12a
1167
(K12a
1167
)
A knot diagram
1
Linearized knot diagam
4 9 10 12 2 3 1 11 6 7 5 8
Solving Sequence
8,12 1,5
4 2 6 7 11 9 10 3
c
12
c
4
c
1
c
5
c
7
c
11
c
8
c
10
c
3
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4.59872 × 10
1554
u
217
− 9.84331 × 10
1554
u
216
+ ··· + 7.30909 × 10
1556
b − 1.10702 × 10
1560
,
1.07881 × 10
1569
u
217
+ 1.14742 × 10
1569
u
216
+ ··· + 8.66519 × 10
1570
a + 2.46881 × 10
1575
,
u
218
− u
217
+ ··· + 1084332u + 800958i
I
u
2
= h8.39999 × 10
88
u
59
− 2.76464 × 10
88
u
58
+ ··· + 8.73404 × 10
87
b − 3.20535 × 10
89
,
− 6.26274 × 10
91
u
59
− 5.42884 × 10
91
u
58
+ ··· + 1.55466 × 10
91
a − 9.36581 × 10
92
,
u
60
+ 21u
58
+ ··· + 40u + 20i
* 2 irreducible components of dim
C
= 0, with total 278 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
= h4.60 × 10
1554
u
217
− 9.84 × 10
1554
u
216
+ · · · + 7.31 × 10
1556
b − 1.11 ×
10
1560
, 1.08 × 10
1569
u
217
+ 1.15 × 10
1569
u
216
+ · · · + 8.67 × 10
1570
a + 2.47 ×
10
1575
, u
218
− u
217
+ · · · + 1084332u + 800958i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
−0.0124500u
217
− 0.0132417u
216
+ ··· − 57143.3u − 28491.1
−0.00629178u
217
+ 0.0134672u
216
+ ··· − 5937.11u + 1514.57
a
4
=
−0.0187418u
217
+ 0.000225544u
216
+ ··· − 63080.4u − 26976.6
−0.00629178u
217
+ 0.0134672u
216
+ ··· − 5937.11u + 1514.57
a
2
=
−0.0200316u
217
+ 0.0391073u
216
+ ··· + 40964.8u + 19242.7
−0.0144419u
217
+ 0.0238159u
216
+ ··· − 25081.4u + 1435.38
a
6
=
0.0378271u
217
− 0.0347035u
216
+ ··· + 77782.1u + 773.143
−0.00425950u
217
+ 0.0280317u
216
+ ··· + 14309.1u + 20325.0
a
7
=
−u
u
3
+ u
a
11
=
−0.0210500u
217
+ 0.0336813u
216
+ ··· − 24851.7u + 3718.28
0.0149998u
217
− 0.0269724u
216
+ ··· + 20949.7u − 907.805
a
9
=
0.00566707u
217
+ 0.0502761u
216
+ ··· + 49142.3u + 27148.3
0.0461777u
217
− 0.0612084u
216
+ ··· + 61781.7u + 17922.2
a
10
=
−0.0296511u
217
+ 0.0393404u
216
+ ··· − 37179.5u − 3303.97
0.0174703u
217
− 0.0258301u
216
+ ··· + 23198.2u + 3757.99
a
3
=
−0.0266976u
217
− 0.0219209u
216
+ ··· − 69036.9u − 44256.4
−0.0194184u
217
+ 0.0258173u
216
+ ··· − 36011.2u − 10545.3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.102226u
217
+ 0.313054u
216
+ ··· + 38230.4u + 152101.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
218
+ 7u
217
+ ··· − 325966059u + 13035439
c
2
6(6u
218
− 6u
217
+ ··· − 603u + 1721)
c
3
6(6u
218
+ 6u
217
+ ··· + 603u + 1721)
c
4
, c
11
u
218
+ u
217
+ ··· − 1084332u + 800958
c
5
u
218
− 6u
217
+ ··· − 4497810u + 159275
c
6
u
218
− 7u
217
+ ··· + 5706u + 1086
c
7
, c
12
u
218
− u
217
+ ··· + 1084332u + 800958
c
8
u
218
− 7u
217
+ ··· + 325966059u + 13035439
c
9
u
218
+ 7u
217
+ ··· − 5706u + 1086
c
10
u
218
+ 6u
217
+ ··· + 4497810u + 159275
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
218
− 27y
217
+ ··· − 75149030070299023y + 169922669922721
c
2
, c
3
36(36y
218
+ 228y
217
+ ··· − 2.18635 × 10
8
y + 2961841)
c
4
, c
7
, c
11
c
12
y
218
+ 127y
217
+ ··· + 37988843650536y + 641533717764
c
5
, c
10
y
218
− 26y
217
+ ··· − 2357094900150y + 25368525625
c
6
, c
9
y
218
− 7y
217
+ ··· − 16168524y + 1179396
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437041 + 0.900025I
a = −0.212197 + 0.783889I
b = 0.470183 − 1.256570I
1.89033 + 0.72271I 0
u = −0.437041 − 0.900025I
a = −0.212197 − 0.783889I
b = 0.470183 + 1.256570I
1.89033 − 0.72271I 0
u = −1.003990 + 0.150540I
a = 0.46765 + 1.53202I
b = −0.394463 − 1.163640I
1.04005 − 7.54869I 0
u = −1.003990 − 0.150540I
a = 0.46765 − 1.53202I
b = −0.394463 + 1.163640I
1.04005 + 7.54869I 0
u = −0.100843 + 0.975368I
a = 0.608586 + 0.384135I
b = −0.462739 + 0.668047I
−2.24226 + 5.02667I 0
u = −0.100843 − 0.975368I
a = 0.608586 − 0.384135I
b = −0.462739 − 0.668047I
−2.24226 − 5.02667I 0
u = 0.308123 + 0.973343I
a = 0.052320 + 0.205725I
b = 1.035720 − 0.074637I
−1.48317 + 2.08145I 0
u = 0.308123 − 0.973343I
a = 0.052320 − 0.205725I
b = 1.035720 + 0.074637I
−1.48317 − 2.08145I 0
u = −0.613126 + 0.759553I
a = 1.40770 − 0.75603I
b = 0.499855 + 0.732282I
1.94446 + 0.55451I 0
u = −0.613126 − 0.759553I
a = 1.40770 + 0.75603I
b = 0.499855 − 0.732282I
1.94446 − 0.55451I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462881 + 0.921010I
a = 1.65931 − 0.95682I
b = 0.303325 + 1.215080I
5.39866 − 2.44724I 0
u = −0.462881 − 0.921010I
a = 1.65931 + 0.95682I
b = 0.303325 − 1.215080I
5.39866 + 2.44724I 0
u = 1.035720 + 0.074637I
a = −0.123358 + 1.070400I
