12a
0698
(K12a
0698
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 12 1 11 2 5 7 9 4
Solving Sequence
4,10 5,12
6 1 7 3 9 11 8 2
c
4
c
5
c
12
c
6
c
3
c
9
c
11
c
7
c
2
c
1
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.93801 × 10
1004
u
165
− 6.10876 × 10
1004
u
164
+ ··· + 4.43418 × 10
1003
b + 4.56960 × 10
1008
,
1.93137 × 10
1009
u
165
+ 1.57216 × 10
1009
u
164
+ ··· + 1.53746 × 10
1008
a − 9.46926 × 10
1012
,
3u
166
+ u
165
+ ··· + 158795u − 34673i
I
u
2
= h−3.22786 × 10
28
u
40
− 2.94202 × 10
28
u
39
+ ··· + 7.20126 × 10
23
b + 7.42965 × 10
27
,
2.04412 × 10
29
u
40
+ 2.34054 × 10
29
u
39
+ ··· + 7.20126 × 10
23
a − 2.07039 × 10
28
, 3u
41
+ 4u
40
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 207 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−5.94 × 10
1004
u
165
− 6.11 × 10
1004
u
164
+ · · · + 4.43 × 10
1003
b +
4.57 × 10
1008
, 1.93 × 10
1009
u
165
+ 1.57 × 10
1009
u
164
+ · · · + 1.54 × 10
1008
a −
9.47 × 10
1012
, 3u
166
+ u
165
+ · · · + 158795u − 34673i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
12
=
−12.5620u
165
− 10.2257u
164
+ ··· − 115249.u + 61590.1
13.3914u
165
+ 13.7765u
164
+ ··· + 297471.u − 103054.
a
6
=
4.50111u
165
+ 9.08946u
164
+ ··· + 312445.u − 81523.8
4.18966u
165
− 1.18288u
164
+ ··· − 208987.u + 35460.0
a
1
=
0.829406u
165
+ 3.55083u
164
+ ··· + 182221.u − 41463.9
13.3914u
165
+ 13.7765u
164
+ ··· + 297471.u − 103054.
a
7
=
8.10917u
165
+ 8.55775u
164
+ ··· + 182756.u − 62856.9
1.44500u
165
+ 2.27183u
164
+ ··· + 100018.u − 24448.9
a
3
=
3.72196u
165
− 8.01983u
164
+ ··· − 578450.u + 117911.
−6.77876u
165
− 8.62088u
164
+ ··· − 238138.u + 71425.4
a
9
=
u
u
3
+ u
a
11
=
0.840773u
165
+ 3.51002u
164
+ ··· + 177388.u − 40546.1
15.0557u
165
+ 14.0762u
164
+ ··· + 254436.u − 98072.5
a
8
=
6.77989u
165
+ 11.7779u
164
+ ··· + 387456.u − 104685.
5.30148u
165
− 2.53704u
164
+ ··· − 323400.u + 58111.5
a
2
=
−6.11877u
165
+ 0.116900u
164
+ ··· + 211422.u − 31703.0
2.04072u
165
+ 3.41291u
164
+ ··· + 108062.u − 29669.1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.35284u
165
+ 5.59579u
164
+ ··· + 185940.u − 52310.4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(9u
166
+ 548u
165
+ ··· + 1674688u + 37249)
c
2
, c
8
3(3u
166
+ 10u
165
+ ··· − 72u − 193)
c
3
u
166
− 26u
165
+ ··· − 3326078u + 219087
c
4
, c
9
3(3u
166
+ u
165
+ ··· + 158795u − 34673)
c
5
u
166
+ u
165
+ ··· + 3422516u − 262817
c
6
u
166
+ 2u
165
+ ··· + 2824430u + 436239
c
7
, c
10
u
166
− 49u
164
+ ··· + 2520956u + 2425663
c
11
u
166
+ 9u
165
+ ··· + 3480001987u + 3246415791
c
12
9(9u
166
+ 98u
165
+ ··· − 12u − 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(81y
166
+ 5408y
165
+ ··· − 2.42908 × 10
11
y + 1.38749 × 10
9
)
c
2
, c
8
9(9y
166
+ 548y
165
+ ··· + 1674688y + 37249)
c
3
y
166
− 4y
165
+ ··· + 1995653540696y + 47999113569
c
4
, c
9
9(9y
166
+ 1043y
165
+ ··· + 3.28301 × 10
10
y + 1.20222 × 10
9
)
c
5
y
166
− 27y
165
+ ··· + 21178704987358y + 69072775489
c
6
y
166
+ 34y
165
+ ··· + 7330681481006y + 190304465121
c
7
, c
10
y
166
− 98y
165
+ ··· + 164556690192526y + 5883840989569
c
11
y
166
− 69y
165
+ ··· − 4.67 × 10
20
y + 1.05 × 10
19
c
12
81(81y
166
− 2044y
165
+ ··· + 118y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448185 + 0.894932I
a = 2.49663 − 0.47452I
b = −1.38436 − 0.77923I
2.42095 + 10.29690I 0
u = −0.448185 − 0.894932I
a = 2.49663 + 0.47452I
b = −1.38436 + 0.77923I
2.42095 − 10.29690I 0
u = −0.242605 + 0.974518I
a = 2.69617 + 0.37041I
b = −1.67458 − 1.36534I
−0.32447 + 3.71499I 0
