12n
0415
(K12n
0415
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 9 5 12 7 4 9 8
Solving Sequence
5,7 8,10
4 11 3 9 12 6 2 1
c
7
c
4
c
10
c
3
c
9
c
11
c
6
c
2
c
1
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.62328 × 10
249
u
73
− 7.69335 × 10
248
u
72
+ ··· + 6.16724 × 10
251
b + 2.89562 × 10
253
,
3.89167 × 10
253
u
73
+ 3.50798 × 10
253
u
72
+ ··· + 1.76568 × 10
255
a + 6.42586 × 10
256
,
u
74
− 18u
72
+ ··· + 13014u − 2863i
I
u
2
= h1461328095574788u
22
+ 4128500756671431u
21
+ ··· + 2694132033228847b + 3183360713386177,
1596568487678737u
22
+ 4700269669705836u
21
+ ··· + 2694132033228847a + 3243990326400528,
u
23
+ 3u
22
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 97 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
= h2.62 × 10
249
u
73
− 7.69 × 10
248
u
72
+ · · · + 6.17 × 10
251
b + 2.90 ×
10
253
, 3.89 × 10
253
u
73
+ 3.51 × 10
253
u
72
+ · · · + 1.77 × 10
255
a + 6.43 ×
10
256
, u
74
− 18u
72
+ · · · + 13014u − 2863i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−0.0220406u
73
− 0.0198675u
72
+ ··· + 220.643u − 36.3930
−0.00425356u
73
+ 0.00124745u
72
+ ··· + 110.198u − 46.9517
a
4
=
−0.0000705915u
73
− 0.00699554u
72
+ ··· − 79.9649u + 50.6943
−0.00337096u
73
− 0.00295357u
72
+ ··· + 37.0277u − 13.3009
a
11
=
0.0523964u
73
+ 0.0340422u
72
+ ··· − 668.716u + 180.347
0.00944346u
73
− 0.00258887u
72
+ ··· − 230.912u + 91.9988
a
3
=
0.00494268u
73
− 0.00257029u
72
+ ··· − 133.775u + 57.4216
−0.000435248u
73
− 0.00119965u
72
+ ··· − 6.20955u − 0.631443
a
9
=
−0.0262941u
73
− 0.0186201u
72
+ ··· + 330.841u − 83.3447
−0.00425356u
73
+ 0.00124745u
72
+ ··· + 110.198u − 46.9517
a
12
=
0.0478425u
73
+ 0.0317582u
72
+ ··· − 609.789u + 166.141
0.00647358u
73
− 0.00178615u
72
+ ··· − 156.506u + 66.0267
a
6
=
−0.0105705u
73
− 0.00873866u
72
+ ··· + 119.067u − 31.9627
−0.00592470u
73
− 0.00536770u
72
+ ··· + 55.6302u − 8.52990
a
2
=
0.00824933u
73
+ 0.00495099u
72
+ ··· − 115.733u + 38.0504
0.00567037u
73
+ 0.00516383u
72
+ ··· − 56.2245u + 5.68267
a
1
=
−0.0375306u
73
− 0.0237185u
72
+ ··· + 489.967u − 141.244
−0.00173001u
73
+ 0.00381214u
72
+ ··· + 81.4010u − 43.0091
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0209656u
73
+ 0.000371330u
72
+ ··· − 411.018u + 116.524
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 24u
73
+ ··· + 43970u + 2209
c
2
, c
5
u
74
+ 4u
73
+ ··· + 52u + 47
c
3
u
74
+ 29u
72
+ ··· − 70400u − 24287
c
4
, c
10
u
74
+ 3u
73
+ ··· − 43360u − 4517
c
6
, c
9
u
74
+ 3u
73
+ ··· − 132u + 2447
c
7
u
74
− 18u
72
+ ··· + 13014u − 2863
c
8
, c
11
, c
12
u
74
+ 4u
73
+ ··· − 148u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 64y
73
+ ··· − 202684506y + 4879681
c
2