b = 0.308123 − 0.973343I
1.48317 + 2.08145I 0
u = 1.035720 − 0.074637I
a = −0.123358 − 1.070400I
b = 0.308123 + 0.973343I
1.48317 − 2.08145I 0
u = −1.019800 + 0.230367I
a = 0.04271 − 1.76667I
b = −0.245349 + 1.164410I
5.69009 + 2.69649I 0
u = −1.019800 − 0.230367I
a = 0.04271 + 1.76667I
b = −0.245349 − 1.164410I
5.69009 − 2.69649I 0
u = −0.940943 + 0.473748I
a = −0.511895 + 1.294760I
b = 0.551520 − 1.222040I
3.67220 + 6.74825I 0
u = −0.940943 − 0.473748I
a = −0.511895 − 1.294760I
b = 0.551520 + 1.222040I
3.67220 − 6.74825I 0
u = 0.417538 + 0.847320I
a = −0.434386 − 1.022500I
b = 0.14556 + 1.62539I
3.61073 + 9.93097I 0
u = 0.417538 − 0.847320I
a = −0.434386 + 1.022500I
b = 0.14556 − 1.62539I
3.61073 − 9.93097I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.918583 + 0.207533I
a = 0.158984 + 1.222530I
b = 0.617526 − 0.420082I
−0.55926 − 1.41093I 0
u = 0.918583 − 0.207533I
a = 0.158984 − 1.222530I
b = 0.617526 + 0.420082I
−0.55926 + 1.41093I 0
u = −0.876472 + 0.598057I
a = 0.85061 − 1.35338I
b = −0.212076 + 1.158300I
4.47322 + 1.53890I 0
u = −0.876472 − 0.598057I
a = 0.85061 + 1.35338I
b = −0.212076 − 1.158300I
4.47322 − 1.53890I 0
u = 0.280150 + 1.026020I
a = 2.78942 + 0.08607I
b = 0.222875 − 1.137530I
1.77355 + 9.93813I 0
u = 0.280150 − 1.026020I
a = 2.78942 − 0.08607I
b = 0.222875 + 1.137530I
1.77355 − 9.93813I 0
u = −0.305306 + 0.885243I
a = −1.67577 + 0.37643I
b = −0.441025 − 1.259580I
4.46515 − 1.74939I 0
u = −0.305306 − 0.885243I
a = −1.67577 − 0.37643I
b = −0.441025 + 1.259580I
4.46515 + 1.74939I 0
u = −0.683089 + 0.622922I
a = −1.30428 + 2.09014I
b = 0.169104 − 0.739046I
0.471008 + 0.398019I 0
u = −0.683089 − 0.622922I
a = −1.30428 − 2.09014I
b = 0.169104 + 0.739046I
0.471008 − 0.398019I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599761 + 0.900295I
a = 0.936810 + 0.857137I
b = 0.535570 − 1.197750I
1.59135 + 1.88450I 0
u = 0.599761 − 0.900295I
a = 0.936810 − 0.857137I
b = 0.535570 + 1.197750I
1.59135 − 1.88450I 0
u = 0.654387 + 0.863274I
a = −1.18552 − 0.97649I
b = −0.712791 + 1.018320I
3.35203 + 9.91892I 0
u = 0.654387 − 0.863274I
a = −1.18552 + 0.97649I
b = −0.712791 − 1.018320I
3.35203 − 9.91892I 0
u = 0.852196 + 0.669721I
a = −0.078282 − 0.811383I
b = 0.465569 + 1.148550I
3.96693 − 4.42004I 0
u = 0.852196 − 0.669721I
a = −0.078282 + 0.811383I
b = 0.465569 − 1.148550I
3.96693 + 4.42004I 0
u = −0.297555 + 0.858019I
a = −1.63283 + 1.32850I
b = −0.11319 − 1.61653I
5.12076 − 1.34522I 0
u = −0.297555 − 0.858019I
a = −1.63283 − 1.32850I
b = −0.11319 + 1.61653I
5.12076 + 1.34522I 0
u = 0.048733 + 0.898701I
a = −0.637885 + 0.115788I
b = −1.56815 − 0.17899I
−5.09439 − 4.03171I 0
u = 0.048733 − 0.898701I
a = −0.637885 − 0.115788I
b = −1.56815 + 0.17899I
−5.09439 + 4.03171I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231329 + 1.076970I
a = 0.210849 + 0.060273I
b = 1.45238 + 0.43315I
−6.24818 + 5.10916I 0
u = 0.231329 − 1.076970I
a = 0.210849 − 0.060273I
b = 1.45238 − 0.43315I
−6.24818 − 5.10916I 0
u = −0.231325 + 1.078200I
a = 0.154807 − 0.301137I
b = 1.31711 − 0.51509I
−6.50971 + 3.37301I 0
u = −0.231325 − 1.078200I
a = 0.154807 + 0.301137I
b = 1.31711 + 0.51509I
−6.50971 − 3.37301I 0
u = 0.457581 + 1.005390I
a = 0.838236 + 0.551028I
b = 0.80753 − 1.19940I
2.18813 + 2.01931I 0
u = 0.457581 − 1.005390I
a = 0.838236 − 0.551028I
b = 0.80753 + 1.19940I
2.18813 − 2.01931I 0
u = −0.456995 + 1.006320I
a = 0.461164 − 0.001249I
b = 0.659626 − 0.133765I
0.871914 + 0.606568I 0
u = −0.456995 − 1.006320I
a = 0.461164 + 0.001249I
b = 0.659626 + 0.133765I
0.871914 − 0.606568I 0
u = 0.587380 + 0.938448I
a = 0.904126 + 0.520229I
b = −0.141926 − 0.323075I
−1.79288 + 4.49429I 0
u = 0.587380 − 0.938448I
a = 0.904126 − 0.520229I
b = −0.141926 + 0.323075I
−1.79288 − 4.49429I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001784 + 0.890176I
a = 1.47851 − 1.97142I
b = 0.414190 + 1.163180I
−1.49293 − 5.19189I 0
u = 0.001784 − 0.890176I
a = 1.47851 + 1.97142I
b = 0.414190 − 1.163180I
−1.49293 + 5.19189I 0
u = 0.499855 + 0.732282I
a = −0.63104 − 2.00328I
b = −0.613126 + 0.759553I
−1.94446 − 0.55451I 0
u = 0.499855 − 0.732282I
a = −0.63104 + 2.00328I
b = −0.613126 − 0.759553I
−1.94446 + 0.55451I 0
u = −0.400012 + 0.781762I
a = 1.55396 − 2.03173I
b = 0.02640 + 1.45390I
6.08780 − 1.75437I 0
u = −0.400012 − 0.781762I
a = 1.55396 + 2.03173I
b = 0.02640 − 1.45390I
6.08780 + 1.75437I 0
u = −0.249759 + 0.838626I