u = −0.242605 − 0.974518I
a = 2.69617 − 0.37041I
b = −1.67458 + 1.36534I
−0.32447 − 3.71499I 0
u = 0.029029 + 0.990881I
a = 0.09091 + 1.85495I
b = −0.014668 + 0.843715I
−0.16410 − 2.59463I 0
u = 0.029029 − 0.990881I
a = 0.09091 − 1.85495I
b = −0.014668 − 0.843715I
−0.16410 + 2.59463I 0
u = 0.082464 + 0.984904I
a = −0.1156355 + 0.0157277I
b = 0.304104 − 1.321090I
2.53184 − 2.60316I 0
u = 0.082464 − 0.984904I
a = −0.1156355 − 0.0157277I
b = 0.304104 + 1.321090I
2.53184 + 2.60316I 0
u = 0.027624 + 0.970485I
a = 0.038744 + 0.780028I
b = −0.33961 − 1.73805I
−1.11542 − 1.19066I 0
u = 0.027624 − 0.970485I
a = 0.038744 − 0.780028I
b = −0.33961 + 1.73805I
−1.11542 + 1.19066I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620419 + 0.736789I
a = 0.153850 − 0.200517I
b = 0.171744 + 0.401489I
0.20448 + 1.78532I 0
u = −0.620419 − 0.736789I
a = 0.153850 + 0.200517I
b = 0.171744 − 0.401489I
0.20448 − 1.78532I 0
u = −0.936987 + 0.205652I
a = −0.022756 + 0.192563I
b = −0.662032 + 0.927484I
−4.24556 − 2.17045I 0
u = −0.936987 − 0.205652I
a = −0.022756 − 0.192563I
b = −0.662032 − 0.927484I
−4.24556 + 2.17045I 0
u = 0.042824 + 0.954124I
a = 1.97457 − 1.33109I
b = −1.17101 + 1.26858I
−1.085300 + 0.725929I 0
u = 0.042824 − 0.954124I
a = 1.97457 + 1.33109I
b = −1.17101 − 1.26858I
−1.085300 − 0.725929I 0
u = 0.732322 + 0.609440I
a = −1.13166 − 1.23422I
b = −0.334025 − 1.146573I
3.15263 − 7.69653I 0
u = 0.732322 − 0.609440I
a = −1.13166 + 1.23422I
b = −0.334025 + 1.146573I
3.15263 + 7.69653I 0
u = −0.306864 + 1.006208I
a = 0.843855 − 0.945019I
b = −0.463523 − 0.861437I
−0.28737 + 5.26850I 0
u = −0.306864 − 1.006208I
a = 0.843855 + 0.945019I
b = −0.463523 + 0.861437I
−0.28737 − 5.26850I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591594 + 0.877929I
a = −1.142456 − 0.390484I
b = 0.803497 − 0.899071I
2.43411 − 5.62029I 0
u = 0.591594 − 0.877929I
a = −1.142456 + 0.390484I
b = 0.803497 + 0.899071I
2.43411 + 5.62029I 0
u = −0.271280 + 1.024509I
a = 1.169069 + 0.034547I
b = −0.354249 − 0.155729I
0.71103 + 1.78081I 0
u = −0.271280 − 1.024509I
a = 1.169069 − 0.034547I
b = −0.354249 + 0.155729I
0.71103 − 1.78081I 0
u = 0.076302 + 0.928889I
a = −1.06699 + 1.52148I
b = 0.0647555 − 0.1176325I
−0.19788 + 2.15408I 0
u = 0.076302 − 0.928889I
a = −1.06699 − 1.52148I
b = 0.0647555 + 0.1176325I
−0.19788 − 2.15408I 0
u = −0.387426 + 0.842987I
a = 0.0523906 + 0.0965007I
b = 0.127279 + 0.401261I
0.20278 + 1.72610I 0
u = −0.387426 − 0.842987I
a = 0.0523906 − 0.0965007I
b = 0.127279 − 0.401261I
0.20278 − 1.72610I 0
u = 0.873184 + 0.299580I
a = −0.383994 + 0.137709I
b = −0.484781 + 0.649363I
−3.60365 − 5.60521I 0
u = 0.873184 − 0.299580I
a = −0.383994 − 0.137709I
b = −0.484781 − 0.649363I
−3.60365 + 5.60521I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146459 + 1.069029I
a = 1.99838 − 0.73279I
b = −1.34690 + 0.91318I
1.05603 − 7.10054I 0
u = 0.146459 − 1.069029I
a = 1.99838 + 0.73279I
b = −1.34690 − 0.91318I
1.05603 + 7.10054I 0
u = 0.474367 + 0.971148I
a = −2.31065 − 0.43014I
b = 1.26168 − 0.84363I
3.50302 − 5.39022I 0
u = 0.474367 − 0.971148I
a = −2.31065 + 0.43014I
b = 1.26168 + 0.84363I
3.50302 + 5.39022I 0
u = −0.914242 + 0.062247I
a = 0.259072 − 0.295365I
b = −0.678081 − 0.963901I
−0.42502 + 8.47270I 0
u = −0.914242 − 0.062247I
a = 0.259072 + 0.295365I
b = −0.678081 + 0.963901I
−0.42502 − 8.47270I 0
u = −0.070987 + 1.090673I
a = −1.80924 − 0.83794I
b = 1.20315 + 0.92324I
3.52367 + 2.23626I 0
u = −0.070987 − 1.090673I
a = −1.80924 + 0.83794I
b = 1.20315 − 0.92324I
3.52367 − 2.23626I 0