, c
5
y
74
− 24y
73
+ ··· − 43970y + 2209
c
3
y
74
+ 58y
73
+ ··· − 49646717274y + 589858369
c
4
, c
10
y
74
+ 43y
73
+ ··· + 78391260y + 20403289
c
6
, c
9
y
74
− 39y
73
+ ··· − 103437432y + 5987809
c
7
y
74
− 36y
73
+ ··· − 172879960y + 8196769
c
8
, c
11
, c
12
y
74
+ 26y
73
+ ··· − 6546y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716939 + 0.702052I
a = 0.30263 − 1.41247I
b = −1.177540 + 0.285975I
−1.91366 + 4.24234I 0
u = −0.716939 − 0.702052I
a = 0.30263 + 1.41247I
b = −1.177540 − 0.285975I
−1.91366 − 4.24234I 0
u = 0.816631 + 0.612281I
a = −0.145660 − 1.130310I
b = −0.396070 + 1.216810I
4.09032 − 3.11910I 0
u = 0.816631 − 0.612281I
a = −0.145660 + 1.130310I
b = −0.396070 − 1.216810I
4.09032 + 3.11910I 0
u = −0.725639 + 0.606653I
a = −1.35528 − 0.64131I
b = −0.947841 + 0.475507I
4.37251 + 2.51666I 0. − 3.92703I
u = −0.725639 − 0.606653I
a = −1.35528 + 0.64131I
b = −0.947841 − 0.475507I
4.37251 − 2.51666I 0. + 3.92703I
u = −0.852419 + 0.625156I
a = 1.304660 − 0.001023I
b = 0.820732 − 0.436023I
3.15839 − 4.36525I 0
u = −0.852419 − 0.625156I
a = 1.304660 + 0.001023I
b = 0.820732 + 0.436023I
3.15839 + 4.36525I 0
u = −0.673467 + 0.818072I
a = 1.06661 − 1.08020I
b = −0.880323 + 0.113571I
−3.27559 + 3.44834I 0
u = −0.673467 − 0.818072I
a = 1.06661 + 1.08020I
b = −0.880323 − 0.113571I
−3.27559 − 3.44834I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.06373
a = 1.17437
b = 0.718671
−0.362734 −17.0640
u = −0.903098 + 0.592548I
a = −0.266612 + 0.712330I
b = 1.281040 − 0.243461I
−2.73174 + 0.73218I 0
u = −0.903098 − 0.592548I
a = −0.266612 − 0.712330I
b = 1.281040 + 0.243461I
−2.73174 − 0.73218I 0
u = 0.985502 + 0.449873I
a = −0.196631 − 0.931982I
b = 1.55766 + 0.61167I
−6.28650 − 4.67409I 0
u = 0.985502 − 0.449873I
a = −0.196631 + 0.931982I
b = 1.55766 − 0.61167I
−6.28650 + 4.67409I 0
u = −0.640773 + 0.884634I
a = −0.861652 + 0.852553I
b = 1.057100 − 0.700305I
−5.13856 + 5.00397I 0
u = −0.640773 − 0.884634I
a = −0.861652 − 0.852553I
b = 1.057100 + 0.700305I
−5.13856 − 5.00397I 0
u = −0.948790 + 0.566130I
a = −0.138082 + 1.073610I
b = −0.42227 − 1.37744I
2.82069 + 9.00069I 0
u = −0.948790 − 0.566130I
a = −0.138082 − 1.073610I
b = −0.42227 + 1.37744I
2.82069 − 9.00069I 0
u = 0.707873 + 0.524027I
a = −0.579354 − 0.901201I
b = 1.55178 − 0.11686I
−6.09027 + 3.52399I −9.61885 − 4.91747I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707873 − 0.524027I
a = −0.579354 + 0.901201I
b = 1.55178 + 0.11686I
−6.09027 − 3.52399I −9.61885 + 4.91747I
u = 0.923459 + 0.638543I
a = −1.161220 + 0.518619I
b = −1.000280 − 0.498046I
3.46828 − 9.04581I 0
u = 0.923459 − 0.638543I
a = −1.161220 − 0.518619I
b = −1.000280 + 0.498046I
3.46828 + 9.04581I 0
