12n
0727
(K12n
0727
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 11 1 12 5 4 2 3 7
Solving Sequence
1,4 2,9
5 10 11 6 7 3 12 8
c
1
c
4
c
9
c
10
c
5
c
6
c
3
c
12
c
7
c
2
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.94440 × 10
300
u
70
+ 2.53784 × 10
301
u
69
+ ··· + 3.21640 × 10
303
b + 1.14997 × 10
304
,
− 1.18258 × 10
304
u
70
+ 7.69862 × 10
304
u
69
+ ··· + 3.29038 × 10
306
a + 3.83134 × 10
307
,
u
71
− 6u
70
+ ··· − 4114u − 1331i
I
u
2
= h1.81727 × 10
28
u
25
− 2.58039 × 10
29
u
24
+ ··· + 1.41382 × 10
28
b − 4.03240 × 10
29
,
7.46795 × 10
29
u
25
− 1.06112 × 10
31
u
24
+ ··· + 2.40350 × 10
29
a − 1.63428 × 10
31
,
u
26
− 15u
25
+ ··· − 101u + 17i
* 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
= h−3.94 × 10
300
u
70
+ 2.54 × 10
301
u
69
+ · · · + 3.22 × 10
303
b + 1.15 ×
10
304
, −1.18 × 10
304
u
70
+ 7.70 × 10
304
u
69
+ · · · + 3.29 × 10
306
a + 3.83 ×
10
307
, u
71
− 6u
70
+ · · · − 4114u − 1331i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
0.00359405u
70
− 0.0233974u
69
+ ··· − 10.2765u − 11.6441
0.00122634u
70
− 0.00789030u
69
+ ··· − 6.17758u − 3.57534
a
5
=
0.00598596u
70
− 0.0384900u
69
+ ··· − 20.1705u − 18.3721
−0.000291346u
70
+ 0.00211473u
69
+ ··· + 2.72153u + 0.00758362
a
10
=
0.00359405u
70
− 0.0233974u
69
+ ··· − 10.2765u − 11.6441
0.00223421u
70
− 0.0144905u
69
+ ··· − 8.93510u − 6.01514
a
11
=
0.00236772u
70
− 0.0155071u
69
+ ··· − 4.09892u − 8.06874
0.00196736u
70
− 0.0127690u
69
+ ··· − 8.37761u − 5.30669
a
6
=
0.000944024u
70
− 0.00534102u
69
+ ··· + 2.29413u − 4.92832
−0.00266769u
70
+ 0.0173963u
69
+ ··· + 10.1384u + 5.89187
a
7
=
−0.00172367u
70
+ 0.0120553u
69
+ ··· + 12.4325u + 0.963549
−0.00266769u
70
+ 0.0173963u
69
+ ··· + 10.1384u + 5.89187
a
3
=
−0.00219214u
70
+ 0.0150659u
69
+ ··· + 18.3981u + 2.02950
−0.00416424u
70
+ 0.0270500u
69
+ ··· + 13.2979u + 10.3819
a
12
=
0.00900947u
70
− 0.0586001u
69
+ ··· − 17.8826u − 23.4781
0.00120943u
70
− 0.00763559u
69
+ ··· − 2.89220u − 4.68656
a
8
=
0.00145832u
70
− 0.00974600u
69
+ ··· − 2.07797u − 3.06258
0.00371565u
70
− 0.0241597u
69
+ ··· − 10.5062u − 9.72889
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00212616u
70
− 0.0143000u
69
+ ··· + 4.47275u − 9.19315
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 6u
70
+ ··· − 4114u + 1331
c
2
u
71
+ 21u
69
+ ··· − 83828u + 3624
c
3
u
71
− u
70
+ ··· − 247794u + 25577
c
4
, c
8
, c
9
u
71
+ 9u