u = −0.600344 + 0.678171I
a = 0.376329 − 0.501686I
b = −0.959335 + 1.038481I
1.81149 − 6.08930I 0
u = −0.600344 − 0.678171I
a = 0.376329 + 0.501686I
b = −0.959335 − 1.038481I
1.81149 + 6.08930I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215468 + 1.086565I
a = 0.002641 − 1.176387I
b = 0.205218 − 0.872507I
5.93187 − 4.58568I 0
u = 0.215468 − 1.086565I
a = 0.002641 + 1.176387I
b = 0.205218 + 0.872507I
5.93187 + 4.58568I 0
u = 0.862802 + 0.700688I
a = 0.228193 − 0.468293I
b = 0.428888 + 0.517607I
1.66600 + 0.35256I 0
u = 0.862802 − 0.700688I
a = 0.228193 + 0.468293I
b = 0.428888 − 0.517607I
1.66600 − 0.35256I 0
u = −0.238710 + 1.093908I
a = 0.141706 − 1.387120I
b = −0.237581 − 0.811736I
5.07541 + 10.34460I 0
u = −0.238710 − 1.093908I
a = 0.141706 + 1.387120I
b = −0.237581 + 0.811736I
5.07541 − 10.34460I 0
u = 1.12548
a = 0.340024
b = −0.285517
2.56754 0
u = −1.027901 + 0.459441I
a = −0.232635 − 0.165502I
b = −0.604673 + 0.741566I
0.06352 + 4.52538I 0
u = −1.027901 − 0.459441I
a = −0.232635 + 0.165502I
b = −0.604673 − 0.741566I
0.06352 − 4.52538I 0
u = 0.617295 + 0.594949I
a = −0.290771 − 0.336423I
b = 0.916716 + 0.995629I
2.40378 + 1.08400I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617295 − 0.594949I
a = −0.290771 + 0.336423I
b = 0.916716 − 0.995629I
2.40378 − 1.08400I 0
u = 0.681195 + 0.517309I
a = 0.619353 − 0.571242I
b = 0.553877 + 0.376799I
1.74384 + 0.40504I 0
u = 0.681195 − 0.517309I
a = 0.619353 + 0.571242I
b = 0.553877 − 0.376799I
1.74384 − 0.40504I 0
u = 0.228471 + 0.821072I
a = −2.40118 + 0.11987I
b = 0.066724 − 0.342117I
−2.75019 − 3.06768I 0
u = 0.228471 − 0.821072I
a = −2.40118 − 0.11987I
b = 0.066724 + 0.342117I
−2.75019 + 3.06768I 0
u = 0.190536 + 1.141965I
a = −1.34267 − 0.90127I
b = 1.048590 + 0.778759I
5.73230 − 0.49141I 0
u = 0.190536 − 1.141965I
a = −1.34267 + 0.90127I
b = 1.048590 − 0.778759I
5.73230 + 0.49141I 0
u = 0.203687 + 0.817190I
a = 0.265312 + 1.347979I
b = −0.009909 + 0.924173I
−2.91919 + 0.68991I 0
u = 0.203687 − 0.817190I
a = 0.265312 − 1.347979I
b = −0.009909 − 0.924173I
−2.91919 − 0.68991I 0
u = −0.060223 + 1.164134I
a = 1.284188 + 0.281432I
b = −0.51405 − 1.40896I
7.93477 − 0.69221I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.060223 − 1.164134I
a = 1.284188 − 0.281432I
b = −0.51405 + 1.40896I
7.93477 + 0.69221I 0
u = −0.557267 + 1.026172I
a = 1.288995 − 0.377878I
b = −0.930748 − 0.825516I
1.99183 + 1.00401I 0
u = −0.557267 − 1.026172I
a = 1.288995 + 0.377878I
b = −0.930748 + 0.825516I
1.99183 − 1.00401I 0
u = −0.534286 + 1.038979I
a = 1.60240 − 0.74915I
b = −0.655237 − 0.958567I
2.93870 + 1.12688I 0
u = −0.534286 − 1.038979I
a = 1.60240 + 0.74915I
b = −0.655237 + 0.958567I
2.93870 − 1.12688I 0
u = −0.046916 + 0.829027I
a = 0.957981 + 0.292202I
b = −0.74295 − 1.33646I
−0.30293 + 6.43681I 0
u = −0.046916 − 0.829027I
a = 0.957981 − 0.292202I
b = −0.74295 + 1.33646I
−0.30293 − 6.43681I 0
u = −0.264341 + 1.149304I
a = 1.28218 − 0.88736I
b = −1.126059 + 0.739347I
4.64045 + 6.06656I 0
u = −0.264341 − 1.149304I
a = 1.28218 + 0.88736I
b = −1.126059 − 0.739347I
4.64045 − 6.06656I 0
u = −0.346004 + 0.742861I
a = 0.086740 − 1.148537I
b = −0.88958 + 1.31799I
−0.92183 − 1.13250I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346004 − 0.742861I
a = 0.086740 + 1.148537I
b = −0.88958 − 1.31799I
−0.92183 + 1.13250I 0
u = 0.401528 + 1.116657I
a = −1.98997 − 0.10131I
b = 1.12130 − 1.10072I
3.06095 − 6.19234I 0
u = 0.401528 − 1.116657I
a = −1.98997 + 0.10131I
b = 1.12130 + 1.10072I
3.06095 + 6.19234I 0
u = 0.317069 + 0.747340I