u = 0.987910 + 0.559553I
a = 1.248430 − 0.014833I
b = 0.823741 + 0.340152I
3.57201 − 1.47959I 0
u = 0.987910 − 0.559553I
a = 1.248430 + 0.014833I
b = 0.823741 − 0.340152I
3.57201 + 1.47959I 0
u = 0.877611 + 0.726426I
a = 0.042974 + 0.803893I
b = 0.695871 − 1.040800I
3.64324 + 3.84902I 0
u = 0.877611 − 0.726426I
a = 0.042974 − 0.803893I
b = 0.695871 + 1.040800I
3.64324 − 3.84902I 0
u = 1.103270 + 0.336547I
a = −0.103428 − 1.230930I
b = 1.18743 + 0.79431I
−5.63165 − 5.26461I 0
u = 1.103270 − 0.336547I
a = −0.103428 + 1.230930I
b = 1.18743 − 0.79431I
−5.63165 + 5.26461I 0
u = −0.796570 + 0.190576I
a = 0.010188 + 1.017090I
b = 0.211582 − 1.283020I
−1.99263 + 2.54885I −10.22170 − 5.40906I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796570 − 0.190576I
a = 0.010188 − 1.017090I
b = 0.211582 + 1.283020I
−1.99263 − 2.54885I −10.22170 + 5.40906I
u = −1.066590 + 0.569316I
a = 0.012147 − 0.814089I
b = 0.702734 + 1.086420I
3.27734 + 2.13042I 0
u = −1.066590 − 0.569316I
a = 0.012147 + 0.814089I
b = 0.702734 − 1.086420I
3.27734 − 2.13042I 0
u = 0.727771 + 0.217403I
a = −0.99187 + 1.55253I
b = −1.219090 + 0.099908I
−5.53125 + 1.75381I −18.7515 + 4.1564I
u = 0.727771 − 0.217403I
a = −0.99187 − 1.55253I
b = −1.219090 − 0.099908I
−5.53125 − 1.75381I −18.7515 − 4.1564I
u = −0.745350
a = 0.431663
b = 0.526516
−1.12204 −10.0080
u = 1.094760 + 0.647316I
a = 0.029119 + 1.101910I
b = −1.44938 − 0.46309I
−7.43280 − 8.42443I 0
u = 1.094760 − 0.647316I
a = 0.029119 − 1.101910I
b = −1.44938 + 0.46309I
−7.43280 + 8.42443I 0
u = −1.151840 + 0.553031I
a = −0.327823 + 0.995375I
b = 1.101040 − 0.883548I
−5.16306 + 2.04636I 0
u = −1.151840 − 0.553031I
a = −0.327823 − 0.995375I
b = 1.101040 + 0.883548I
−5.16306 − 2.04636I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548937 + 0.402419I
a = 1.005520 − 0.125825I
b = 0.161005 − 0.487205I
−1.59696 + 0.08613I −7.31610 − 0.28304I
u = −0.548937 − 0.402419I
a = 1.005520 + 0.125825I
b = 0.161005 + 0.487205I
−1.59696 − 0.08613I −7.31610 + 0.28304I
u = 0.587757 + 0.294439I
a = 0.78373 + 2.38110I
b = −0.958294 − 0.111877I
−3.68519 + 2.60434I −6.57430 − 4.30794I
u = 0.587757 − 0.294439I
a = 0.78373 − 2.38110I
b = −0.958294 + 0.111877I
−3.68519 − 2.60434I −6.57430 + 4.30794I
u = 0.349150 + 1.296500I
a = 0.580015 − 0.365543I
b = −0.649378 + 0.576102I
5.27936 + 1.69380I 0
u = 0.349150 − 1.296500I
a = 0.580015 + 0.365543I
b = −0.649378 − 0.576102I
5.27936 − 1.69380I 0
u = −0.582914 + 1.254360I
a = 0.522915 + 0.267349I
b = −0.611014 − 0.628501I
4.67633 + 4.65211I 0
u = −0.582914 − 1.254360I
a = 0.522915 − 0.267349I
b = −0.611014 + 0.628501I
4.67633 − 4.65211I 0
u = 0.512431 + 0.309854I
a = −1.07215 − 2.01686I