a = −0.50515 + 1.32541I
b = 0.17906 − 1.59970I
4.72681 − 0.80347I 0
u = −0.249759 − 0.838626I
a = −0.50515 − 1.32541I
b = 0.17906 + 1.59970I
4.72681 + 0.80347I 0
u = −0.347244 + 0.800650I
a = 0.06808 − 2.15938I
b = 0.146770 + 1.255100I
2.93174 − 5.03893I 0
u = −0.347244 − 0.800650I
a = 0.06808 + 2.15938I
b = 0.146770 − 1.255100I
2.93174 + 5.03893I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.360891 + 0.783303I
a = 2.43073 − 0.59779I
b = −0.028929 + 0.843147I
2.95474 + 1.76216I 0
u = −0.360891 − 0.783303I
a = 2.43073 + 0.59779I
b = −0.028929 − 0.843147I
2.95474 − 1.76216I 0
u = 0.478952 + 0.712106I
a = −1.53516 − 0.79069I
b = −0.423654 + 1.290220I
3.95917 − 6.15252I 0
u = 0.478952 − 0.712106I
a = −1.53516 + 0.79069I
b = −0.423654 − 1.290220I
3.95917 + 6.15252I 0
u = −0.028929 + 0.843147I
a = −2.16685 − 1.18164I
b = −0.360891 + 0.783303I
−2.95474 − 1.76216I 0
u = −0.028929 − 0.843147I
a = −2.16685 + 1.18164I
b = −0.360891 − 0.783303I
−2.95474 + 1.76216I 0
u = 0.222875 + 1.137530I
a = 2.04824 + 2.09156I
b = 0.280150 − 1.026020I
−1.77355 + 9.93813I 0
u = 0.222875 − 1.137530I
a = 2.04824 − 2.09156I
b = 0.280150 + 1.026020I
−1.77355 − 9.93813I 0
u = 0.492848 + 1.054720I
a = 0.066722 − 0.384063I
b = −1.204180 − 0.427493I
−1.31280 + 5.76610I 0
u = 0.492848 − 1.054720I
a = 0.066722 + 0.384063I
b = −1.204180 + 0.427493I
−1.31280 − 5.76610I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485058 + 0.675673I
a = 0.71648 − 1.71839I
b = −0.09723 + 1.42923I
6.16346 − 1.48072I 0
u = −0.485058 − 0.675673I
a = 0.71648 + 1.71839I
b = −0.09723 − 1.42923I
6.16346 + 1.48072I 0
u = −0.334184 + 1.120090I
a = −1.087770 + 0.371028I
b = −0.778130 − 1.146260I
0.68932 − 6.27683I 0
u = −0.334184 − 1.120090I
a = −1.087770 − 0.371028I
b = −0.778130 + 1.146260I
0.68932 + 6.27683I 0
u = −1.128100 + 0.310890I
a = 0.44682 − 1.47507I
b = −0.474782 + 1.184610I
4.45442 + 7.05483I 0
u = −1.128100 − 0.310890I
a = 0.44682 + 1.47507I
b = −0.474782 − 1.184610I
4.45442 − 7.05483I 0
u = −0.212076 + 1.158300I
a = −0.529572 − 0.285491I
b = −0.876472 + 0.598057I
−4.47322 − 1.53890I 0
u = −0.212076 − 1.158300I
a = −0.529572 + 0.285491I
b = −0.876472 − 0.598057I
−4.47322 + 1.53890I 0
u = −0.815024 + 0.089394I
a = 0.298810 + 1.035750I
b = −0.815024 − 0.089394I
10.6392I 0
u = −0.815024 − 0.089394I
a = 0.298810 − 1.035750I
b = −0.815024 + 0.089394I
− 10.6392I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462739 + 0.668047I
a = −0.765955 − 1.027670I
b = −0.100843 + 0.975368I
2.24226 − 5.02667I 0
u = −0.462739 − 0.668047I
a = −0.765955 + 1.027670I
b = −0.100843 − 0.975368I
2.24226 + 5.02667I 0
u = −0.245349 + 1.164410I
a = −0.406813 + 0.382344I
b = −1.019800 + 0.230367I
−5.69009 − 2.69649I 0
u = −0.245349 − 1.164410I
a = −0.406813 − 0.382344I
b = −1.019800 − 0.230367I
−5.69009 + 2.69649I 0
u = 0.633855 + 0.501954I
a = 0.443590 + 1.034730I
b = −0.005538 − 1.314790I
2.61763 + 2.89255I 0
u = 0.633855 − 0.501954I
a = 0.443590 − 1.034730I
b = −0.005538 + 1.314790I
2.61763 − 2.89255I 0
u = −0.305013 + 0.742816I
a = −1.73612 + 0.63594I
b = −0.832514 − 0.986584I
2.55700 − 3.98943I 0
u = −0.305013 − 0.742816I
a = −1.73612 − 0.63594I
b = −0.832514 + 0.986584I
2.55700 + 3.98943I 0
u = −0.650441 + 0.418846I
a = −0.337752 + 0.136335I
b = −0.455370 + 0.573274I
2.53070 − 4.91173I 0
u = −0.650441 − 0.418846I
a = −0.337752 − 0.136335I
b = −0.455370 − 0.573274I
2.53070 + 4.91173I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394463 + 1.163640I
a = −0.310280 − 0.005624I
b = −1.003990 − 0.150540I
−1.04005 − 7.54869I 0
u = −0.394463 − 1.163640I
a = −0.310280 + 0.005624I
b = −1.003990 + 0.150540I
−1.04005 + 7.54869I 0
u = 0.414190 + 1.163180I
a = −1.48076 + 0.09417I
b = 0.001784 + 0.890176I
1.49293 + 5.19189I 0
u = 0.414190 − 1.163180I
a = −1.48076 − 0.09417I
b = 0.001784 − 0.890176I
1.49293 − 5.19189I 0
u = 1.208630 + 0.270590I
a = 0.28128 + 1.41196I
b = −0.507492 − 1.213560I
3.3016 − 15.4845I 0
u = 1.208630 − 0.270590I
a = 0.28128 − 1.41196I
b = −0.507492 + 1.213560I
3.3016 + 15.4845I 0
u = 0.465569 + 1.148550I
a = −0.440419 − 0.087771I
b = 0.852196 + 0.669721I
−3.96693 + 4.42004I 0
u = 0.465569 − 1.148550I
a = −0.440419 + 0.087771I
b = 0.852196 − 0.669721I
−3.96693 − 4.42004I 0
u = 0.169104 + 0.739046I
a = −2.07639 − 0.56469I
b = −0.683089 − 0.622922I
−0.471008 + 0.398019I 0
u = 0.169104 − 0.739046I
a = −2.07639 + 0.56469I
b = −0.683089 + 0.622922I