a = −1.14247 − 1.99034I
b = 0.202394 + 0.420897I
5.75829 + 0.21644I 0
u = 0.317069 − 0.747340I
a = −1.14247 + 1.99034I
b = 0.202394 − 0.420897I
5.75829 − 0.21644I 0
u = 0.114182 + 1.184578I
a = −1.49405 + 0.31447I
b = 0.68863 − 1.39879I
7.90958 − 5.38606I 0
u = 0.114182 − 1.184578I
a = −1.49405 − 0.31447I
b = 0.68863 + 1.39879I
7.90958 + 5.38606I 0
u = −0.314627 + 0.737087I
a = 1.49494 − 1.68840I
b = −0.105188 + 0.453919I
5.26774 + 5.47721I 0
u = −0.314627 − 0.737087I
a = 1.49494 + 1.68840I
b = −0.105188 − 0.453919I
5.26774 − 5.47721I 0
u = 0.531591 + 1.094841I
a = −1.81374 − 0.54647I
b = 0.929079 − 0.958393I
3.75312 − 6.57195I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531591 − 1.094841I
a = −1.81374 + 0.54647I
b = 0.929079 + 0.958393I
3.75312 + 6.57195I 0
u = 1.220878 + 0.145006I
a = 0.019639 − 0.161767I
b = −1.004585 − 0.913813I
4.1100 + 14.1102I 0
u = 1.220878 − 0.145006I
a = 0.019639 + 0.161767I
b = −1.004585 + 0.913813I
4.1100 − 14.1102I 0
u = 0.758910 + 0.055289I
a = −0.213196 − 0.483966I
b = 0.692951 − 0.949247I
0.82750 − 3.32659I 0
u = 0.758910 − 0.055289I
a = −0.213196 + 0.483966I
b = 0.692951 + 0.949247I
0.82750 + 3.32659I 0
u = −1.234587 + 0.144130I
a = 0.024846 − 0.212812I
b = 1.045983 − 0.906369I
5.66903 − 7.73769I 0
u = −1.234587 − 0.144130I
a = 0.024846 + 0.212812I
b = 1.045983 + 0.906369I
5.66903 + 7.73769I 0
u = −0.420624 + 1.195042I
a = −1.84369 + 0.19464I
b = 1.031117 + 0.158463I
8.14971 + 9.54900I 0
u = −0.420624 − 1.195042I
a = −1.84369 − 0.19464I
b = 1.031117 − 0.158463I
8.14971 − 9.54900I 0
u = −0.325482 + 1.228524I
a = −1.72693 − 0.09658I
b = 1.110376 + 0.421926I
5.04880 + 4.50134I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325482 − 1.228524I
a = −1.72693 + 0.09658I
b = 1.110376 − 0.421926I
5.04880 − 4.50134I 0
u = −0.574184 + 0.429912I
a = 0.493243 + 0.347495I
b = 0.252289 + 0.651123I
−0.94950 + 1.69253I 0
u = −0.574184 − 0.429912I
a = 0.493243 − 0.347495I
b = 0.252289 − 0.651123I
−0.94950 − 1.69253I 0
u = −0.588713 + 1.140278I
a = −0.749426 + 1.002063I
b = 0.478478 + 0.284830I
7.10339 − 1.20294I 0
u = −0.588713 − 1.140278I
a = −0.749426 − 1.002063I
b = 0.478478 − 0.284830I
7.10339 + 1.20294I 0
u = 0.432886 + 1.215377I
a = 1.77333 + 0.27267I
b = −0.940619 + 0.170869I
8.89538 − 4.43132I 0
u = 0.432886 − 1.215377I
a = 1.77333 − 0.27267I
b = −0.940619 − 0.170869I
8.89538 + 4.43132I 0
u = 0.631674 + 0.304895I
a = −0.067306 + 0.565212I
b = 0.707815 + 0.717572I
1.58616 + 2.00474I 0
u = 0.631674 − 0.304895I
a = −0.067306 − 0.565212I
b = 0.707815 − 0.717572I
1.58616 − 2.00474I 0
u = 0.256776 + 0.639731I
a = −1.249302 − 0.460250I
b = 0.758236 − 0.997030I
1.24514 − 2.92828I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256776 − 0.639731I
a = −1.249302 + 0.460250I
b = 0.758236 + 0.997030I
1.24514 + 2.92828I 0
u = 0.561342 + 1.191430I
a = 1.006085 + 0.833390I
b = −0.545398 + 0.282525I
8.09514 − 4.40790I 0
u = 0.561342 − 1.191430I
a = 1.006085 − 0.833390I
b = −0.545398 − 0.282525I
8.09514 + 4.40790I 0
u = 0.678945 + 0.041699I
a = 1.032783 − 0.654295I
b = −0.625010 + 0.272982I
5.29456 − 0.25778I 0
u = 0.678945 − 0.041699I
a = 1.032783 + 0.654295I
b = −0.625010 − 0.272982I
5.29456 + 0.25778I 0
u = 1.319254 + 0.040356I
a = −0.208584 − 0.119476I
b = −1.101186 − 0.606365I
−2.84695 + 5.81263I 0
u = 1.319254 − 0.040356I
a = −0.208584 + 0.119476I
b = −1.101186 + 0.606365I
−2.84695 − 5.81263I 0
u = −0.535596 + 1.231878I
a = 1.61476 − 0.14815I
b = −0.99839 − 1.06777I
−1.03750 + 7.48926I 0
u = −0.535596 − 1.231878I
