12n
0627
(K12n
0627
)
A knot diagram
1
Linearized knot diagam
3 8 6 11 1 10 2 11 7 4 8 5
Solving Sequence
3,8
2
1,5
6 4 7 12 11 9 10
c
2
c
1
c
5
c
3
c
7
c
12
c
11
c
8
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.15596 × 10
158
u
88
+ 1.94754 × 10
158
u
87
+ ··· + 1.32736 × 10
158
b + 3.28316 × 10
159
,
− 1.68579 × 10
158
u
88
− 4.29784 × 10
158
u
87
+ ··· + 6.63682 × 10
158
a − 1.27829 × 10
160
,
u
89
− u
88
+ ··· + 14u − 10i
I
u
2
= h−348239602u
30
+ 191579437u
29
+ ··· + 56778667b + 357913195,
24113204363u
30
− 13246278164u
29
+ ··· + 1249130674a − 59799820088,
u
31
− 10u
29
+ ··· + 19u
2
− 2i
* 2 irreducible components of dim
C
= 0, with total 120 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−1.16 × 10
158
u
88
+ 1.95 × 10
158
u
87
+ · · · + 1.33 × 10
158
b + 3.28 ×
10
159
, −1.69 × 10
158
u
88
− 4.30 × 10
158
u
87
+ · · · + 6.64 × 10
158
a − 1.28 ×
10
160
, u
89
− u
88
+ · · · + 14u − 10i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
0.254006u
88
+ 0.647575u
87
+ ··· + 7.38084u + 19.2605
0.870871u
88
− 1.46722u
87
+ ··· + 42.4211u − 24.7345
a
6
=
0.390082u
88
+ 0.0955497u
87
+ ··· + 14.2030u + 11.8426
0.488241u
88
− 1.26681u
87
+ ··· + 33.9619u − 22.3972
a
4
=
0.657824u
88
+ 0.241125u
87
+ ··· + 10.9756u + 16.1052
−1.86162u
88
+ 2.32381u
87
+ ··· − 85.2070u + 17.8243
a
7
=
u
−u
3
+ u
a
12
=
−0.601779u
88
+ 1.28338u
87
+ ··· − 25.4051u + 11.2090
2.36178u
88
− 2.87861u
87
+ ··· + 87.7562u − 25.7398
a
11
=
−0.601779u
88
+ 1.28338u
87
+ ··· − 25.4051u + 11.2090
2.40515u
88
− 3.22281u
87
+ ··· + 103.316u − 32.5558
a
9
=
0.667097u
88
+ 0.529294u
87
+ ··· + 4.21757u + 13.2911
0.694535u
88
− 0.923902u
87
+ ··· − 9.67099u − 6.07093
a
10
=
0.0615361u
88
+ 1.49254u
87
+ ··· − 11.2489u + 21.9763
0.289929u
88
− 0.306028u
87
+ ··· − 14.0743u − 0.962515
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.83185u
88
− 9.58904u
87
+ ··· + 2.19711u − 73.4222
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
+ 47u
88
+ ··· + 2796u + 100
c
2
, c
7
u
89
− u
88
+ ··· + 14u − 10
c
3
u
89
− 2u
88
+ ··· + 459338u + 255793
c
4
, c
10
u
89
+ u
88
+ ··· + 119758u + 26770
c
5
, c
12
u
89
− 2u
88
+ ··· + 897u − 487
c
6
, c
9
u
89
− 2u
88
+ ··· + 39310u − 17077
c
8
, c
11
u
89
− 6u
88
+ ··· − 24u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 9y
88
+ ··· + 125616y −10000
c
2
, c
7
y
89
− 47y
88
+ ··· + 2796y −100
c
3
y
89
− 66y
88
+ ··· + 699981667796y −65430058849
c
4
, c
10
y
89
− 47y
88
+ ··· + 24496053724y −716632900
c
5
, c
12
y
89
− 42y
88
+ ··· + 7221321y −237169
c
6
, c
9
y
89
+ 46y
88
+ ··· − 11363262354y −291623929
c
8
, c
11
y
89
− 58y
88
+ ··· + 1046y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.244565 + 0.962025I
a = 1.53167 − 0.13930I
b = 0.176114 + 0.504007I