69
+ ··· + 19u − 1
c
5
u
71
+ u
70
+ ··· − 2u + 11
c
6
, c
7
, c
12
u
71
+ 39u
69
+ ··· − 5u + 27
c
10
u
71
− 34u
69
+ ··· + 56160u + 8128
c
11
u
71
− 4u
70
+ ··· + 1157u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
− 78y
70
+ ··· + 1815484y −1771561
c
2
y
71
+ 42y
70
+ ··· + 1092384208y −13133376
c
3
y
71
− 23y
70
+ ··· + 22971145086y −654182929
c
4
, c
8
, c
9
y
71
+ 18y
70
+ ··· + 101y −1
c
5
y
71
− 5y
70
+ ··· + 4008y −121
c
6
, c
7
, c
12
y
71
+ 78y
70
+ ··· − 65369y −729
c
10
y
71
− 68y
70
+ ··· − 2954669056y −66064384
c
11
y
71
+ 20y
70
+ ··· + 471071y −289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855093 + 0.691769I
a = −0.819852 + 0.703890I
b = 0.751162 + 1.181190I
−4.12043 − 2.13457I 0
u = −0.855093 − 0.691769I
a = −0.819852 − 0.703890I
b = 0.751162 − 1.181190I
−4.12043 + 2.13457I 0
u = −0.945495 + 0.576536I
a = 0.383796 − 0.492811I
b = −0.313568 − 1.042450I
1.80017 − 2.63067I 0
u = −0.945495 − 0.576536I
a = 0.383796 + 0.492811I
b = −0.313568 + 1.042450I
1.80017 + 2.63067I 0
u = 0.410222 + 0.694548I
a = 0.629449 + 0.468517I
b = 0.892647 − 0.752338I
1.07011 − 1.96163I 4.17135 + 0.I
u = 0.410222 − 0.694548I
a = 0.629449 − 0.468517I
b = 0.892647 + 0.752338I
1.07011 + 1.96163I 4.17135 + 0.I
u = 0.710634 + 1.047830I
a = −0.754572 − 0.114387I
b = −0.168552 + 0.356847I
−4.75391 − 4.28782I 0
u = 0.710634 − 1.047830I
a = −0.754572 + 0.114387I
b = −0.168552 − 0.356847I
−4.75391 + 4.28782I 0
u = −0.722568 + 0.079323I
a = 0.05240 − 2.01983I
b = −0.108948 − 0.811922I
5.63700 − 3.03551I 11.5234 − 18.6135I
u = −0.722568 − 0.079323I
a = 0.05240 + 2.01983I
b = −0.108948 + 0.811922I
5.63700 + 3.03551I 11.5234 + 18.6135I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29924
a = −0.201632
b = −1.10829
−2.21745 0
u = 0.421745 + 0.482603I
a = 1.286390 − 0.505129I
b = 0.17570 + 2.03467I
−7.18912 − 6.23246I −7.19469 + 7.21845I
u = 0.421745 − 0.482603I
a = 1.286390 + 0.505129I
b = 0.17570 − 2.03467I
−7.18912 + 6.23246I −7.19469 − 7.21845I
u = −1.394060 + 0.131721I
a = 0.938577 − 0.467693I
b = 2.02334 − 0.02777I
−13.85970 − 0.07874I 0
u = −1.394060 − 0.131721I
a = 0.938577 + 0.467693I
b = 2.02334 + 0.02777I
−13.85970 + 0.07874I 0
u = 0.174970 + 0.540137I
a = 0.639636 − 0.981256I
b = −0.071320 − 0.148905I
−1.21580 − 0.98742I −6.40420 + 1.68200I
u = 0.174970 − 0.540137I
a = 0.639636 + 0.981256I
b = −0.071320 + 0.148905I
−1.21580 + 0.98742I −6.40420 − 1.68200I
