12a
0785
(K12a
0785
)
A knot diagram
1
Linearized knot diagam
3 8 11 10 9 4 2 1 12 7 6 5
Solving Sequence
9,12 6,10
5 1 4 7 8 11 3 2
c
9
c
5
c
12
c
4
c
6
c
8
c
11
c
3
c
2
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−440u
19
− 7822u
18
+ ··· + b − 83010, 101350u
19
+ 1884588u
18
+ ··· + 419a + 33060194,
u
20
+ 19u
19
+ ··· + 4045u + 419i
I
u
2
= h−55u
25
− 1474u
24
+ ··· + b − 140189, −17044u
25
− 361672u
24
+ ··· + 2239a + 75396086,
u
26
+ 27u
25
+ ··· + 29107u + 2239i
I
u
3
= h−5.90378 × 10
27
a
17
u
3
+ 2.02102 × 10
27
a
16
u
3
+ ··· − 6.93993 × 10
27
a − 7.66958 × 10
27
,
− a
17
u
3
− 3a
16
u
3
+ ··· − 143936a + 299131, u
4
− u
3
+ 2u + 1i
I
u
4
= h8.04582 × 10
32
a
17
u + 5.01372 × 10
32
a
16
u + ··· − 7.33139 × 10
32
a − 5.03241 × 10
33
,
− 2a
17
u + 3a
16
u + ··· + 36a + 9, u
2
− u + 1i
I
u
5
= h1.00210 × 10
26
u
37
− 1.30856 × 10
27
u
36
+ ··· + 8.88085 × 10
25
b − 1.95986 × 10
26
,
9.57765 × 10
25
u
37
− 1.33504 × 10
27
u
36
+ ··· + 8.88085 × 10
25
a − 6.26187 × 10
25
, u
38
− 14u
37
+ ··· + u + 1i
I
u
6
= hb
2
+ ba − a
2
− 1, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
I
u
7
= hb + 1, a, u − 1i
I
v
1
= ha, b
9
+ b
8
+ 2b
7
+ b
6
+ 3b
5
+ b
4
+ 2b
3
+ b − 1, v −1i
* 8 irreducible components of dim
C
= 0, with total 220 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−440u
19
− 7822u
18
+ · · · + b − 83010, 1.01 × 10
5
u
19
+ 1.88 ×
10
6
u
18
+ · · · + 419a + 3.31 × 10
7
, u
20
+ 19u
19
+ · · · + 4045u + 419i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
6
=
−241.885u
19
− 4497.82u
18
+ ··· − 728143.u − 78902.6
440u
19
+ 7822u
18
+ ··· + 797266u + 83010
a
10
=
1
u
2
a
5
=
198.115u
19
+ 3324.18u
18
+ ··· + 69123.0u + 4107.39
440u
19
+ 7822u
18
+ ··· + 797266u + 83010
a
1
=
0.498807u
19
+ 8.47733u
18
+ ··· + 82.9165u − 5.32697
u
19
+ 18u
18
+ ··· + 2024u + 209
a
4
=
296.115u
19
+ 5559.18u
18
+ ··· + 968647.u + 105457.