1.89844 − 3.40493I 0
u = −0.244565 − 0.962025I
a = 1.53167 + 0.13930I
b = 0.176114 − 0.504007I
1.89844 + 3.40493I 0
u = 0.933890 + 0.327481I
a = 0.62035 + 1.46865I
b = 0.351461 + 1.150610I
−4.92041 − 1.30903I 0
u = 0.933890 − 0.327481I
a = 0.62035 − 1.46865I
b = 0.351461 − 1.150610I
−4.92041 + 1.30903I 0
u = 0.961254 + 0.394274I
a = −0.771016 − 0.926200I
b = −1.13991 + 0.95033I
4.21665 − 2.92405I 0
u = 0.961254 − 0.394274I
a = −0.771016 + 0.926200I
b = −1.13991 − 0.95033I
4.21665 + 2.92405I 0
u = 0.984368 + 0.348236I
a = −0.171491 − 0.166467I
b = 0.615879 + 0.898837I
−0.92696 − 3.77876I 0
u = 0.984368 − 0.348236I
a = −0.171491 + 0.166467I
b = 0.615879 − 0.898837I
−0.92696 + 3.77876I 0
u = −0.930123 + 0.518617I
a = −0.526672 + 0.968906I
b = −0.159656 − 0.114899I
5.18137 + 2.01747I 0
u = −0.930123 − 0.518617I
a = −0.526672 − 0.968906I
b = −0.159656 + 0.114899I
5.18137 − 2.01747I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006170 + 0.430405I
a = −0.438623 + 0.856778I
b = −2.20252 + 1.49810I
−2.68981 + 4.03468I 0
u = −1.006170 − 0.430405I
a = −0.438623 − 0.856778I
b = −2.20252 − 1.49810I
−2.68981 − 4.03468I 0
u = 1.039120 + 0.367975I
a = −0.563115 − 0.858898I
b = −2.46344 − 1.22813I
−1.38793 + 2.34054I 0
u = 1.039120 − 0.367975I
a = −0.563115 + 0.858898I
b = −2.46344 + 1.22813I
−1.38793 − 2.34054I 0
u = −0.725494 + 0.521426I
a = −0.89511 + 1.20991I
b = −1.47632 + 0.97253I
5.84354 + 2.20534I 0
u = −0.725494 − 0.521426I
a = −0.89511 − 1.20991I
b = −1.47632 − 0.97253I
5.84354 − 2.20534I 0
u = 1.007390 + 0.511262I
a = −0.398190 − 1.199040I
b = −0.46816 − 1.60706I
−2.16350 − 1.93019I 0
u = 1.007390 − 0.511262I
a = −0.398190 + 1.199040I
b = −0.46816 + 1.60706I
−2.16350 + 1.93019I 0
u = 0.385380 + 1.077170I
a = −1.57779 + 0.35617I
b = −0.413188 + 0.978791I
4.95394 + 10.81390I 0
u = 0.385380 − 1.077170I
a = −1.57779 − 0.35617I
b = −0.413188 − 0.978791I
4.95394 − 10.81390I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550489 + 1.004510I
a = −1.115950 − 0.400395I
b = −0.275463 − 1.059970I
1.00206 − 3.24358I 0
u = −0.550489 − 1.004510I
a = −1.115950 + 0.400395I
b = −0.275463 + 1.059970I
1.00206 + 3.24358I 0
u = 0.193852 + 0.828020I
a = 1.149260 − 0.120601I
b = 0.025384 − 0.661444I
0.840044 + 0.487278I 3.75141 + 1.24704I
u = 0.193852 − 0.828020I
a = 1.149260 + 0.120601I
b = 0.025384 + 0.661444I
0.840044 − 0.487278I 3.75141 − 1.24704I
u = 0.755613 + 0.358139I
a = −0.30612 − 1.66985I
b = −2.39351 − 0.85784I
4.96330 − 0.31485I 3.79476 − 1.00054I
u = 0.755613 − 0.358139I
a = −0.30612 + 1.66985I
b = −2.39351 + 0.85784I
4.96330 + 0.31485I 3.79476 + 1.00054I
u = 0.670677 + 0.495093I
a = −1.56847 − 0.88463I
b = 0.036229 + 0.286376I
−1.01560 − 2.22245I 1.10851 + 6.52104I
u = 0.670677 − 0.495093I