−0.471008 − 0.398019I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712791 + 1.018320I
a = 0.47230 − 1.58594I
b = 0.654387 + 0.863274I
−3.35203 − 9.91892I 0
u = −0.712791 − 1.018320I
a = 0.47230 + 1.58594I
b = 0.654387 − 0.863274I
−3.35203 + 9.91892I 0
u = −0.169692 + 1.232880I
a = −0.057350 + 0.475952I
b = 0.539677 + 0.075169I
−4.55571 + 1.39410I 0
u = −0.169692 − 1.232880I
a = −0.057350 − 0.475952I
b = 0.539677 − 0.075169I
−4.55571 − 1.39410I 0
u = 0.040178 + 0.753764I
a = 4.35446 + 0.61006I
b = 0.040178 − 0.753764I
− 8.63608I 0
u = 0.040178 − 0.753764I
a = 4.35446 − 0.61006I
b = 0.040178 + 0.753764I
8.63608I 0
u = 0.725964 + 0.188776I
a = 0.34164 + 1.91784I
b = 0.451957 − 1.184490I
1.37563 + 4.28259I 0
u = 0.725964 − 0.188776I
a = 0.34164 − 1.91784I
b = 0.451957 + 1.184490I
1.37563 − 4.28259I 0
u = 0.303325 + 1.215080I
a = −1.08607 − 1.21454I
b = −0.462881 + 0.921010I
−5.39866 + 2.44724I 0
u = 0.303325 − 1.215080I
a = −1.08607 + 1.21454I
b = −0.462881 − 0.921010I
−5.39866 − 2.44724I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617526 + 0.420082I
a = 0.071190 + 1.406190I
b = 0.918583 − 0.207533I
0.55926 − 1.41093I 0
u = 0.617526 − 0.420082I
a = 0.071190 − 1.406190I
b = 0.918583 + 0.207533I
0.55926 + 1.41093I 0
u = 0.470758 + 1.166590I
a = 0.90729 + 1.23869I
b = 0.73676 − 1.26291I
−3.85707 + 3.73345I 0
u = 0.470758 − 1.166590I
a = 0.90729 − 1.23869I
b = 0.73676 + 1.26291I
−3.85707 − 3.73345I 0
u = −0.611244 + 1.099830I
a = 0.79969 − 1.47275I
b = 0.453658 + 1.273930I
2.80969 − 7.03935I 0
u = −0.611244 − 1.099830I
a = 0.79969 + 1.47275I
b = 0.453658 − 1.273930I
2.80969 + 7.03935I 0
u = 0.146770 + 1.255100I
a = −0.441704 + 0.465763I
b = −0.347244 + 0.800650I
−2.93174 + 5.03893I 0
u = 0.146770 − 1.255100I
a = −0.441704 − 0.465763I
b = −0.347244 − 0.800650I
−2.93174 − 5.03893I 0
u = 1.250100 + 0.201164I
a = −0.136026 − 1.301990I
b = 0.433149 + 1.189940I
2.15430 − 6.74283I 0
u = 1.250100 − 0.201164I
a = −0.136026 + 1.301990I
b = 0.433149 − 1.189940I
2.15430 + 6.74283I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.433149 + 1.189940I
a = −0.046827 + 0.314042I
b = 1.250100 + 0.201164I
−2.15430 + 6.74283I 0
u = 0.433149 − 1.189940I
a = −0.046827 − 0.314042I
b = 1.250100 − 0.201164I
−2.15430 − 6.74283I 0
u = 0.451957 + 1.184490I
a = 0.379669 + 0.514378I
b = 0.725964 − 0.188776I
−1.37563 + 4.28259I 0
u = 0.451957 − 1.184490I
a = 0.379669 − 0.514378I
b = 0.725964 + 0.188776I
−1.37563 − 4.28259I 0
u = −0.455370 + 0.573274I
a = 1.034710 − 0.440478I
b = −0.650441 + 0.418846I
−2.53070 + 4.91173I 0
u = −0.455370 − 0.573274I
a = 1.034710 + 0.440478I
b = −0.650441 − 0.418846I
−2.53070 − 4.91173I 0
u = 0.434473 + 1.195780I
a = −1.31107 − 1.19134I
b = −0.547865 + 1.287550I
−2.29993 + 8.31240I 0
u = 0.434473 − 1.195780I
a = −1.31107 + 1.19134I
b = −0.547865 − 1.287550I
−2.29993 − 8.31240I 0
u = −0.474782 + 1.184610I
a = −0.196482 + 0.181604I
b = −1.128100 + 0.310890I
−4.45442 − 7.05483I 0
u = −0.474782 − 1.184610I
a = −0.196482 − 0.181604I
b = −1.128100 − 0.310890I
−4.45442 + 7.05483I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.204180 + 0.427493I
a = −0.200985 + 1.257090I
b = 0.492848 − 1.054720I
1.31280 + 5.76610I 0
u = −1.204180 − 0.427493I
a = −0.200985 − 1.257090I
b = 0.492848 + 1.054720I
1.31280 − 5.76610I 0
u = 0.717471 + 0.067440I
a = 0.499171 − 0.085517I
b = −0.459887 − 0.102542I
1.92837 + 0.04107I 0
u = 0.717471 − 0.067440I
a = 0.499171 + 0.085517I
b = −0.459887 + 0.102542I
1.92837 − 0.04107I 0
u = 0.133802 + 0.702055I
a = −0.269370 + 0.587036I
b = −0.30749 − 1.71403I
3.84197 + 1.01021I 0
u = 0.133802 − 0.702055I
a = −0.269370 − 0.587036I
b = −0.30749 + 1.71403I
3.84197 − 1.01021I 0
u = −0.832514 + 0.986584I
a = −0.54477 + 1.51782I
b = −0.305013 − 0.742816I
−2.55700 − 3.98943I 0
u = −0.832514 − 0.986584I
a = −0.54477 − 1.51782I
b = −0.305013 + 0.742816I
−2.55700 + 3.98943I 0
u = 0.240365 + 0.655131I
a = 0.28756 + 3.11518I
b = −0.186101 − 1.338880I
3.03308 − 7.46850I 0
u = 0.240365 − 0.655131I
a = 0.28756 − 3.11518I
b = −0.186101 + 1.338880I
3.03308 + 7.46850I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694261 + 0.058031I
a = 0.852789 + 1.068380I
b = −0.670310 − 0.118989I
1.34576 + 2.65416I 0
u = 0.694261 − 0.058031I
a = 0.852789 − 1.068380I
b = −0.670310 + 0.118989I
1.34576 − 2.65416I 0
u = 0.535570 + 1.197750I
a = 0.410032 + 1.176650I
b = 0.599761 − 0.900295I