u = 0.476772 + 0.258180I
a = −1.49190 + 1.16051I
b = 0.063631 + 0.926165I
−8.00321 + 1.13862I −8.21760 + 1.16511I
u = 0.476772 − 0.258180I
a = −1.49190 − 1.16051I
b = 0.063631 − 0.926165I
−8.00321 − 1.13862I −8.21760 − 1.16511I
u = −1.42761 + 0.39916I
a = −0.864889 + 0.393780I
b = −1.89045 + 0.33289I
−5.91928 + 4.99041I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42761 − 0.39916I
a = −0.864889 − 0.393780I
b = −1.89045 − 0.33289I
−5.91928 − 4.99041I 0
u = −1.32126 + 0.67554I
a = 0.0726928 + 0.0562535I
b = 0.348804 + 0.734113I
−1.86664 − 2.54988I 0
u = −1.32126 − 0.67554I
a = 0.0726928 − 0.0562535I
b = 0.348804 − 0.734113I
−1.86664 + 2.54988I 0
u = −0.479123 + 0.152614I
a = −1.28987 + 0.59984I
b = −0.740321 + 0.170047I
−0.70765 + 1.68837I −1.63894 − 3.69018I
u = −0.479123 − 0.152614I
a = −1.28987 − 0.59984I
b = −0.740321 − 0.170047I
−0.70765 − 1.68837I −1.63894 + 3.69018I
u = 0.27206 + 1.47654I
a = −0.388494 + 0.277917I
b = −0.289408 − 0.266420I
0.11277 − 4.26226I 0
u = 0.27206 − 1.47654I
a = −0.388494 − 0.277917I
b = −0.289408 + 0.266420I
0.11277 + 4.26226I 0
u = −1.50420 + 0.03923I
a = −0.686049 + 0.733307I
b = −1.58379 + 0.51372I
−5.23867 + 2.59454I 0
u = −1.50420 − 0.03923I
a = −0.686049 − 0.733307I
b = −1.58379 − 0.51372I
−5.23867 − 2.59454I 0
u = −0.487748 + 0.064878I
a = 1.03010 − 3.02691I
b = −0.711670 − 0.570558I
−3.00603 + 4.33794I −5.75149 − 2.20133I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487748 − 0.064878I
a = 1.03010 + 3.02691I
b = −0.711670 + 0.570558I
−3.00603 − 4.33794I −5.75149 + 2.20133I
u = 1.47327 + 0.47471I
a = −0.938303 − 0.554952I
b = −1.58558 − 0.11609I
−10.53540 − 5.22803I 0
u = 1.47327 − 0.47471I
a = −0.938303 + 0.554952I
b = −1.58558 + 0.11609I
−10.53540 + 5.22803I 0
u = −1.56403 + 0.07841I
a = 0.649067 + 0.652560I
b = 1.61142 + 0.17827I
−6.26383 + 3.91447I 0
u = −1.56403 − 0.07841I
a = 0.649067 − 0.652560I
b = 1.61142 − 0.17827I
−6.26383 − 3.91447I 0
u = 0.382869 + 0.152364I
a = −0.700984 − 0.217875I
b = −0.16005 − 1.81276I
0.89217 − 2.87299I −12.8712 + 10.4575I
u = 0.382869 − 0.152364I
a = −0.700984 + 0.217875I
b = −0.16005 + 1.81276I
0.89217 + 2.87299I −12.8712 − 10.4575I
u = 0.148157 + 0.376556I
a = 1.93101 + 0.10965I
b = 0.023725 − 0.684740I
0.53283 − 1.57625I −0.35637 + 4.67830I
u = 0.148157 − 0.376556I
a = 1.93101 − 0.10965I
b = 0.023725 + 0.684740I
0.53283 + 1.57625I −0.35637 − 4.67830I
u = −1.59234 + 0.18903I