b = 1.167200 + 0.731529I
−5.26261 − 1.53830I −8.07293 − 0.86476I
u = 0.512431 − 0.309854I
a = −1.07215 + 2.01686I
b = 1.167200 − 0.731529I
−5.26261 + 1.53830I −8.07293 + 0.86476I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167408 + 0.549877I
a = 0.176866 + 0.792527I
b = 0.612175 − 0.774514I
−0.94767 + 2.37842I 1.45207 − 6.62770I
u = −0.167408 − 0.549877I
a = 0.176866 − 0.792527I
b = 0.612175 + 0.774514I
−0.94767 − 2.37842I 1.45207 + 6.62770I
u = 1.45999 + 0.14673I
a = −0.257995 + 0.912915I
b = −0.978818 − 0.301296I
−9.34243 − 0.54949I 0
u = 1.45999 − 0.14673I
a = −0.257995 − 0.912915I
b = −0.978818 + 0.301296I
−9.34243 + 0.54949I 0
u = 0.357638 + 0.335061I
a = 0.47848 − 1.58337I
b = −0.124566 + 0.560482I
1.26391 − 1.01316I 4.15434 + 2.93912I
u = 0.357638 − 0.335061I
a = 0.47848 + 1.58337I
b = −0.124566 − 0.560482I
1.26391 + 1.01316I 4.15434 − 2.93912I
u = −1.33023 + 0.79257I
a = 0.103633 + 0.876670I
b = 1.130880 − 0.742570I
2.09763 + 2.66972I 0
u = −1.33023 − 0.79257I
a = 0.103633 − 0.876670I
b = 1.130880 + 0.742570I
2.09763 − 2.66972I 0
u = 1.43130 + 0.70692I
a = 0.126806 − 0.913430I
b = 1.151750 + 0.760760I
1.66250 − 8.85630I 0
u = 1.43130 − 0.70692I
a = 0.126806 + 0.913430I
b = 1.151750 − 0.760760I
1.66250 + 8.85630I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32165 + 0.93185I
a = 0.107037 − 0.955241I
b = −1.30349 + 0.69335I
1.08526 + 9.88947I 0
u = −1.32165 − 0.93185I
a = 0.107037 + 0.955241I
b = −1.30349 − 0.69335I
1.08526 − 9.88947I 0
u = 1.63837 + 0.07026I
a = −0.334265 + 0.455015I
b = −0.981857 − 0.453814I
−7.20676 − 4.22563I 0
u = 1.63837 − 0.07026I
a = −0.334265 − 0.455015I
b = −0.981857 + 0.453814I
−7.20676 + 4.22563I 0
u = 1.43230 + 0.87405I
a = 0.073145 + 0.937596I
b = −1.33985 − 0.75216I
−0.2552 − 16.3943I 0
u = 1.43230 − 0.87405I
a = 0.073145 − 0.937596I
b = −1.33985 + 0.75216I
−0.2552 + 16.3943I 0
u = −0.75225 + 1.53216I
a = −0.575876 + 0.020768I
b = 0.927838 + 0.313898I
3.25869 − 1.35968I 0
u = −0.75225 − 1.53216I
a = −0.575876 − 0.020768I
b = 0.927838 − 0.313898I
3.25869 + 1.35968I 0
u = 0.53309 + 1.67694I
a = −0.606198 + 0.062510I
b = 0.913932 − 0.375862I
2.90226 + 7.73992I 0
u = 0.53309 − 1.67694I
a = −0.606198 − 0.062510I
b = 0.913932 + 0.375862I
2.90226 − 7.73992I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.78852 + 0.02547I
a = −0.125774 − 0.413957I
b = −0.890367 + 0.466218I
−6.84616 − 0.38474I 0
u = −1.78852 − 0.02547I
a = −0.125774 + 0.413957I
b = −0.890367 − 0.466218I
−6.84616 + 0.38474I 0
u = −1.71798 + 0.50060I
a = 0.105225 − 0.669355I
b = −0.847647 + 0.313678I
−8.79128 + 2.04137I 0
u = −1.71798 − 0.50060I
a = 0.105225 + 0.669355I
b = −0.847647 − 0.313678I
−8.79128 − 2.04137I 0
12
II.