a = −1.56847 + 0.88463I
b = 0.036229 − 0.286376I
−1.01560 + 2.22245I 1.10851 − 6.52104I
u = −1.047730 + 0.520787I
a = −0.428255 + 1.175960I
b = −0.149308 + 1.361530I
−0.36097 + 8.88020I 0
u = −1.047730 − 0.520787I
a = −0.428255 − 1.175960I
b = −0.149308 − 1.361530I
−0.36097 − 8.88020I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135466 + 0.812923I
a = 0.0767182 − 0.0995383I
b = 0.694405 + 0.225698I
7.98738 + 2.98075I 6.24007 − 3.70589I
u = 0.135466 − 0.812923I
a = 0.0767182 + 0.0995383I
b = 0.694405 − 0.225698I
7.98738 − 2.98075I 6.24007 + 3.70589I
u = −1.093460 + 0.434573I
a = 0.091617 + 0.515957I
b = −0.56916 + 2.20034I
6.64364 + 5.23146I 0
u = −1.093460 − 0.434573I
a = 0.091617 − 0.515957I
b = −0.56916 − 2.20034I
6.64364 − 5.23146I 0
u = 1.184860 + 0.009536I
a = −0.068200 + 1.014210I
b = 0.194397 + 0.996138I
−6.31122 − 1.42992I 0
u = 1.184860 − 0.009536I
a = −0.068200 − 1.014210I
b = 0.194397 − 0.996138I
−6.31122 + 1.42992I 0
u = −1.037570 + 0.577206I
a = 0.264692 − 1.356690I
b = 1.86795 − 1.60205I
−2.93078 + 4.54020I 0
u = −1.037570 − 0.577206I
a = 0.264692 + 1.356690I
b = 1.86795 + 1.60205I
−2.93078 − 4.54020I 0
u = 1.069300 + 0.535238I
a = −0.212727 − 0.410896I
b = −1.03867 − 1.58194I
7.46229 − 1.93692I 0
u = 1.069300 − 0.535238I
a = −0.212727 + 0.410896I
b = −1.03867 + 1.58194I
7.46229 + 1.93692I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.515011 + 0.603128I
a = 1.64276 − 0.39430I
b = 0.492067 + 0.826898I
−1.41949 + 0.21530I −1.33212 − 0.94894I
u = −0.515011 − 0.603128I
a = 1.64276 + 0.39430I
b = 0.492067 − 0.826898I
−1.41949 − 0.21530I −1.33212 + 0.94894I
u = −0.864934 + 0.865784I
a = 0.37365 + 1.86763I
b = −0.69775 + 1.96712I
7.10528 − 0.44632I 0
u = −0.864934 − 0.865784I
a = 0.37365 − 1.86763I
b = −0.69775 − 1.96712I
7.10528 + 0.44632I 0
u = −1.178880 + 0.353943I
a = 0.754751 − 1.024090I
b = 0.733978 − 1.009140I
−3.35558 − 1.16932I 0
u = −1.178880 − 0.353943I
a = 0.754751 + 1.024090I
b = 0.733978 + 1.009140I
−3.35558 + 1.16932I 0
u = 1.125660 + 0.509560I
a = 0.137200 + 1.400810I
b = 1.92996 + 2.24231I
−2.31939 − 9.19141I 0
u = 1.125660 − 0.509560I
a = 0.137200 − 1.400810I
b = 1.92996 − 2.24231I
−2.31939 + 9.19141I 0
u = −0.939369 + 0.825652I
a = −1.75974 − 1.01547I
b = −0.34731 − 1.89934I
6.86423 + 6.71990I 0
u = −0.939369 − 0.825652I
a = −1.75974 + 1.01547I
b = −0.34731 + 1.89934I
6.86423 − 6.71990I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704939 + 0.128997I
a = 0.678583 − 0.630657I
b = 0.201233 + 0.306478I
−1.278980 + 0.553347I −4.94268 − 0.11935I
u = −0.704939 − 0.128997I
a = 0.678583 + 0.630657I
b = 0.201233 − 0.306478I
−1.278980 − 0.553347I −4.94268 + 0.11935I
u = −0.502799 + 0.482734I
a = −1.90347 + 1.26712I
b = −0.306144 + 0.452430I