a = 0.687009 − 0.705876I
b = 1.62510 − 0.75960I
−12.3054 + 8.0119I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59234 − 0.18903I
a = 0.687009 + 0.705876I
b = 1.62510 + 0.75960I
−12.3054 − 8.0119I 0
u = 1.10230 + 1.16672I
a = −0.466795 − 0.288870I
b = −1.165100 + 0.306719I
−4.13954 − 5.68269I 0
u = 1.10230 − 1.16672I
a = −0.466795 + 0.288870I
b = −1.165100 − 0.306719I
−4.13954 + 5.68269I 0
u = −1.61148 + 0.10779I
a = −0.756015 − 0.575680I
b = −1.88784 + 0.14386I
−14.5113 + 8.0913I 0
u = −1.61148 − 0.10779I
a = −0.756015 + 0.575680I
b = −1.88784 − 0.14386I
−14.5113 − 8.0913I 0
u = 1.46018 + 0.70741I
a = 0.768889 + 0.351230I
b = 1.313330 + 0.199314I
−3.54491 − 4.46297I 0
u = 1.46018 − 0.70741I
a = 0.768889 − 0.351230I
b = 1.313330 − 0.199314I
−3.54491 + 4.46297I 0
u = −0.322767 + 0.162961I
a = 1.33442 − 3.57982I
b = 0.254043 + 0.172356I
4.14941 − 3.70094I −11.43399 + 0.94316I
u = −0.322767 − 0.162961I
a = 1.33442 + 3.57982I
b = 0.254043 − 0.172356I
4.14941 + 3.70094I −11.43399 − 0.94316I
u = 1.65016 + 0.01664I
a = −0.429508 + 0.544500I
b = −1.48683 − 0.09273I
−4.20874 + 1.34264I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65016 − 0.01664I
a = −0.429508 − 0.544500I
b = −1.48683 + 0.09273I
−4.20874 − 1.34264I 0
u = 1.67418 + 0.32491I
a = 0.379399 − 0.718688I
b = 2.07435 + 0.18801I
−11.38140 + 1.75020I 0
u = 1.67418 − 0.32491I
a = 0.379399 + 0.718688I
b = 2.07435 − 0.18801I
−11.38140 − 1.75020I 0
u = −1.62600 + 0.55530I
a = 0.746967 − 0.398701I
b = 1.83339 − 0.57222I
−5.92756 + 11.43370I 0
u = −1.62600 − 0.55530I
a = 0.746967 + 0.398701I
b = 1.83339 + 0.57222I
−5.92756 − 11.43370I 0
u = 1.72385 + 0.18316I
a = 0.585265 + 0.329500I
b = 1.205890 + 0.199118I
−4.64355 − 2.14704I 0
u = 1.72385 − 0.18316I
a = 0.585265 − 0.329500I
b = 1.205890 − 0.199118I
−4.64355 + 2.14704I 0
u = −0.015750 + 0.241127I
a = −4.15863 + 0.61171I
b = −0.308108 − 1.085500I
2.55861 − 3.61261I 2.20434 + 4.61612I
u = −0.015750 − 0.241127I
a = −4.15863 − 0.61171I
b = −0.308108 + 1.085500I
2.55861 + 3.61261I 2.20434 − 4.61612I
u = 1.65996 + 0.62813I
a = 0.221771 + 0.297064I
b = 1.114910 + 0.227577I
−6.13318 − 2.83653I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65996 − 0.62813I
a = 0.221771 − 0.297064I
b = 1.114910 − 0.227577I
−6.13318 + 2.83653I 0
u = 1.64032 + 0.80088I
a = −0.569497 − 0.254760I
b = −1.56673 − 0.52622I
−4.25059 − 4.20433I 0
u = 1.64032 − 0.80088I
a = −0.569497 + 0.254760I
