ··· − 25y + 1)
· (y
171
− 30y
170
+ ··· + 167534946682y −52112214961)
c
9
, c
12
(y
42
+ 40y
41
+ ··· + 57y + 1)
· (y
171
+ 131y
170
+ ··· − 270117680y −14318656)
c
10
(y
42
+ 27y
41
+ ··· + 2y + 1)
· (y
171
+ 50y
170
+ ··· − 24962763117y −2472376729)
34