a = 1.61476 + 0.14815I
b = −0.99839 + 1.06777I
−1.03750 − 7.48926I 0
u = 0.318615 + 1.317654I
a = 1.024191 + 0.925156I
b = −1.70376 − 1.19223I
8.54211 − 10.96890I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.318615 − 1.317654I
a = 1.024191 − 0.925156I
b = −1.70376 + 1.19223I
8.54211 + 10.96890I 0
u = −0.599127 + 0.213716I
a = 0.093233 + 0.872852I
b = −0.745623 + 0.558575I
0.78402 + 3.14364I 0
u = −0.599127 − 0.213716I
a = 0.093233 − 0.872852I
b = −0.745623 − 0.558575I
0.78402 − 3.14364I 0
u = −0.291029 + 1.341918I
a = 0.486628 + 0.001682I
b = −0.328573 + 0.051011I
0.46842 + 1.69442I 0
u = −0.291029 − 1.341918I
a = 0.486628 − 0.001682I
b = −0.328573 − 0.051011I
0.46842 − 1.69442I 0
u = 0.450099 + 1.300479I
a = −1.67367 − 0.01734I
b = 0.98071 − 1.09810I
4.91319 − 7.91635I 0
u = 0.450099 − 1.300479I
a = −1.67367 + 0.01734I
b = 0.98071 + 1.09810I
4.91319 + 7.91635I 0
u = 0.454828 + 1.320970I
a = 1.324429 + 0.158785I
b = −0.792156 + 0.420783I
7.04494 − 5.34627I 0
u = 0.454828 − 1.320970I
a = 1.324429 − 0.158785I
b = −0.792156 − 0.420783I
7.04494 + 5.34627I 0
u = 0.991380 + 0.998425I
a = 0.109759 − 0.352932I
b = 0.128947 + 0.570046I
2.81028 − 2.00564I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.991380 − 0.998425I
a = 0.109759 + 0.352932I
b = 0.128947 − 0.570046I
2.81028 + 2.00564I 0
u = −0.481221 + 1.323076I
a = 1.63686 − 0.01632I
b = −0.97578 − 1.08771I
3.79621 + 13.52400I 0
u = −0.481221 − 1.323076I
a = 1.63686 + 0.01632I
b = −0.97578 + 1.08771I
3.79621 − 13.52400I 0
u = −0.30486 + 1.39032I
a = −1.055288 + 0.766304I
b = 1.77086 − 0.95744I
10.60710 + 4.53264I 0
u = −0.30486 − 1.39032I
a = −1.055288 − 0.766304I
b = 1.77086 + 0.95744I
10.60710 − 4.53264I 0
u = −0.574676 + 0.003661I
a = −1.22652 − 0.97562I
b = 0.669754 + 0.381753I
4.75088 + 5.61590I 7.39538 − 6.42605I
u = −0.574676 − 0.003661I
a = −1.22652 + 0.97562I
b = 0.669754 − 0.381753I
4.75088 − 5.61590I 7.39538 + 6.42605I
u = −0.95840 + 1.06122I
a = −0.119955 − 0.311015I
b = −0.041253 + 0.550469I
2.36684 − 2.79502I 0
u = −0.95840 − 1.06122I
a = −0.119955 + 0.311015I
b = −0.041253 − 0.550469I
2.36684 + 2.79502I 0
u = −0.21904 + 1.41890I
a = −1.37697 − 0.35692I
b = 0.964821 + 0.686634I
10.05590 + 0.99246I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21904 − 1.41890I
a = −1.37697 + 0.35692I
b = 0.964821 − 0.686634I
10.05590 − 0.99246I 0
u = 0.27509 + 1.44269I
a = 1.323524 − 0.291923I
b = −0.916201 + 0.663878I
10.24700 − 6.50428I 0
u = 0.27509 − 1.44269I
a = 1.323524 + 0.291923I
b = −0.916201 − 0.663878I
10.24700 + 6.50428I 0
u = 0.203171 + 0.474532I
a = 3.28050 − 2.03544I
b = 0.441287 + 0.040171I
4.02734 + 2.54233I 4.33601 + 3.58741I
u = 0.203171 − 0.474532I
a = 3.28050 + 2.03544I
b = 0.441287 − 0.040171I
4.02734 − 2.54233I 4.33601 − 3.58741I
u = −0.69263 + 1.31237I
a = −0.669076 + 0.314977I
b = 0.504102 + 0.450663I
2.14809 + 5.00005I 0
u = −0.69263 − 1.31237I
a = −0.669076 − 0.314977I
b = 0.504102 − 0.450663I
2.14809 − 5.00005I 0
u = 0.62037 + 1.35880I
a = 1.52882 + 0.23711I
b = −1.16990 + 1.20947I
7.9654 − 20.5595I 0
u = 0.62037 − 1.35880I
a = 1.52882 − 0.23711I
b = −1.16990 − 1.20947I
7.9654 + 20.5595I 0
u = 0.57595 + 1.38604I
a = 1.41734 + 0.16084I
b = −1.28855 + 1.24873I
1.52157 − 12.21380I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57595 − 1.38604I
a = 1.41734 − 0.16084I
b = −1.28855 − 1.24873I
1.52157 + 12.21380I 0
u = −0.61781 + 1.36893I
a = −1.49609 + 0.24994I
b = 1.17057 + 1.24176I
9.5841 + 14.2280I 0
u = −0.61781 − 1.36893I
a = −1.49609 − 0.24994I
b = 1.17057 − 1.24176I