−1.59135 + 1.88450I 0
u = 0.535570 − 1.197750I
a = 0.410032 − 1.176650I
b = 0.599761 + 0.900295I
−1.59135 − 1.88450I 0
u = −0.005538 + 1.314790I
a = 0.033562 + 0.317961I
b = 0.633855 − 0.501954I
−2.61763 + 2.89255I 0
u = −0.005538 − 1.314790I
a = 0.033562 − 0.317961I
b = 0.633855 + 0.501954I
−2.61763 − 2.89255I 0
u = −0.507492 + 1.213560I
a = 0.029317 − 0.281791I
b = 1.208630 − 0.270590I
−3.3016 − 15.4845I 0
u = −0.507492 − 1.213560I
a = 0.029317 + 0.281791I
b = 1.208630 + 0.270590I
−3.3016 + 15.4845I 0
u = −0.670310 + 0.118989I
a = 0.275481 − 0.950205I
b = 0.694261 − 0.058031I
−1.34576 + 2.65416I 0
u = −0.670310 − 0.118989I
a = 0.275481 + 0.950205I
b = 0.694261 + 0.058031I
−1.34576 − 2.65416I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.659626 + 0.133765I
a = 0.89925 + 1.62106I
b = −0.456995 − 1.006320I
−0.871914 + 0.606568I 0
u = 0.659626 − 0.133765I
a = 0.89925 − 1.62106I
b = −0.456995 + 1.006320I
−0.871914 − 0.606568I 0
u = −0.648449 + 1.161100I
a = −0.97380 + 1.35083I
b = −0.71755 − 1.28381I
1.48839 − 12.59350I 0
u = −0.648449 − 1.161100I
a = −0.97380 − 1.35083I
b = −0.71755 + 1.28381I
1.48839 + 12.59350I 0
u = −0.441025 + 1.259580I
a = −0.78093 + 1.40720I
b = −0.305306 − 0.885243I
−4.46515 − 1.74939I 0
u = −0.441025 − 1.259580I
a = −0.78093 − 1.40720I
b = −0.305306 + 0.885243I
−4.46515 + 1.74939I 0
u = 0.551520 + 1.222040I
a = −0.0117497 − 0.0640070I
b = −0.940943 − 0.473748I
−3.67220 + 6.74825I 0
u = 0.551520 − 1.222040I
a = −0.0117497 + 0.0640070I
b = −0.940943 + 0.473748I
−3.67220 − 6.74825I 0
u = 0.470183 + 1.256570I
a = 0.224627 + 0.332881I
b = −0.437041 − 0.900025I
−1.89033 + 0.72271I 0
u = 0.470183 − 1.256570I
a = 0.224627 − 0.332881I
b = −0.437041 + 0.900025I
−1.89033 − 0.72271I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186101 + 1.338880I
a = 0.245514 − 0.885078I
b = 0.240365 − 0.655131I
−3.03308 − 7.46850I 0
u = −0.186101 − 1.338880I
a = 0.245514 + 0.885078I
b = 0.240365 + 0.655131I
−3.03308 + 7.46850I 0
u = 0.453658 + 1.273930I
a = −0.909141 − 0.753474I
b = −0.611244 + 1.099830I
−2.80969 + 7.03935I 0
u = 0.453658 − 1.273930I
a = −0.909141 + 0.753474I
b = −0.611244 − 1.099830I
−2.80969 − 7.03935I 0
u = −0.423654 + 1.290220I
a = 0.511274 − 1.170730I
b = 0.478952 + 0.712106I
−3.95917 + 6.15252I 0
u = −0.423654 − 1.290220I
a = 0.511274 + 1.170730I
b = 0.478952 − 0.712106I
−3.95917 − 6.15252I 0
u = −0.481157 + 1.273590I
a = 0.733520 − 1.009610I
b = 0.73972 + 1.32017I
−3.15931 − 12.53180I 0
u = −0.481157 − 1.273590I
a = 0.733520 + 1.009610I
b = 0.73972 − 1.32017I
−3.15931 + 12.53180I 0
u = −0.404101 + 1.302230I
a = −0.555826 + 0.886295I
b = −0.404101 − 1.302230I
− 2.14632I 0
u = −0.404101 − 1.302230I
a = −0.555826 − 0.886295I
b = −0.404101 + 1.302230I
2.14632I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.778130 + 1.146260I
a = −0.48859 + 1.63320I
b = −0.334184 − 1.120090I
−0.68932 − 6.27683I 0
u = −0.778130 − 1.146260I
a = −0.48859 − 1.63320I
b = −0.334184 + 1.120090I
−0.68932 + 6.27683I 0
u = −0.547865 + 1.287550I
a = 1.17610 − 1.21708I
b = 0.434473 + 1.195780I
2.29993 − 8.31240I 0
u = −0.547865 − 1.287550I
a = 1.17610 + 1.21708I
b = 0.434473 − 1.195780I
2.29993 + 8.31240I 0
u = 1.31711 + 0.51509I
a = 0.102019 + 1.308380I
b = −0.231325 − 1.078200I
6.50971 + 3.37301I 0
u = 1.31711 − 0.51509I
a = 0.102019 − 1.308380I
b = −0.231325 + 1.078200I
6.50971 − 3.37301I 0
u = −0.64650 + 1.26072I
a = 0.84740 − 1.37280I
b = 0.64921 + 1.32913I
1.42727 − 13.32260I 0
u = −0.64650 − 1.26072I
a = 0.84740 + 1.37280I
b = 0.64921 − 1.32913I
1.42727 + 13.32260I 0
u = −0.09723 + 1.42923I
a = −0.394062 − 0.046651I
b = −0.485058 + 0.675673I
−6.16346 + 1.48072I 0
u = −0.09723 − 1.42923I
a = −0.394062 + 0.046651I
b = −0.485058 − 0.675673I
−6.16346 − 1.48072I 0
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.80753 + 1.19940I
a = 0.236384 + 1.330520I
b = 0.457581 − 1.005390I
−2.18813 + 2.01931I 0
u = 0.80753 − 1.19940I
a = 0.236384 − 1.330520I
b = 0.457581 + 1.005390I
−2.18813 − 2.01931I 0
u = 0.41756 + 1.38513I
a = 0.105789 + 0.186038I
b = −0.221369 − 0.445432I
−2.89620 + 3.52272I 0
u = 0.41756 − 1.38513I
a = 0.105789 − 0.186038I
b = −0.221369 + 0.445432I
−2.89620 − 3.52272I 0
u = 0.02640 + 1.45390I
a = −1.006150 − 0.142374I
b = −0.400012 + 0.781762I
−6.08780 + 1.75437I 0
u = 0.02640 − 1.45390I
a = −1.006150 + 0.142374I
b = −0.400012 − 0.781762I
−6.08780 − 1.75437I 0
u = 0.539677 + 0.075169I