1.30667 − 4.62534I 2.58741 + 1.79100I
u = −0.502799 − 0.482734I
a = −1.90347 − 1.26712I
b = −0.306144 − 0.452430I
1.30667 + 4.62534I 2.58741 − 1.79100I
u = 1.185270 + 0.561749I
a = 0.106817 + 0.932579I
b = 1.35872 + 1.78506I
−2.03233 − 5.61518I 0
u = 1.185270 − 0.561749I
a = 0.106817 − 0.932579I
b = 1.35872 − 1.78506I
−2.03233 + 5.61518I 0
u = 0.462387 + 0.498609I
a = −0.355623 − 0.428534I
b = 1.184450 + 0.682440I
9.29816 − 2.41390I 1.98968 + 2.16516I
u = 0.462387 − 0.498609I
a = −0.355623 + 0.428534I
b = 1.184450 − 0.682440I
9.29816 + 2.41390I 1.98968 − 2.16516I
u = 1.187720 + 0.576982I
a = −0.0159480 − 0.0353645I
b = −0.578942 − 0.722269I
5.01786 − 8.11410I 0
u = 1.187720 − 0.576982I
a = −0.0159480 + 0.0353645I
b = −0.578942 + 0.722269I
5.01786 + 8.11410I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.809665 + 1.047990I
a = −0.578466 + 1.211320I
b = 0.20865 + 1.46420I
7.99506 − 3.76404I 0
u = 0.809665 − 1.047990I
a = −0.578466 − 1.211320I
b = 0.20865 − 1.46420I
7.99506 + 3.76404I 0
u = −1.297580 + 0.343196I
a = 0.265023 − 0.728750I
b = −0.019555 − 0.999504I
−3.72640 + 3.60063I 0
u = −1.297580 − 0.343196I
a = 0.265023 + 0.728750I
b = −0.019555 + 0.999504I
−3.72640 − 3.60063I 0
u = −1.210270 + 0.608884I
a = 0.366434 − 1.056420I
b = 1.51925 − 1.86407I
−1.01252 + 9.05504I 0
u = −1.210270 − 0.608884I
a = 0.366434 + 1.056420I
b = 1.51925 + 1.86407I
−1.01252 − 9.05504I 0
u = −1.145810 + 0.725166I
a = 0.081475 + 1.179080I
b = −1.23733 + 1.76256I
−0.87540 + 9.52648I 0
u = −1.145810 − 0.725166I
a = 0.081475 − 1.179080I
b = −1.23733 − 1.76256I
−0.87540 − 9.52648I 0
u = 0.119389 + 0.627414I
a = 2.62220 − 0.47010I
b = 0.273086 − 0.906877I
0.32407 + 4.80711I 2.84174 − 5.69896I
u = 0.119389 − 0.627414I
a = 2.62220 + 0.47010I
b = 0.273086 + 0.906877I
0.32407 − 4.80711I 2.84174 + 5.69896I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019810 + 0.909269I
a = 0.814306 − 1.101550I
b = −0.26325 − 1.57950I
7.32281 − 3.25014I 0
u = 1.019810 − 0.909269I
a = 0.814306 + 1.101550I
b = −0.26325 + 1.57950I
7.32281 + 3.25014I 0
u = −1.267540 + 0.515469I
a = 0.124014 + 0.094273I
b = 0.062531 + 0.820397I
4.05888 + 1.69142I 0
u = −1.267540 − 0.515469I
a = 0.124014 − 0.094273I
b = 0.062531 − 0.820397I
4.05888 − 1.69142I 0
u = −0.571300 + 0.255504I
a = −0.152207 + 1.389420I
b = 0.055604 − 0.780948I
−1.30408 − 0.70841I −3.23715 − 2.79209I
u = −0.571300 − 0.255504I
a = −0.152207 − 1.389420I
b = 0.055604 + 0.780948I
−1.30408 + 0.70841I −3.23715 + 2.79209I
u = 1.225220 + 0.689448I
a = −0.069523 − 1.329850I
b = −1.36230 − 2.11676I
2.3330 − 17.1358I 0
u = 1.225220 − 0.689448I
a = −0.069523 + 1.329850I
b = −1.36230 + 2.11676I
2.3330 + 17.1358I 0
u = −0.535112 + 0.234522I
a = −0.662387 + 0.280870I