9.5841 − 14.2280I 0
u = 0.400082 + 0.287391I
a = 0.680854 + 0.167600I
b = 0.692103 + 0.958396I
0.64000 + 2.60943I −1.77010 − 7.39216I
u = 0.400082 − 0.287391I
a = 0.680854 − 0.167600I
b = 0.692103 − 0.958396I
0.64000 − 2.60943I −1.77010 + 7.39216I
u = −0.117335 + 0.463678I
a = −4.06301 − 2.20754I
b = −0.434760 − 0.045713I
3.03377 − 8.30316I 0.43502 + 1.68786I
u = −0.117335 − 0.463678I
a = −4.06301 + 2.20754I
b = −0.434760 + 0.045713I
3.03377 + 8.30316I 0.43502 − 1.68786I
u = 0.59338 + 1.42884I
a = 0.902018 + 0.057147I
b = −0.611265 + 0.550295I
7.50795 − 6.27771I 0
u = 0.59338 − 1.42884I
a = 0.902018 − 0.057147I
b = −0.611265 − 0.550295I
7.50795 + 6.27771I 0
u = −0.63004 + 1.45731I
a = −1.286788 + 0.246723I
b = 1.36353 + 1.51276I
7.68284 + 7.80353I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63004 − 1.45731I
a = −1.286788 − 0.246723I
b = 1.36353 − 1.51276I
7.68284 − 7.80353I 0
u = −0.34206 + 1.55242I
a = −0.815539 + 0.454646I
b = 1.335917 − 0.377885I
11.57840 − 1.74366I 0
u = −0.34206 − 1.55242I
a = −0.815539 − 0.454646I
b = 1.335917 + 0.377885I
11.57840 + 1.74366I 0
u = −0.64633 + 1.45560I
a = −0.795823 + 0.012560I
b = 0.559743 + 0.579297I
6.16958 + 11.62650I 0
u = −0.64633 − 1.45560I
a = −0.795823 − 0.012560I
b = 0.559743 − 0.579297I
6.16958 − 11.62650I 0
u = −0.337970 + 0.189929I
a = −2.25796 + 1.44717I
b = −0.697496 + 0.144318I
−2.30648 − 2.46302I −2.28126 + 2.27214I
u = −0.337970 − 0.189929I
a = −2.25796 − 1.44717I
b = −0.697496 − 0.144318I
−2.30648 + 2.46302I −2.28126 − 2.27214I
u = 0.33792 + 1.58016I
a = 0.748437 + 0.425459I
b = −1.195290 − 0.337266I
10.02920 + 8.07714I 0
u = 0.33792 − 1.58016I
a = 0.748437 − 0.425459I
b = −1.195290 + 0.337266I
10.02920 − 8.07714I 0
u = 0.373675 + 0.068791I
a = −1.42062 + 0.08374I
b = −0.234606 + 0.971145I
−3.80303 + 1.15603I −8.29159 − 1.10528I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373675 − 0.068791I
a = −1.42062 − 0.08374I
b = −0.234606 − 0.971145I
−3.80303 − 1.15603I −8.29159 + 1.10528I
u = 0.29728 + 1.59894I
a = 1.123534 + 0.263705I
b = −2.13725 + 0.18735I
3.20426 − 0.61985I 0
u = 0.29728 − 1.59894I
a = 1.123534 − 0.263705I
b = −2.13725 − 0.18735I
3.20426 + 0.61985I 0
u = −2.14203
a = 0.728333
b = 4.33847
3.35814 0
u = −0.16954 + 2.29789I
a = 0.053699 + 0.132773I
b = −0.057367 − 0.134865I
2.11726 − 2.33696I 0
u = −0.16954 − 2.29789I
a = 0.053699 − 0.132773I
b = −0.057367 + 0.134865I
2.11726 + 2.33696I 0
21
II. I
u
2
= h−3.23 × 10
28
u
40
− 2.94 × 10
28
u
39
+ · · · + 7.20 × 10
23
b + 7.43 ×
10
27
, 2.04 × 10
29
u
40
+ 2.34 × 10
29
u
39
+ · · · + 7.20 × 10
23
a − 2.07 ×
10
28
, 3u
41
+ 4u
40
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
12
=
−283856.u
40
− 325018.u
39
+ ··· − 211340.u + 28750.4
44823.5u
40
+ 40854.2u
39
+ ··· + 44467.3u − 10317.2
a
6
=
−9641.58u
40
− 638454.u
39
+ ··· + 667403.u − 336332.
1265.52u
40
− 7380.22u
39
+ ··· + 10710.7u − 5069.46
a
1
=
−239032.u
40
− 284164.u
39
+ ··· − 166873.u + 18433.2
44823.5u
40
+ 40854.2u
39
+ ··· + 44467.3u − 10317.2
a
7
=
−24384.4u
40
− 91228.4u
39
+ ··· + 50606.2u − 31785.6
48237.7u
40
+ 113631.u
39
+ ··· − 26777.6u + 26225.3
a
3
=
−22433.6u
40
+ 627576.u
39
+ ··· − 719475.u + 353807.
−3048.26u
40
+ 13665.2u
39
+ ··· − 21035.4u + 9784.89
a
9
=
u
u
3
+ u
a
11
=
−188833.u
40
− 222556.u
39
+ ··· − 133856.u + 15631.8
81083.3u
40
+ 79871.9u
39
+ ··· + 74120.9u − 15357.5
a
8
=
−53514.5u
40
− 404575.u
39
+ ··· + 331630.u − 180071.
49956.7u
40
+ 160332.u
39
+ ··· − 74183.9u + 50449.8
a
2
=
897198.u
40
+ 1.67537 × 10
6
u
39
+ ··· − 31554.3u + 257956.