a = 1.25696 − 1.10365I
b = −0.169692 + 1.232880I
4.55571 − 1.39410I 0
u = 0.539677 − 0.075169I
a = 1.25696 + 1.10365I
b = −0.169692 − 1.232880I
4.55571 + 1.39410I 0
u = 0.73676 + 1.26291I
a = 0.84984 + 1.13098I
b = 0.470758 − 1.166590I
3.85707 + 3.73345I 0
u = 0.73676 − 1.26291I
a = 0.84984 − 1.13098I
b = 0.470758 + 1.166590I
3.85707 − 3.73345I 0
23
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.66634 + 1.30774I
a = 0.90056 + 1.28249I
b = 0.66634 − 1.30774I
22.0594I 0
u = 0.66634 − 1.30774I
a = 0.90056 − 1.28249I
b = 0.66634 + 1.30774I
− 22.0594I 0
u = −0.71755 + 1.28381I
a = −0.85336 + 1.27064I
b = −0.648449 − 1.161100I
−1.48839 − 12.59350I 0
u = −0.71755 − 1.28381I
a = −0.85336 − 1.27064I
b = −0.648449 + 1.161100I
−1.48839 + 12.59350I 0
u = 0.64921 + 1.32913I
a = −0.89254 − 1.12251I
b = −0.64650 + 1.26072I
−1.42727 + 13.32260I 0
u = 0.64921 − 1.32913I
a = −0.89254 + 1.12251I
b = −0.64650 − 1.26072I
−1.42727 − 13.32260I 0
u = 0.189220 + 0.478100I
a = 0.668648 + 0.541128I
b = 0.189220 − 0.478100I
1.16154I 0
u = 0.189220 − 0.478100I
a = 0.668648 − 0.541128I
b = 0.189220 + 0.478100I
− 1.16154I 0
u = −0.221369 + 0.445432I
a = −0.204931 + 0.800117I
b = 0.41756 − 1.38513I
2.89620 + 3.52272I 8.89827 + 0.I
u = −0.221369 − 0.445432I
a = −0.204931 − 0.800117I
b = 0.41756 + 1.38513I
2.89620 − 3.52272I 8.89827 + 0.I
24
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.73972 + 1.32017I
a = −0.638784 − 1.194480I
b = −0.481157 + 1.273590I
3.15931 + 12.53180I 0
u = 0.73972 − 1.32017I
a = −0.638784 + 1.194480I
b = −0.481157 − 1.273590I
3.15931 − 12.53180I 0
u = 1.45238 + 0.43315I
a = −0.266576 − 1.232410I
b = 0.231329 + 1.076970I
6.24818 − 5.10916I 0
u = 1.45238 − 0.43315I
a = −0.266576 + 1.232410I
b = 0.231329 − 1.076970I
6.24818 + 5.10916I 0
u = −0.459887 + 0.102542I
a = 0.023560 + 0.292884I
b = 0.717471 − 0.067440I
−1.92837 + 0.04107I −5.86831 + 1.18325I
u = −0.459887 − 0.102542I
a = 0.023560 − 0.292884I
b = 0.717471 + 0.067440I
−1.92837 − 0.04107I −5.86831 − 1.18325I
u = −1.56815 + 0.17899I
a = −0.174589 + 1.246310I
b = 0.048733 − 0.898701I
5.09439 − 4.03171I 0
u = −1.56815 − 0.17899I
a = −0.174589 − 1.246310I
b = 0.048733 + 0.898701I
5.09439 + 4.03171I 0
u = 0.17906 + 1.59970I
a = −0.148067 + 0.178133I
b = −0.249759 − 0.838626I
−4.72681 − 0.80347I 0
u = 0.17906 − 1.59970I
a = −0.148067 − 0.178133I
b = −0.249759 + 0.838626I
−4.72681 + 0.80347I 0
25
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11319 + 1.61653I
a = −0.836418 + 0.532832I
b = −0.297555 − 0.858019I
−5.12076 − 1.34522I 0
u = −0.11319 − 1.61653I
a = −0.836418 − 0.532832I
b = −0.297555 + 0.858019I
−5.12076 + 1.34522I 0
u = 0.14556 + 1.62539I
a = 0.030241 − 0.385776I
b = 0.417538 + 0.847320I
−3.61073 − 9.93097I 0
u = 0.14556 − 1.62539I
a = 0.030241 + 0.385776I
b = 0.417538 − 0.847320I
−3.61073 + 9.93097I 0
u = −0.141926 + 0.323075I
a = 2.45571 − 0.26571I
b = 0.587380 − 0.938448I
1.79288 + 4.49429I −0.07810 − 11.91705I
u = −0.141926 − 0.323075I
a = 2.45571 + 0.26571I
b = 0.587380 + 0.938448I
1.79288 − 4.49429I −0.07810 + 11.91705I
u = −0.30749 + 1.71403I
a = −0.241741 + 0.459945I
b = 0.133802 − 0.702055I
−3.84197 + 1.01021I 0
u = −0.30749 − 1.71403I
a = −0.241741 − 0.459945I
b = 0.133802 + 0.702055I
−3.84197 − 1.01021I 0
26
II. I
u
2
= h8.40 × 10
88
u
59
− 2.76 × 10
88
u
58
+ · · · + 8.73 × 10
87
b − 3.21 ×
10
89
, −6.26 × 10
91
u
59
− 5.43 × 10
91
u
58
+ · · · + 1.55 × 10
91
a − 9.37 ×
10
92
, u
60
+ 21u
58
+ · · · + 40u + 20i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
4.02837u
59
+ 3.49198u
58
+ ··· + 250.773u + 60.2435
−9.61754u
59
+ 3.16536u
58
+ ··· − 303.153u + 36.6995
a
4
=
−5.58916u
59
+ 6.65734u
58
+ ··· − 52.3797u + 96.9431
−9.61754u
59
+ 3.16536u
58
+ ··· − 303.153u + 36.6995
a
2
=
−10.1505u
59
+ 3.66139u
58
+ ··· − 69.6267u + 191.290
0.950423u
59
+ 1.05095u
58
+ ··· + 2.55106u − 13.8649
a
6
=
10.6921u
59
− 1.19824u
58
+ ··· + 270.184u − 63.9013
2.29210u
59
+ 8.34141u
58
+ ··· + 702.735u + 361.114
a
7
=
−u
u
3
+ u
a
11
=
8.45175u
59
− 4.95512u
58
+ ··· + 59.0636u − 180.678
−1.43574u
59
− 6.42234u
58
+ ··· − 317.329u − 213.684
a
9
=
−2.91317u
59
+ 10.6671u
58
+ ··· + 851.073u + 429.926
−1.67991u
59
− 8.66305u
58
+ ··· − 732.948u − 350.826
a
10
=
6.55456u
59
− 9.36272u
58
+ ··· − 228.752u − 362.054
−2.65594u
59
− 3.55605u
58
+ ··· − 243.762u − 120.461
a
3
=
6.16767u
59
− 3.60517u
58
+ ··· − 118.311u − 136.710
−3.68209u