I
u
2
= h1.46 × 10
15
u
22
+ 4.13 × 10
15
u
21
+ · · · + 2.69 × 10
15
b + 3.18 × 10
15
, 1.60 ×
10
15
u
22
+4.70×10
15
u
21
+· · ·+2.69×10
15
a+3.24×10
15
, u
23
+3u
22
+· · ·+6u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−0.592610u
22
− 1.74463u
21
+ ··· − 6.32240u − 1.20409
−0.542411u
22
− 1.53240u
21
+ ··· − 5.91499u − 1.18159
a
4
=
−0.117334u
22
− 0.263754u
21
+ ··· + 0.501536u − 0.270027
0.102622u
22
+ 0.248072u
21
+ ··· − 0.0954132u − 0.532814
a
11
=
−0.270027u
22
− 0.692746u
21
+ ··· − 6.61102u − 1.12170
−0.623415u
22
− 1.71095u
21
+ ··· − 6.71583u − 1.17090
a
3
=
−0.0420606u
22
− 0.0511738u
21
+ ··· + 0.818276u − 0.714593
0.100823u
22
+ 0.342981u
21
+ ··· − 0.0912474u − 0.519574
a
9
=
−1.13502u
22
− 3.27704u
21
+ ··· − 12.2374u − 2.38569
−0.542411u
22
− 1.53240u
21
+ ··· − 5.91499u − 1.18159
a
12
=
−0.210231u
22
− 0.649178u
21
+ ··· − 5.46247u − 3.01907
−0.563620u
22
− 1.66738u
21
+ ··· − 5.56728u − 2.06828
a
6
=
1.05719u
22
+ 3.25881u
21
+ ··· + 9.50823u + 5.19583
0.524378u
22
+ 1.55775u
21
+ ··· + 4.33437u + 2.09435
a
2
=
−1.01297u
22
− 3.07951u
21
+ ··· − 9.11724u − 5.56190
−0.415388u
22
− 1.17628u
21
+ ··· − 4.24093u − 2.41225
a
1
=
−0.714593u
22
− 2.10172u
21
+ ··· − 11.3509u − 5.10583
−0.579370u
22
− 1.70311u
21
+ ··· − 5.42619u − 2.12882
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
2841804052879228
2694132033228847
u
22
+
7206898421736419
2694132033228847
u
21
+ ··· +
44791864499482061
2694132033228847
u −
4765268002334834
2694132033228847
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 11u
22
+ ··· + 16u − 1
c
2
u
23
+ u
22
+ ··· + 8u
2
− 1
c
3
u
23
− u
22
+ ··· + 4u − 1
c
4
u
23
+ 10u
21
+ ··· − 15u
2
− 1
c
5
u
23
− u
22
+ ··· − 8u
2
+ 1
c
6
u
23
− 4u
22
+ ··· + 4u − 1
c
7
u
23
+ 3u
22
+ ··· + 6u + 1
c
8
u
23
+ 3u
22
+ ··· + 10u
2
+ 1
c
9
u
23
+ 4u
22
+ ··· + 4u + 1
c
10
u
23
+ 10u
21
+ ··· + 15u
2
+ 1
c
11
, c
12
u
23
− 3u
22
+ ··· − 10u
2
− 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 13y
22
+ ··· + 24y −1
c
2
, c
5
y
23
− 11y
22
+ ··· + 16y −1
c
3
y
23
− 9y
22
+ ··· − 16y −1
c
4
, c
10
y
23
+ 20y
22
+ ··· − 30y −1
c
6
, c
9
y
23
− 14y
22