266600.u
40
+ 307579.u
39
+ ··· + 194952.u − 25819.3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
814976054887987479555004736175
720125855629320298449497
u
40
−
379397826460624632971152463282
720125855629320298449497
u
39
+ ··· −
1204788679366910132778002056829
720125855629320298449497
u +
381900534479216968138767445795
720125855629320298449497
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
9(9u
41
− 161u
40
+ ··· − 11u + 1)
c
2
3(3u
41
+ u
40
+ ··· − 5u + 1)
c
3
u
41
+ 7u
40
+ ··· + 37u − 9
c
4
3(3u
41
+ 4u
40
+ ··· − 2u + 1)
c
5
u
41
+ 4u
40
+ ··· − 3u − 1
c
6
u
41
− u
40
+ ··· + 319u − 27
c
7
u
41
− 5u
40
+ ··· − 5u + 1
c
8
3(3u
41
− u
40
+ ··· − 5u − 1)
c
9
3(3u
41
− 4u
40
+ ··· − 2u − 1)
c
10
u
41
+ 5u
40
+ ··· − 5u − 1
c
11
u
41
− 12u
40
+ ··· + 112u − 3
c
12
9(9u
41
+ u
40
+ ··· + 11u + 1)
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(81y
41
+ 521y
40
+ ··· + 13y −1)
c
2
, c
8
9(9y
41
+ 161y
40
+ ··· − 11y −1)
c
3
y
41
− 31y
40
+ ··· + 73y −81
c
4
, c
9
9(9y
41
+ 296y
40
+ ··· − 46y −1)
c
5
y
41
+ 22y
40
+ ··· − 13y −1
c
6
y
41
+ 19y
40
+ ··· + 198151y −729
c
7
, c
10
y
41
− 9y
40
+ ··· + 35y −1
c
11
y
41
+ 12y
39
+ ··· + 4594y −9
c
12
81(81y
41
− 127y
40
+ ··· − 177y −1)
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.480191 + 0.920755I
a = −0.634429 − 0.222220I
b = 0.437014 − 0.917013I
0.54268 − 4.08928I 0
u = 0.480191 − 0.920755I
a = −0.634429 + 0.222220I
b = 0.437014 + 0.917013I
0.54268 + 4.08928I 0
u = 0.411995 + 1.050934I
a = −2.20155 − 0.17198I
b = 1.20390 − 0.87381I
2.56335 − 5.17455I 0
u = 0.411995 − 1.050934I
a = −2.20155 + 0.17198I
b = 1.20390 + 0.87381I
2.56335 + 5.17455I 0
u = −1.109696 + 0.220006I
a = −0.351439 − 0.293279I
b = −0.859084 − 0.449194I
−3.03997 + 5.13057I 0
u = −1.109696 − 0.220006I
a = −0.351439 + 0.293279I
b = −0.859084 + 0.449194I
−3.03997 − 5.13057I 0
u = −0.193521 + 0.843223I
a = 2.30431 − 0.20332I
b = −1.27662 − 1.03418I
−0.62129 + 3.15132I 0
u = −0.193521 − 0.843223I
a = 2.30431 + 0.20332I
b = −1.27662 + 1.03418I
−0.62129 − 3.15132I 0
u = 0.577494 + 1.003061I
a = −1.87567 − 0.73640I
b = 0.79704 − 1.21707I
4.40855 − 7.17341I 0
u = 0.577494 − 1.003061I
a = −1.87567 + 0.73640I
b = 0.79704 + 1.21707I
4.40855 + 7.17341I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392106 + 1.118094I
a = 1.97980 − 0.01262I
b = −1.36113 − 0.98881I
1.28363 + 8.58828I 0
u = −0.392106 − 1.118094I
a = 1.97980 + 0.01262I
b = −1.36113 + 0.98881I
1.28363 − 8.58828I 0
u = − 66.10 + 0.786404I
a = 0.775316 + 0.700854I
b = −0.198381 + 1.033307I
−2.66480 + 1.42721I 0
u = − 66.10 − 0.786404I
a = 0.775316 − 0.700854I
b = −0.198381 − 1.033307I
−2.66480 − 1.42721I 0
u = 0.000131 + 0.786213I
a = 0.44498 + 2.80699I
b = −0.053879 + 0.678414I
−0.90736 − 2.44785I 0
u = 0.000131 − 0.786213I
a = 0.44498 − 2.80699I
b = −0.053879 − 0.678414I
−0.90736 + 2.44785I 0
u = −0.493518 + 1.130604I
a = 0.558706 − 0.627835I
b = −0.904785 + 0.324293I
0.696172 − 0.429971I 0
u = −0.493518 − 1.130604I
a = 0.558706 + 0.627835I
b = −0.904785 − 0.324293I
0.696172 + 0.429971I 0
u = −0.159389 + 0.673175I
a = 0.812171 − 1.023145I
b = −0.85413 + 1.29701I
−0.76477 − 6.02453I 0
u = −0.159389 − 0.673175I
a = 0.812171 + 1.023145I
b = −0.85413 − 1.29701I
−0.76477 + 6.02453I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.049419 + 0.680291I
a = 0.92873 − 1.54109I
b = −0.47747 + 1.52214I
−2.05419 + 0.90894I −5.37869 + 0.I
u = 0.049419 − 0.680291I
a = 0.92873 + 1.54109I
b = −0.47747 − 1.52214I
−2.05419 − 0.90894I −5.37869 + 0.I
u = 0.313090 + 0.596517I
a = −0.243419 − 0.548328I
b = 0.788012 + 1.080917I
0.98219 + 1.89202I 0
u = 0.313090 − 0.596517I
a = −0.243419 + 0.548328I
b = 0.788012 − 1.080917I
0.98219 − 1.89202I 0