59
+ 8.36937u
58
+ ··· + 444.922u + 286.317
(ii) Obstruction class = 1
(iii) Cusp Shapes = −23.6979u
59
+ 16.4750u
58
+ ··· − 628.013u + 7.17849
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
− 10u
59
+ ··· − 27u + 1
c
2
20(20u
60
+ 154u
58
+ ··· − u + 1)
c
3
20(20u
60
+ 154u
58
+ ··· + u + 1)
c
4
, c
7
u
60
+ 21u
58
+ ··· − 40u + 20
c
5
u
60
− 7u
59
+ ··· + 98u + 17
c
6
u
60
+ 6u
58
+ ··· + 60u + 20
c
8
u
60
+ 10u
59
+ ··· + 27u + 1
c
9
u
60
+ 6u
58
+ ··· − 60u + 20
c
10
u
60
+ 7u
59
+ ··· − 98u + 17
c
11
, c
12
u
60
+ 21u
58
+ ··· + 40u + 20
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
60
− 34y
59
+ ··· + 457y + 1
c
2
, c
3
400(400y
60
+ 6160y
59
+ ··· + 25y + 1)
c
4
, c
7
, c
11
c
12
y
60
+ 42y
59
+ ··· + 13360y + 400
c
5
, c
10
y
60
+ 11y
59
+ ··· − 5898y + 289
c
6
, c
9
y
60
+ 12y
59
+ ··· + 1760y + 400
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131190 + 1.004020I
a = −0.138539 + 0.050844I
b = −1.43489 + 0.25712I
−5.59648 + 3.65482I 0
u = −0.131190 − 1.004020I
a = −0.138539 − 0.050844I
b = −1.43489 − 0.25712I
−5.59648 − 3.65482I 0
u = −0.112128 + 0.964969I
a = 0.736674 − 0.124692I
b = 1.45382 − 0.06539I
−5.42405 − 4.63396I 0. + 10.05646I
u = −0.112128 − 0.964969I
a = 0.736674 + 0.124692I
b = 1.45382 + 0.06539I
−5.42405 + 4.63396I 0. − 10.05646I
u = −0.368132 + 0.824846I
a = −1.82697 + 1.92653I
b = −0.04379 − 1.52117I
5.63343 − 1.62076I 0. + 3.74752I
u = −0.368132 − 0.824846I
a = −1.82697 − 1.92653I
b = −0.04379 + 1.52117I
5.63343 + 1.62076I 0. − 3.74752I
u = −0.292272 + 0.842468I
a = 1.48680 − 1.22320I
b = 0.13469 + 1.64288I
5.30312 − 1.36980I 23.8552 + 3.9437I
u = −0.292272 − 0.842468I
a = 1.48680 + 1.22320I
b = 0.13469 − 1.64288I
5.30312 + 1.36980I 23.8552 − 3.9437I
u = 0.378592 + 1.054480I
a = −0.421580 + 0.136481I
b = 0.615933 + 0.370912I
−2.31061 + 3.49178I 0
u = 0.378592 − 1.054480I
a = −0.421580 − 0.136481I
b = 0.615933 − 0.370912I
−2.31061 − 3.49178I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.671642 + 0.901971I
a = 0.42749 − 2.09202I
b = 0.324123 + 1.104910I
−0.16334 − 6.73234I 0
u = −0.671642 − 0.901971I
a = 0.42749 + 2.09202I
b = 0.324123 − 1.104910I
−0.16334 + 6.73234I 0
u = −0.515101 + 1.023490I
a = 0.845785 − 0.645661I
b = 0.649661 + 1.212210I
2.08919 − 1.71421I 0
u = −0.515101 − 1.023490I
a = 0.845785 + 0.645661I
b = 0.649661 − 1.212210I
2.08919 + 1.71421I 0
u = 0.324123 + 1.104910I
a = −1.211690 − 0.006521I
b = −0.671642 + 0.901971I
0.16334 + 6.73234I 0
u = 0.324123 − 1.104910I
a = −1.211690 + 0.006521I
b = −0.671642 − 0.901971I
0.16334 − 6.73234I 0
u = −1.099140 + 0.358345I
a = −0.312202 + 1.269850I
b = 0.470992 − 1.165410I
2.77087 + 6.10267I 0
u = −1.099140 − 0.358345I
a = −0.312202 − 1.269850I
b = 0.470992 + 1.165410I
2.77087 − 6.10267I 0
u = 0.604618 + 1.003560I
a = −1.06620 − 1.08699I
b = −0.182224 + 0.633368I
−2.35068 + 3.35821I 0
u = 0.604618 − 1.003560I
a = −1.06620 + 1.08699I
b = −0.182224 − 0.633368I
−2.35068 − 3.35821I 0
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220472 + 0.794913I
a = 3.81702 + 1.48670I
b = 0.220472 − 0.794913I
9.36044I 0. − 11.85016I
u = 0.220472 − 0.794913I
a = 3.81702 − 1.48670I
b = 0.220472 + 0.794913I
− 9.36044I 0. + 11.85016I
u = −0.173571 + 0.763541I
a = 0.022820 − 0.893568I
b = −0.24840 + 1.69652I
3.69736 − 1.21321I −5.3217 + 13.6875I
u = −0.173571 − 0.763541I
a = 0.022820 + 0.893568I
b = −0.24840 − 1.69652I
3.69736 + 1.21321I −5.3217 − 13.6875I
u = 0.719717 + 0.278031I
a = 0.129476 + 1.405720I
b = 0.719717 − 0.278031I
− 1.59818I 0. + 6.83850I
u = 0.719717 − 0.278031I
a = 0.129476 − 1.405720I
b = 0.719717 + 0.278031I
1.59818I 0. − 6.83850I
u = 0.470992 + 1.165410I
a = 0.020481 − 0.173598I
b = −1.099140 − 0.358345I
−2.77087 + 6.10267I 0
u = 0.470992 − 1.165410I
a = 0.020481 + 0.173598I
b = −1.099140 + 0.358345I
−2.77087 − 6.10267I 0
u = 0.296145 + 1.232840I
a = 1.36869 + 0.98077I
b = 0.296145 − 1.232840I
9.41326I 0
u = 0.296145 − 1.232840I
a = 1.36869 − 0.98077I
b = 0.296145 + 1.232840I
− 9.41326I 0
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615933 + 0.370912I
a = 0.264938 − 0.804155I
b = 0.378592 + 1.054480I
2.31061 − 3.49178I 2.58790 + 4.01633I
u = 0.615933 − 0.370912I
a = 0.264938 + 0.804155I
b = 0.378592 − 1.054480I
2.31061 + 3.49178I 2.58790 − 4.01633I
u = −0.007654 + 0.709640I
a = 1.76736 + 1.97597I
b = −0.043743 − 1.367470I
2.67190 − 8.20442I 0.58399 + 9.24559I
u = −0.007654 − 0.709640I