b = 1.93398 − 0.90821I
8.70160 − 1.90871I 7.78540 + 9.95719I
u = −0.535112 − 0.234522I
a = −0.662387 − 0.280870I
b = 1.93398 + 0.90821I
8.70160 + 1.90871I 7.78540 − 9.95719I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.258887 + 0.501698I
a = 0.645831 − 0.321842I
b = −0.399572 − 0.528257I
1.169890 + 0.562593I 6.08302 − 1.22520I
u = 0.258887 − 0.501698I
a = 0.645831 + 0.321842I
b = −0.399572 + 0.528257I
1.169890 − 0.562593I 6.08302 + 1.22520I
u = 1.40041 + 0.31914I
a = 0.425074 + 0.891756I
b = 0.47358 + 1.45542I
−3.47015 − 1.06999I 0
u = 1.40041 − 0.31914I
a = 0.425074 − 0.891756I
b = 0.47358 − 1.45542I
−3.47015 + 1.06999I 0
u = −1.50427 + 0.13904I
a = −0.652895 + 0.680071I
b = −0.576514 + 0.878599I
−1.87227 − 6.46093I 0
u = −1.50427 − 0.13904I
a = −0.652895 − 0.680071I
b = −0.576514 − 0.878599I
−1.87227 + 6.46093I 0
u = 0.444561 + 0.091212I
a = 0.83158 − 3.45351I
b = −0.793166 + 1.093540I
0.70679 − 4.99686I 6.49732 + 8.11595I
u = 0.444561 − 0.091212I
a = 0.83158 + 3.45351I
b = −0.793166 − 1.093540I
0.70679 + 4.99686I 6.49732 − 8.11595I
u = 1.62650
a = −0.224051
b = −0.115481
−7.34147 0
13
II. I
u
2
=
h−3.48×10
8
u
30
+1.92×10
8
u
29
+· · ·+5.68×10
7
b+3.58×10
8
, 2.41×10
10
u
30
−
1.32 × 10
10
u
29
+ · · · + 1.25 × 10
9
a − 5.98 × 10
10
, u
31
− 10u
29
+ · · · + 19u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
−19.3040u
30
+ 10.6044u
29
+ ··· − 92.5487u + 47.8731
6.13328u
30
− 3.37414u
29
+ ··· + 28.2670u − 6.30366
a
6
=
−21.3460u
30
+ 13.6987u
29
+ ··· − 107.471u + 61.2222
7.93390u
30
− 4.43203u
29
+ ··· + 35.9523u − 14.6081
a
4
=
−19.3040u
30
+ 11.6044u
29
+ ··· − 92.5487u + 48.8731
8.67259u
30
− 7.31759u
29
+ ··· + 25.8679u − 29.1657
a
7
=
u
−u
3
+ u
a
12
=
−5.44279u
30
+ 5.08584u
29
+ ··· − 14.5913u + 19.3089
3.13409u
30
− 2.82571u
29
+ ··· + 30.3713u − 6.39981
a
11
=
−5.44279u
30
+ 5.08584u
29
+ ··· − 14.5913u + 19.3089
7.08069u
30
− 4.71151u
29
+ ··· + 41.2569u − 16.5715
a
9
=
8.31564u
30
− 6.17835u
29
+ ··· + 30.5855u − 19.7424
−9.59968u
30
+ 7.28331u
29
+ ··· − 40.1587u + 25.6795
a
10
=
14.7121u
30
− 10.9749u
29
+ ··· + 58.2461u − 38.1995
−6.19108u
30
+ 4.57744u
29
+ ··· − 25.2909u + 16.8155
(ii) Obstruction class = 1
(iii) Cusp Shapes =
24124619479
624565337
u
30
−
17404745881
624565337
u
29
+ ··· +
139983567026
624565337
u −
83899224330
624565337
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
31
− 20u
30
+ ··· + 76u − 4
c
2
u
31
− 10u
29
+ ··· + 19u
2
− 2
c
3
u
31
+ 7u
30
+ ··· − u + 1
c
4
u
31
− 10u
29
+ ··· − 5u
2
+ 2
c
5
u
31
+ u
30
+ ··· + 4u + 1
c
6
u
31
− 3u
30
+ ··· + u + 1
c
7
u
31
− 10u
29
+ ··· − 19u
2
+ 2
c
8
u
31
− 7u
30
+ ··· − u − 1
c
9
u
31
+ 3u
30
+ ··· + u − 1
c
10
u
31
− 10u
29
+ ··· + 5u
2
− 2
c
11
u
31
+ 7u
30
+ ··· − u + 1
c
12
u
31
− u
30