b = −1.56673 + 0.52622I
−4.25059 + 4.20433I 0
u = 1.83846 + 0.15287I
a = −0.758538 − 0.383840I
b = −1.331450 − 0.464071I
−11.84970 − 3.46057I 0
u = 1.83846 − 0.15287I
a = −0.758538 + 0.383840I
b = −1.331450 + 0.464071I
−11.84970 + 3.46057I 0
u = −1.83511 + 0.54816I
a = −0.671789 + 0.461716I
b = −1.84620 + 0.81072I
−13.2269 + 16.1533I 0
u = −1.83511 − 0.54816I
a = −0.671789 − 0.461716I
b = −1.84620 − 0.81072I
−13.2269 − 16.1533I 0
u = 1.88229 + 0.64838I
a = 0.595875 + 0.243854I
b = 2.08889 + 1.05320I
−12.11790 − 5.04846I 0
u = 1.88229 − 0.64838I
a = 0.595875 − 0.243854I
b = 2.08889 − 1.05320I
−12.11790 + 5.04846I 0
u = 0.95261 + 2.08261I
a = 0.368349 − 0.051748I
b = 0.369727 + 0.475458I
−4.97472 − 7.25323I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.95261 − 2.08261I
a = 0.368349 + 0.051748I
b = 0.369727 − 0.475458I
−4.97472 + 7.25323I 0
12
II. I
u
2
=
h1.82×10
28
u
25
−2.58×10
29
u
24
+· · ·+1.41×10
28
b−4.03×10
29
, 7.47×10
29
u
25
−
1.06 × 10
31
u
24
+ · · · + 2.40 × 10
29
a − 1.63 × 10
31
, u
26
− 15u
25
+ · · · − 101u + 17i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
−3.10711u
25
+ 44.1490u
24
+ ··· − 328.871u + 67.9957
−1.28536u
25
+ 18.2511u
24
+ ··· − 135.744u + 28.5212
a
5
=
−0.655818u
25
+ 9.30697u
24
+ ··· − 95.1260u + 20.8098
−0.530299u
25
+ 7.41367u
24
+ ··· − 44.4278u + 10.1489
a
10
=
−3.10711u
25
+ 44.1490u
24
+ ··· − 328.871u + 67.9957
−3.37677u
25
+ 47.7008u
24
+ ··· − 331.152u + 70.3022
a
11
=
−1.82176u
25
+ 25.8978u
24
+ ··· − 193.127u + 39.4744
−2.44472u
25
+ 34.7318u
24
+ ··· − 249.052u + 52.8055
a
6
=
0.591281u
25
− 8.46536u
24
+ ··· + 70.0301u − 12.0716
1.20833u
25
− 17.2333u
24
+ ··· + 125.414u − 27.5409
a
7
=
1.79962u
25
− 25.6987u
24
+ ··· + 195.444u − 39.6125
1.20833u
25
− 17.2333u
24
+ ··· + 125.414u − 27.5409
a
3
=
0.602497u
25
− 8.55949u
24
+ ··· + 83.4410u − 15.2225
0.390285u
25
− 5.51948u
24
+ ··· + 40.4172u − 8.92985
a
12
=
−1.85417u
25
+ 26.3205u
24
+ ··· − 177.574u + 38.8645
−2.37946u
25
+ 33.8095u
24
+ ··· − 241.981u + 51.5010
a
8
=
3.18445u
25
− 45.6260u
24
+ ··· + 342.896u − 71.8998
2.94676u
25
− 42.1104u
24
+ ··· + 309.393u − 67.3954
(ii) Obstruction class = 1
(iii) Cusp Shapes = 37.5068u
25
− 533.454u
24
+ ··· + 3882.73u − 825.984
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 15u
25
+ ··· − 101u + 17
c
2
u
26
+ 5u
25
+ ··· − 5u + 1
c
3
u
26
+ 3u
24
+ ··· − 3u + 1
c
4
u
26
+ u
25
+ ··· + 15u