a = 1.76736 − 1.97597I
b = −0.043743 + 1.367470I
2.67190 + 8.20442I 0.58399 − 9.24559I
u = −0.182224 + 0.633368I
a = 2.10114 − 1.07750I
b = 0.604618 + 1.003560I
2.35068 − 3.35821I 0.72073 + 1.67334I
u = −0.182224 − 0.633368I
a = 2.10114 + 1.07750I
b = 0.604618 − 1.003560I
2.35068 + 3.35821I 0.72073 − 1.67334I
u = 0.415613 + 1.284520I
a = −0.552164 − 0.122726I
b = −0.029330 + 0.485040I
−2.63975 + 3.91996I 0
u = 0.415613 − 1.284520I
a = −0.552164 + 0.122726I
b = −0.029330 − 0.485040I
−2.63975 − 3.91996I 0
u = 0.071503 + 1.359220I
a = −0.560386 − 0.397252I
b = −0.327373 + 0.283384I
−5.47005 + 0.45372I 0
u = 0.071503 − 1.359220I
a = −0.560386 + 0.397252I
b = −0.327373 − 0.283384I
−5.47005 − 0.45372I 0
33
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.043743 + 1.367470I
a = 0.879746 − 0.353566I
b = −0.007654 − 0.709640I
−2.67190 − 8.20442I 0
u = −0.043743 − 1.367470I
a = 0.879746 + 0.353566I
b = −0.007654 + 0.709640I
−2.67190 + 8.20442I 0
u = 0.649661 + 1.212210I
a = −0.330143 − 1.290740I
b = −0.515101 + 1.023490I
−2.08919 + 1.71421I 0
u = 0.649661 − 1.212210I
a = −0.330143 + 1.290740I
b = −0.515101 − 1.023490I
−2.08919 − 1.71421I 0
u = −0.675294 + 1.242130I
a = −0.83231 + 1.25712I
b = −0.675294 − 1.242130I
− 12.4379I 0
u = −0.675294 − 1.242130I
a = −0.83231 − 1.25712I
b = −0.675294 + 1.242130I
12.4379I 0
u = 1.45382 + 0.06539I
a = 0.10861 + 1.46371I
b = −0.112128 − 0.964969I
5.42405 − 4.63396I 0
u = 1.45382 − 0.06539I
a = 0.10861 − 1.46371I
b = −0.112128 + 0.964969I
5.42405 + 4.63396I 0
u = −1.43489 + 0.25712I
a = 0.126630 − 1.106420I
b = −0.131190 + 1.004020I
5.59648 − 3.65482I 0
u = −1.43489 − 0.25712I
a = 0.126630 + 1.106420I
b = −0.131190 − 1.004020I
5.59648 + 3.65482I 0
34
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029330 + 0.485040I
a = 1.13719 − 1.52653I
b = 0.415613 + 1.284520I
2.63975 − 3.91996I 0.94596 + 7.77730I
u = −0.029330 − 0.485040I
a = 1.13719 + 1.52653I
b = 0.415613 − 1.284520I
2.63975 + 3.91996I 0.94596 − 7.77730I
u = −0.04379 + 1.52117I
a = −1.104890 + 0.264741I
b = −0.368132 − 0.824846I
−5.63343 − 1.62076I 0
u = −0.04379 − 1.52117I
a = −1.104890 − 0.264741I
b = −0.368132 + 0.824846I
−5.63343 + 1.62076I 0
u = −0.327373 + 0.283384I
a = 1.99564 − 1.98327I
b = 0.071503 + 1.359220I
5.47005 − 0.45372I 7.45689 + 1.65001I
u = −0.327373 − 0.283384I
a = 1.99564 + 1.98327I
b = 0.071503 − 1.359220I
5.47005 + 0.45372I 7.45689 − 1.65001I
u = 0.13469 + 1.64288I
a = −0.710767 − 0.561949I
b = −0.292272 + 0.842468I
−5.30312 + 1.36980I 0
u = 0.13469 − 1.64288I
a = −0.710767 + 0.561949I
b = −0.292272 − 0.842468I
−5.30312 − 1.36980I 0
u = −0.24840 + 1.69652I
a = 0.131326 − 0.357528I
b = −0.173571 + 0.763541I
−3.69736 + 1.21321I 0
u = −0.24840 − 1.69652I
a = 0.131326 + 0.357528I
b = −0.173571 − 0.763541I
−3.69736 − 1.21321I 0
35
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
60
− 10u
59
+ ··· − 27u + 1)
· (u
218
+ 7u
217
+ ··· − 325966059u + 13035439)
c
2
120(20u
60
+ 154u
58
+ ··· − u + 1)(6u
218
− 6u
217
+ ··· − 603u + 1721)
c
3
120(20u
60
+ 154u
58
+ ··· + u + 1)(6u
218
+ 6u
217
+ ··· + 603u + 1721)
c
4
(u
60
+ 21u
58
+ ··· − 40u + 20)
· (u
218
+ u
217
+ ··· − 1084332u + 800958)
c
5
(u
60
− 7u
59
+ ··· + 98u + 17)
· (u
218
− 6u
217
+ ··· − 4497810u + 159275)
c
6
(u
60
+ 6u
58
+ ··· + 60u + 20)(u
218
− 7u
217
+ ··· + 5706u + 1086)
c
7
(u
60
+ 21u
58
+ ··· − 40u + 20)
· (u
218
− u
217
+ ··· + 1084332u + 800958)
c
8
(u
60
+ 10u
59
+ ··· + 27u + 1)
· (u
218
− 7u
217
+ ··· + 325966059u + 13035439)
c
9
(u
60
+ 6u
58
+ ··· − 60u + 20)(u
218
+ 7u
217
+ ··· − 5706u + 1086)
c
10
(u
60
+ 7u
59
+ ··· − 98u + 17)
· (u
218
+ 6u
217
+ ··· + 4497810u + 159275)
c
11
(u
60
+ 21u
58
+ ··· + 40u + 20)
· (u
218
+ u
217
+ ··· − 1084332u + 800958)
c
12
(u
60
+ 21u
58
+ ··· + 40u + 20)
· (u
218
− u
217
+ ··· + 1084332u + 800958)
36
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
60
− 34y
59
+ ··· + 457y + 1)
· (y
218
− 27y
217
+ ··· − 75149030070299023y + 169922669922721)
c
2
, c
3
14400(400y
60
+ 6160y
59
+ ··· + 25y + 1)
· (36y
218
+ 228y
217
+ ··· − 218634597y + 2961841)
c
4
, c
7
, c
11
c
12
(y
60
+ 42y
59
+ ··· + 13360y + 400)
· (y
218
+ 127y
217
+ ··· + 37988843650536y + 641533717764)
c
5
, c
10
(y
60
+ 11y
59
+ ··· − 5898y + 289)
· (y
218
− 26y
217
+ ··· − 2357094900150y + 25368525625)
c
6
, c
9
(y
60
+ 12y
59
+ ··· + 1760y + 400)
· (y
218
− 7y
217
+ ··· − 16168524y + 1179396)
37