+ ··· + 4u − 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 20y
29
+ ··· + 8y −16
c
2
, c
7
y
31
− 20y
30
+ ··· + 76y −4
c
3
y
31
− 31y
30
+ ··· + 13y −1
c
4
, c
10
y
31
− 20y
30
+ ··· + 20y −4
c
5
, c
12
y
31
− 19y
30
+ ··· + 14y −1
c
6
, c
9
y
31
+ 17y
30
+ ··· − 13y −1
c
8
, c
11
y
31
− 15y
30
+ ··· − 13y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982568 + 0.207175I
a = 0.35982 + 1.42586I
b = 0.483461 + 1.108490I
−5.23586 − 0.81132I −4.38603 − 2.94703I
u = 0.982568 − 0.207175I
a = 0.35982 − 1.42586I
b = 0.483461 − 1.108490I
−5.23586 + 0.81132I −4.38603 + 2.94703I
u = −0.696507 + 0.756440I
a = −0.388503 − 0.996344I
b = 0.86594 − 1.51309I
10.41040 + 3.06803I 7.43606 − 4.02587I
u = −0.696507 − 0.756440I
a = −0.388503 + 0.996344I
b = 0.86594 + 1.51309I
10.41040 − 3.06803I 7.43606 + 4.02587I
u = −0.410503 + 0.794774I
a = 1.246480 − 0.021501I
b = 0.101573 + 0.831224I
−0.05983 − 1.72000I 1.00900 + 1.90497I
u = −0.410503 − 0.794774I
a = 1.246480 + 0.021501I
b = 0.101573 − 0.831224I
−0.05983 + 1.72000I 1.00900 − 1.90497I
u = 0.775233 + 0.836328I
a = −0.07343 − 1.83726I
b = −1.06617 − 1.58292I
7.51530 − 0.06475I 9.22266 + 2.76574I
u = 0.775233 − 0.836328I
a = −0.07343 + 1.83726I
b = −1.06617 + 1.58292I
7.51530 + 0.06475I 9.22266 − 2.76574I
u = 1.094090 + 0.399098I
a = −0.086828 − 0.135133I
b = −0.46570 − 1.71167I
6.85605 − 4.63054I 4.49675 + 0.27840I
u = 1.094090 − 0.399098I
a = −0.086828 + 0.135133I
b = −0.46570 + 1.71167I
6.85605 + 4.63054I 4.49675 − 0.27840I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110110 + 0.434879I
a = −0.297972 + 0.640110I
b = −0.571480 − 0.219426I
3.15670 + 1.49764I −2.81572 − 0.33383I
u = −1.110110 − 0.434879I
a = −0.297972 − 0.640110I
b = −0.571480 + 0.219426I
3.15670 − 1.49764I −2.81572 + 0.33383I
u = −0.705459 + 0.273226I
a = −0.66198 + 1.69572I
b = −2.17848 + 0.30056I
4.79170 + 1.50898I 1.21271 − 2.64841I
u = −0.705459 − 0.273226I
a = −0.66198 − 1.69572I
b = −2.17848 − 0.30056I
4.79170 − 1.50898I 1.21271 + 2.64841I
u = −1.272730 + 0.053951I
a = −0.355601 − 0.878152I
b = −0.75493 − 1.52255I
−2.31923 + 4.99144I −0.79371 − 3.48912I
u = −1.272730 − 0.053951I
a = −0.355601 + 0.878152I
b = −0.75493 + 1.52255I
−2.31923 − 4.99144I −0.79371 + 3.48912I
u = −1.135470 + 0.587695I
a = 0.154244 − 1.110710I
b = 1.54935 − 1.84109I
−2.29051 + 6.94631I −0.79999 − 6.24825I
u = −1.135470 − 0.587695I
a = 0.154244 + 1.110710I
b = 1.54935 + 1.84109I
−2.29051 − 6.94631I −0.79999 + 6.24825I
u = 0.652835 + 0.301948I
a = 0.081700 + 0.433186I
b = 2.11052 + 1.10836I
8.54946 + 1.55362I −0.60356 + 8.66470I
u = 0.652835 − 0.301948I
a = 0.081700 − 0.433186I
b = 2.11052 − 1.10836I
8.54946 − 1.55362I −0.60356 − 8.66470I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.242900 + 0.328168I