2
+ 1
c
5
u
26
+ 2u
24
+ ··· + u + 1
c
6
, c
7
u
26
+ u
25
+ ··· + 12u
2
+ 1
c
8
, c
9
u
26
− u
25
+ ··· + 15u
2
+ 1
c
10
u
26
+ u
25
+ ··· + 2u + 1
c
11
u
26
− 3u
25
+ ··· + 4u
2
+ 1
c
12
u
26
− u
25
+ ··· + 12u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 25y
25
+ ··· + 5779y + 289
c
2
y
26
+ 7y
25
+ ··· − 17y + 1
c
3
y
26
+ 6y
25
+ ··· − 7y + 1
c
4
, c
8
, c
9
y
26
+ 19y
25
+ ··· + 30y + 1
c
5
y
26
+ 4y
25
+ ··· + 15y + 1
c
6
, c
7
, c
12
y
26
+ 27y
25
+ ··· + 24y + 1
c
10
y
26
− 3y
25
+ ··· + 18y + 1
c
11
y
26
− 3y
25
+ ··· + 8y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864308 + 0.204939I
a = 0.186119 − 1.391440I
b = 0.204230 + 0.442832I
1.11658 − 3.25284I −4.16744 + 2.63544I
u = −0.864308 − 0.204939I
a = 0.186119 + 1.391440I
b = 0.204230 − 0.442832I
1.11658 + 3.25284I −4.16744 − 2.63544I
u = 0.849606 + 0.867710I
a = 0.803097 + 0.746392I
b = 0.054218 + 0.580187I
−1.91725 − 5.67035I −0.92317 + 5.56816I
u = 0.849606 − 0.867710I
a = 0.803097 − 0.746392I
b = 0.054218 − 0.580187I
−1.91725 + 5.67035I −0.92317 − 5.56816I
u = −0.580864 + 0.526165I
a = 0.533785 − 0.477846I
b = −0.244597 − 1.212810I
1.40384 − 2.95716I −4.93957 + 6.03245I
u = −0.580864 − 0.526165I
a = 0.533785 + 0.477846I
b = −0.244597 + 1.212810I
1.40384 + 2.95716I −4.93957 − 6.03245I
u = 0.776301 + 0.021090I
a = −0.16415 − 1.90935I
b = −0.126508 − 0.814918I
5.55935 − 3.18078I −11.4069 + 23.8136I
u = 0.776301 − 0.021090I
a = −0.16415 + 1.90935I
b = −0.126508 + 0.814918I
5.55935 + 3.18078I −11.4069 − 23.8136I
u = 1.54475 + 0.13063I
a = −0.574750 − 0.512807I
b = −1.39653 − 0.25903I
−3.49621 − 2.32528I 0
u = 1.54475 − 0.13063I
a = −0.574750 + 0.512807I
b = −1.39653 + 0.25903I
−3.49621 + 2.32528I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134314 + 0.405030I
a = 1.052970 + 0.305581I
b = 0.09833 − 1.66833I
1.21192 − 2.75463I 9.33595 + 4.66646I
u = 0.134314 − 0.405030I
a = 1.052970 − 0.305581I
b = 0.09833 + 1.66833I
1.21192 + 2.75463I 9.33595 − 4.66646I
u = 1.42907 + 0.69274I
a = −0.722395 − 0.301247I
b = −1.356760 − 0.328411I
−3.25675 − 3.77350I 0
u = 1.42907 − 0.69274I
a = −0.722395 + 0.301247I
b = −1.356760 + 0.328411I
−3.25675 + 3.77350I 0
u = −0.009597 + 0.317703I
a = −4.07677 + 0.50597I
b = −0.192964 − 0.537531I
4.48592 − 3.78471I 11.82654 + 6.62208I
u = −0.009597 − 0.317703I
a = −4.07677 − 0.50597I
b = −0.192964 + 0.537531I
4.48592 + 3.78471I 11.82654 − 6.62208I
u = 0.87400 + 1.47831I