+ ··· + 2y −1
c
7
y
23
− 19y
22
+ ··· + 18y −1
c
8
, c
11
, c
12
y
23
+ 19y
22
+ ··· − 20y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097082 + 0.991659I
a = 0.444791 − 0.593937I
b = 0.149236 − 0.531911I
3.82576 + 6.25542I −3.51359 − 5.00794I
u = 0.097082 − 0.991659I
a = 0.444791 + 0.593937I
b = 0.149236 + 0.531911I
3.82576 − 6.25542I −3.51359 + 5.00794I
u = −0.397411 + 0.909180I
a = 0.535050 + 0.552383I
b = 0.252207 + 0.450516I
4.33752 − 0.13788I −1.94233 − 0.17804I
u = −0.397411 − 0.909180I
a = 0.535050 − 0.552383I
b = 0.252207 − 0.450516I
4.33752 + 0.13788I −1.94233 + 0.17804I
u = −0.961508
a = 1.04087
b = 0.520017
0.0445346 3.78180
u = 0.872955 + 0.391799I
a = −0.323038 − 1.284040I
b = 1.55292 + 0.84258I
−6.98893 − 5.61250I −13.5942 + 7.8509I
u = 0.872955 − 0.391799I
a = −0.323038 + 1.284040I
b = 1.55292 − 0.84258I
−6.98893 + 5.61250I −13.5942 − 7.8509I
u = −0.977976 + 0.506225I
a = −0.445016 + 1.128470I
b = 1.07432 − 0.99007I
−5.53290 + 2.77009I −10.96973 − 6.70873I
u = −0.977976 − 0.506225I
a = −0.445016 − 1.128470I
b = 1.07432 + 0.99007I
−5.53290 − 2.77009I −10.96973 + 6.70873I
u = −0.569838 + 0.674226I
a = −1.15917 + 1.45654I
b = 0.980600 − 0.294865I
−3.04705 + 4.07672I −5.80689 − 10.51567I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569838 − 0.674226I
a = −1.15917 − 1.45654I
b = 0.980600 + 0.294865I
−3.04705 − 4.07672I −5.80689 + 10.51567I
u = 0.568784 + 0.293534I
a = 0.16725 − 2.08764I
b = 1.287630 − 0.060312I
−5.24112 + 2.07673I −6.26908 − 7.23881I
u = 0.568784 − 0.293534I
a = 0.16725 + 2.08764I
b = 1.287630 + 0.060312I
−5.24112 − 2.07673I −6.26908 + 7.23881I
u = 1.42807 + 0.41817I
a = 0.000706 + 0.731151I
b = −1.148590 + 0.004763I
−8.86000 + 1.96377I −10.83420 − 2.39028I
u = 1.42807 − 0.41817I
a = 0.000706 − 0.731151I
b = −1.148590 − 0.004763I
−8.86000 − 1.96377I −10.83420 + 2.39028I
u = 1.48753 + 0.16424I
a = −0.075659 + 0.763221I
b = −1.199090 − 0.600094I
−9.27667 − 4.28031I −11.14224 + 4.83692I
u = 1.48753 − 0.16424I
a = −0.075659 − 0.763221I
b = −1.199090 + 0.600094I
−9.27667 + 4.28031I −11.14224 − 4.83692I
u = −1.66536 + 0.15472I
a = −0.102078 − 0.714089I