a = 0.376668 + 1.016840I
b = 0.51312 + 1.44718I
−4.48639 − 1.20604I −5.60895 + 0.94515I
u = 1.242900 − 0.328168I
a = 0.376668 − 1.016840I
b = 0.51312 − 1.44718I
−4.48639 + 1.20604I −5.60895 − 0.94515I
u = −1.073660 + 0.718909I
a = 0.608450 + 0.753784I
b = −0.31799 + 1.77272I
9.24150 + 2.59852I 6.52430 − 2.25864I
u = −1.073660 − 0.718909I
a = 0.608450 − 0.753784I
b = −0.31799 − 1.77272I
9.24150 − 2.59852I 6.52430 + 2.25864I
u = 1.008110 + 0.824251I
a = −1.39431 + 0.69851I
b = −0.38935 + 1.51889I
6.81366 − 6.13871I 3.40544 + 0.77515I
u = 1.008110 − 0.824251I
a = −1.39431 − 0.69851I
b = −0.38935 − 1.51889I
6.81366 + 6.13871I 3.40544 − 0.77515I
u = −0.672314 + 0.039094I
a = 0.58739 + 2.51103I
b = −0.672858 − 0.565949I
0.17885 + 4.88804I −8.54177 − 5.66057I
u = −0.672314 − 0.039094I
a = 0.58739 − 2.51103I
b = −0.672858 + 0.565949I
0.17885 − 4.88804I −8.54177 + 5.66057I
u = 0.525158 + 0.276936I
a = 1.86486 + 1.42047I
b = −0.588234 − 0.322507I
−1.56820 − 1.69000I −6.18264 + 1.41203I
u = 0.525158 − 0.276936I
a = 1.86486 − 1.42047I
b = −0.588234 + 0.322507I
−1.56820 + 1.69000I −6.18264 − 1.41203I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59174
a = −0.0419671
b = −0.237529
−7.44021 −41.1490
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 20u
30
+ ··· + 76u − 4)(u
89
+ 47u
88
+ ··· + 2796u + 100)
c
2
(u
31
− 10u
29
+ ··· + 19u
2
− 2)(u
89
− u
88
+ ··· + 14u − 10)
c
3
(u
31
+ 7u
30
+ ··· − u + 1)(u
89
− 2u
88
+ ··· + 459338u + 255793)
c
4
(u
31
− 10u
29
+ ··· − 5u
2
+ 2)(u
89
+ u
88
+ ··· + 119758u + 26770)
c
5
(u
31
+ u
30
+ ··· + 4u + 1)(u
89
− 2u
88
+ ··· + 897u − 487)
c
6
(u
31
− 3u
30
+ ··· + u + 1)(u
89
− 2u
88
+ ··· + 39310u − 17077)
c
7
(u
31
− 10u
29
+ ··· − 19u
2
+ 2)(u
89
− u
88
+ ··· + 14u − 10)
c
8
(u
31
− 7u
30
+ ··· − u − 1)(u
89
− 6u
88
+ ··· − 24u + 1)
c
9
(u
31
+ 3u
30
+ ··· + u − 1)(u
89
− 2u
88
+ ··· + 39310u − 17077)
c
10
(u
31
− 10u
29
+ ··· + 5u
2
− 2)(u
89
+ u
88
+ ··· + 119758u + 26770)
c
11
(u
31
+ 7u
30
+ ··· − u + 1)(u
89
− 6u
88
+ ··· − 24u + 1)
c
12
(u
31
− u
30
+ ··· + 4u − 1)(u
89
− 2u
88
+ ··· + 897u − 487)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
31
− 20y
29
+ ··· + 8y −16)(y
89
+ 9y
88
+ ··· + 125616y −10000)
c
2
, c
7
(y
31
− 20y
30
+ ··· + 76y −4)(y
89
− 47y
88
+ ··· + 2796y −100)
c
3
(y
31
− 31y
30
+ ··· + 13y −1)
· (y
89
− 66y
88
+ ··· + 699981667796y −65430058849)
c
4
, c
10
(y
31
− 20y
30
+ ··· + 20y −4)
· (y
89
− 47y
88
+ ··· + 24496053724y −716632900)
c
5
, c
12
(y
31
− 19y
30
+ ··· + 14y −1)
· (y
89
− 42y
88
+ ··· + 7221321y −237169)
c
6
, c
9
(y
31
+ 17y
30
+ ··· − 13y −1)
· (y
89
+ 46y
88
+ ··· − 11363262354y −291623929)
c
8
, c
11
(y
31
− 15y
30
+ ··· − 13y −1)(y
89
− 58y
88
+ ··· + 1046y −1)
24