a = −0.353593 − 0.101977I
b = −0.554591 + 0.920025I
−5.03069 − 6.13674I 0
u = 0.87400 − 1.47831I
a = −0.353593 + 0.101977I
b = −0.554591 − 0.920025I
−5.03069 + 6.13674I 0
u = 1.71960 + 0.30377I
a = 0.738522 + 0.421344I
b = 1.66000 + 0.51845I
−11.21240 − 4.02957I 0
u = 1.71960 − 0.30377I
a = 0.738522 − 0.421344I
b = 1.66000 − 0.51845I
−11.21240 + 4.02957I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64718 + 0.72109I
a = −0.189318 + 0.319878I
b = 0.262918 + 0.821704I
−1.23857 − 2.33603I 0
u = −1.64718 − 0.72109I
a = −0.189318 − 0.319878I
b = 0.262918 − 0.821704I
−1.23857 + 2.33603I 0
u = 1.80081 + 0.23661I
a = 0.225923 − 0.567408I
b = 0.980847 − 0.181371I
−6.18238 − 0.70471I 0
u = 1.80081 − 0.23661I
a = 0.225923 + 0.567408I
b = 0.980847 + 0.181371I
−6.18238 + 0.70471I 0
u = 1.47350 + 1.23126I
a = 0.569959 + 0.170947I
b = 1.111410 + 0.223196I
−6.11739 − 5.18649I 0
u = 1.47350 − 1.23126I
a = 0.569959 − 0.170947I
b = 1.111410 − 0.223196I
−6.11739 + 5.18649I 0
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 15u
25
+ ··· − 101u + 17)(u
71
+ 6u
70
+ ··· − 4114u + 1331)
c
2
(u
26
+ 5u
25
+ ··· − 5u + 1)(u
71
+ 21u
69
+ ··· − 83828u + 3624)
c
3
(u
26
+ 3u
24
+ ··· − 3u + 1)(u
71
− u
70
+ ··· − 247794u + 25577)
c
4
(u
26
+ u
25
+ ··· + 15u
2
+ 1)(u
71
+ 9u
69
+ ··· + 19u − 1)
c
5
(u
26
+ 2u
24
+ ··· + u + 1)(u
71
+ u
70
+ ··· − 2u + 11)
c
6
, c
7
(u
26
+ u
25
+ ··· + 12u
2
+ 1)(u
71
+ 39u
69
+ ··· − 5u + 27)
c
8
, c
9
(u
26
− u
25
+ ··· + 15u
2
+ 1)(u
71
+ 9u
69
+ ··· + 19u − 1)
c
10
(u
26
+ u
25
+ ··· + 2u + 1)(u
71
− 34u
69
+ ··· + 56160u + 8128)
c
11
(u
26
− 3u
25
+ ··· + 4u
2
+ 1)(u
71
− 4u
70
+ ··· + 1157u + 17)
c
12
(u
26
− u
25
+ ··· + 12u
2
+ 1)(u
71
+ 39u
69
+ ··· − 5u + 27)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 25y
25
+ ··· + 5779y + 289)
· (y
71
− 78y
70
+ ··· + 1815484y −1771561)
c
2
(y
26
+ 7y
25
+ ··· − 17y + 1)
· (y
71
+ 42y
70
+ ··· + 1092384208y −13133376)
c
3
(y
26
+ 6y
25
+ ··· − 7y + 1)
· (y
71
− 23y
70
+ ··· + 22971145086y −654182929)
c
4
, c
8
, c
9
(y
26
+ 19y
25
+ ··· + 30y + 1)(y
71
+ 18y
70
+ ··· + 101y −1)
c
5
(y
26
+ 4y
25
+ ··· + 15y + 1)(y
71
− 5y
70
+ ··· + 4008y −121)
c
6
, c
7
, c
12
(y
26
+ 27y
25
+ ··· + 24y + 1)(y
71
+ 78y
70
+ ··· − 65369y −729)
c
10
(y
26
− 3y
25
+ ··· + 18y + 1)
· (y
71
− 68y
70
+ ··· − 2954669056y −66064384)
c
11
(y
26
− 3y
25
+ ··· + 8y + 1)(y
71
+ 20y
70
+ ··· + 471071y −289)
20