b = −0.841750 + 0.536468I
−7.98540 + 0.49241I −7.97071 − 0.07690I
u = −1.66536 − 0.15472I
a = −0.102078 + 0.714089I
b = −0.841750 − 0.536468I
−7.98540 − 0.49241I −7.97071 + 0.07690I
u = −1.62734 + 0.46856I
a = −0.023907 − 0.681032I
b = −0.856175 + 0.112603I
−7.54516 + 2.39900I −7.00245 − 3.48589I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62734 − 0.46856I
a = −0.023907 + 0.681032I
b = −0.856175 − 0.112603I
−7.54516 − 2.39900I −7.00245 + 3.48589I
u = −0.235742 + 0.140970I
a = 0.460643 − 0.882128I
b = 0.488678 − 0.957391I
−1.41139 + 1.89306I −5.84545 + 1.64063I
u = −0.235742 − 0.140970I
a = 0.460643 + 0.882128I
b = 0.488678 + 0.957391I
−1.41139 − 1.89306I −5.84545 − 1.64063I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 11u
22
+ ··· + 16u − 1)(u
74
+ 24u
73
+ ··· + 43970u + 2209)
c
2
(u
23
+ u
22
+ ··· + 8u
2
− 1)(u
74
+ 4u
73
+ ··· + 52u + 47)
c
3
(u
23
− u
22
+ ··· + 4u − 1)(u
74
+ 29u
72
+ ··· − 70400u − 24287)
c
4
(u
23
+ 10u
21
+ ··· − 15u
2
− 1)(u
74
+ 3u
73
+ ··· − 43360u − 4517)
c
5
(u
23
− u
22
+ ··· − 8u
2
+ 1)(u
74
+ 4u
73
+ ··· + 52u + 47)
c
6
(u
23
− 4u
22
+ ··· + 4u − 1)(u
74
+ 3u
73
+ ··· − 132u + 2447)
c
7
(u
23
+ 3u
22
+ ··· + 6u + 1)(u
74
− 18u
72
+ ··· + 13014u − 2863)
c
8
(u
23
+ 3u
22
+ ··· + 10u
2
+ 1)(u
74
+ 4u
73
+ ··· − 148u − 7)
c
9
(u
23
+ 4u
22
+ ··· + 4u + 1)(u
74
+ 3u
73
+ ··· − 132u + 2447)
c
10
(u
23
+ 10u
21
+ ··· + 15u
2
+ 1)(u
74
+ 3u
73
+ ··· − 43360u − 4517)
c
11
, c
12
(u
23
− 3u
22
+ ··· − 10u
2
− 1)(u
74
+ 4u
73
+ ··· − 148u − 7)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 13y
22
+ ··· + 24y −1)
· (y
74
+ 64y
73
+ ··· − 202684506y + 4879681)
c
2
, c
5
(y
23
− 11y
22
+ ··· + 16y −1)(y
74
− 24y
73
+ ··· − 43970y + 2209)
c
3
(y
23
− 9y
22
+ ··· − 16y −1)
· (y
74
+ 58y
73
+ ··· − 49646717274y + 589858369)
c
4
, c
10
(y
23
+ 20y
22
+ ··· − 30y −1)
· (y
74
+ 43y
73
+ ··· + 78391260y + 20403289)
c
6
, c
9
(y
23
− 14y
22
+ ··· + 2y −1)
· (y
74
− 39y
73
+ ··· − 103437432y + 5987809)
c
7
(y
23
− 19y
22
+ ··· + 18y −1)
· (y
74
− 36y
73
+ ··· − 172879960y + 8196769)
c
8
, c
11
, c
12
(y
23
+ 19y
22
+ ··· − 20y −1)(y
74
+ 26y
73
+ ··· − 6546y + 49)
20