u = 0.344075 + 1.284564I
a = 1.053821 − 0.167107I
b = −0.808506 − 0.149587I
6.81076 − 9.86539I 0
u = 0.344075 − 1.284564I
a = 1.053821 + 0.167107I
b = −0.808506 + 0.149587I
6.81076 + 9.86539I 0
u = −0.073010 + 0.657575I
a = 2.84171 − 2.51549I
b = −0.732889 − 0.384795I
3.41554 + 8.75299I 9.2926 − 11.4300I
u = −0.073010 − 0.657575I
a = 2.84171 + 2.51549I
b = −0.732889 + 0.384795I
3.41554 − 8.75299I 9.2926 + 11.4300I
u = −0.376259 + 1.284785I
a = −1.366301 − 0.100912I
b = 0.806048 + 0.127375I
8.06838 + 4.66157I 0
u = −0.376259 − 1.284785I
a = −1.366301 + 0.100912I
b = 0.806048 − 0.127375I
8.06838 − 4.66157I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.463614 + 1.296551I
a = −1.45284 + 0.26842I
b = 0.864083 + 0.591497I
7.56625 + 5.71988I 0
u = −0.463614 − 1.296551I
a = −1.45284 − 0.26842I
b = 0.864083 − 0.591497I
7.56625 − 5.71988I 0
u = 0.089874 + 0.587467I
a = −2.07691 − 2.87472I
b = 0.661641 − 0.505089I
4.28437 − 3.16642I 8.91907 + 6.46038I
u = 0.089874 − 0.587467I
a = −2.07691 + 2.87472I
b = 0.661641 + 0.505089I
4.28437 + 3.16642I 8.91907 − 6.46038I
u = −1.59061
a = 0.479307
b = 2.18124
3.41205 0
u = 0.73177 + 1.47236I
a = −0.262923 − 0.135084I
b = 0.306280 − 0.061588I
0.58079 − 1.89733I 0
u = 0.73177 − 1.47236I
a = −0.262923 + 0.135084I
b = 0.306280 + 0.061588I
0.58079 + 1.89733I 0
u = 0.152897 + 0.317630I
a = 0.60227 − 1.96600I
b = 0.602674 + 1.036424I
1.20495 + 2.04696I 5.19785 − 1.44013I
u = 0.152897 − 0.317630I
a = 0.60227 + 1.96600I
b = 0.602674 − 1.036424I
1.20495 − 2.04696I 5.19785 + 1.44013I
u = 0.23882 + 2.13469I
a = −0.076001 + 0.146749I
b = 0.0251091 − 0.0891723I
2.12729 + 2.35613I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23882 − 2.13469I
a = −0.076001 − 0.146749I
b = 0.0251091 + 0.0891723I
2.12729 − 2.35613I 0
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
81(9u
41
− 161u
40
+ ··· − 11u + 1)
· (9u
166
+ 548u
165
+ ··· + 1674688u + 37249)
c
2
9(3u
41
+ u
40
+ ··· − 5u + 1)(3u
166
+ 10u
165
+ ··· − 72u − 193)
c
3
(u
41
+ 7u
40
+ ··· + 37u − 9)
· (u
166
− 26u
165
+ ··· − 3326078u + 219087)
c
4
9(3u
41
+ 4u
40
+ ··· − 2u + 1)(3u
166
+ u
165
+ ··· + 158795u − 34673)
c
5
(u
41
+ 4u
40
+ ··· − 3u − 1)(u
166
+ u
165
+ ··· + 3422516u − 262817)
c
6
(u
41
− u
40
+ ··· + 319u − 27)
· (u
166
+ 2u
165
+ ··· + 2824430u + 436239)
c
7
(u
41
− 5u
40
+ ··· − 5u + 1)
· (u
166
− 49u
164
+ ··· + 2520956u + 2425663)
c
8
9(3u
41
− u
40
+ ··· − 5u − 1)(3u
166
+ 10u
165
+ ··· − 72u − 193)
c
9
9(3u
41
− 4u
40
+ ··· − 2u − 1)(3u
166
+ u
165
+ ··· + 158795u − 34673)
c
10
(u
41
+ 5u
40
+ ··· − 5u − 1)
· (u
166
− 49u
164
+ ··· + 2520956u + 2425663)
c
11
(u
41
− 12u
40
+ ··· + 112u − 3)
· (u
166
+ 9u
165
+ ··· + 3480001987u + 3246415791)
c
12
81(9u
41
+ u
40
+ ··· + 11u + 1)(9u
166
+ 98u
165
+ ··· − 12u − 1)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
6561(81y
41
+ 521y
40
+ ··· + 13y −1)
· (81y
166
+ 5408y
165
+ ··· − 242908207900y + 1387488001)
c
2
, c
8
81(9y
41
+ 161y
40
+ ··· − 11y −1)
· (9y
166
+ 548y
165
+ ··· + 1674688y + 37249)
c
3
(y
41
− 31y
40
+ ··· + 73y −81)
· (y
166
− 4y
165
+ ··· + 1995653540696y + 47999113569)
c
4
, c
9
81(9y
41
+ 296y
40
+ ··· − 46y −1)
· (9y
166
+ 1043y
165
+ ··· + 32830078583y + 1202216929)
c
5
(y
41
+ 22y
40
+ ··· − 13y −1)
· (y
166
− 27y
165
+ ··· + 21178704987358y + 69072775489)
c
6
(y
41
+ 19y
40
+ ··· + 198151y −729)
· (y
166
+ 34y
165
+ ··· + 7330681481006y + 190304465121)
c
7
, c
10
(y
41
− 9y
40
+ ··· + 35y −1)
· (y
166
− 98y
165
+ ··· + 164556690192526y + 5883840989569)
c
11
(y
41
+ 12y
39
+ ··· + 4594y −9)
· (y
166
− 69y
165
+ ··· − 4.67 × 10
20
y + 1.05 × 10
19
)
c
12
6561(81y
41
− 127y
40
+ ··· − 177y −1)
· (81y
166
− 2044y
165
+ ··· + 118y + 1)
33