−679u
19
− 11745u
18
+ ··· − 752581u − 73277
a
7
=
−174.885u
19
− 2643.82u
18
+ ··· + 364183.u + 45169.4
−716u
19
− 13126u
18
+ ··· − 1876012u − 201491
a
8
=
4.25060u
19
+ 81.7613u
18
+ ··· + 18071.5u + 1994.66
−2u
19
− 27u
18
+ ··· + 11364u + 1362
a
11
=
−0.501193u
19
− 8.52267u
18
+ ··· − 127.084u − 4.32697
−u
18
− 17u
17
+ ··· − 1812u − 210
a
3
=
−532.943u
19
− 9436.91u
18
+ ··· − 915041.u − 94759.3
−73u
19
− 1966u
18
+ ··· − 1107172u − 125676
a
2
=
10.5609u
19
+ 95.6563u
18
+ ··· − 125604.u − 14672.3
90u
19
+ 1670u
18
+ ··· + 266050u + 28727
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −272u
19
−4238u
18
−31694u
17
−149912u
16
−499032u
15
−1231956u
14
−2311268u
13
−
3295698u
12
− 3426358u
11
− 2150740u
10
+ 263316u
9
+ 2695132u
8
+ 4037400u
7
+
4211956u
6
+ 3957808u
5
+ 3582696u
4
+ 2698114u
3
+ 1385042u
2
+ 391594u + 50234
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 10u
19
+ ··· − 160u + 64
c
2
, c
7
u
20
− 6u
19
+ ··· − 40u + 8
c
3
, c
5
, c
10
c
12
u
20
+ u
19
+ ··· − u + 1
c
4
, c
11
u
20
+ u
19
+ ··· + 2u + 26
c
6
, c
9
u
20
− 19u
19
+ ··· − 4045u + 419
c
8
u
20
− 18u
19
+ ··· − 24920u + 3688
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 2y
19
+ ··· − 23040y + 4096
c
2
, c
7
y
20
− 10y
19
+ ··· + 160y + 64
c
3
, c
5
, c
10
c
12
y
20
− y
19
+ ··· + 11y + 1
c
4
, c
11
y
20
+ 21y
19
+ ··· + 10448y + 676
c
6
, c
9
y
20
− 9y
19
+ ··· − 853997y + 175561
c
8
y
20
− 4y
19
+ ··· + 14317984y + 13601344
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512099 + 0.698028I
a = −0.757073 − 0.694555I
b = 0.169556 + 0.506438I
−0.63165 − 1.63991I −3.29731 + 4.07135I
u = 0.512099 − 0.698028I
a = −0.757073 + 0.694555I
b = 0.169556 − 0.506438I
−0.63165 + 1.63991I −3.29731 − 4.07135I
u = 0.00580 + 1.43849I
a = 0.706982 + 0.120837I
b = −0.419757 − 0.411483I
−4.80670 − 5.98648I −6.00000 + 11.08698I
u = 0.00580 − 1.43849I
a = 0.706982 − 0.120837I
b = −0.419757 + 0.411483I
−4.80670 + 5.98648I −6.00000 − 11.08698I
u = −1.16335 + 1.05046I
a = −0.242193 + 1.117750I
b = 1.31614 − 1.05420I
−8.2024 + 21.0457I 0
u = −1.16335 − 1.05046I
a = −0.242193 − 1.117750I
b = 1.31614 + 1.05420I
−8.2024 − 21.0457I 0
u = −1.17748 + 1.05342I
a = 0.232775 − 1.068910I
b = −1.25568 + 1.02028I
−5.1187 + 15.7823I 0
u = −1.17748 − 1.05342I
a = 0.232775 + 1.068910I
b = −1.25568 − 1.02028I
−5.1187 − 15.7823I 0
u = −1.17927 + 1.07828I
a = −0.298894 + 1.028330I
b = 1.27177 − 0.91287I
−9.8158 + 11.6670I 0
u = −1.17927 − 1.07828I
a = −0.298894 − 1.028330I
b = 1.27177 + 0.91287I
−9.8158 − 11.6670I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.26927 + 1.01007I
a = 0.086517 − 0.867442I
b = −0.909643 + 1.001230I
−0.48741 + 13.75390I 0
u = −1.26927 − 1.01007I
a = 0.086517 + 0.867442I
b = −0.909643 − 1.001230I
−0.48741 − 13.75390I 0
u = −0.290662 + 0.201866I
a = −1.20981 + 1.20451I
b = 0.079084 + 0.815354I
1.78290 − 2.14893I 0.04329 + 4.23950I
u = −0.290662 − 0.201866I
a = −1.20981 − 1.20451I
b = 0.079084 − 0.815354I
1.78290 + 2.14893I 0.04329 − 4.23950I
u = −1.34983 + 0.99384I
a = −0.068669 + 0.743707I
b = 0.756125 − 0.916597I
0.45556 + 8.22051I 0
u = −1.34983 − 0.99384I
a = −0.068669 − 0.743707I
b = 0.756125 + 0.916597I
0.45556 − 8.22051I 0
u = −1.49300 + 1.31522I
a = 0.274286 − 0.533423I
b = −0.698441 + 0.483867I
−7.23704 + 6.69767I 0
u = −1.49300 − 1.31522I
a = 0.274286 + 0.533423I
b = −0.698441 − 0.483867I
−7.23704 − 6.69767I 0
u = −2.09503 + 0.56369I
a = −0.029412 + 0.377289I
b = 0.190855 − 0.638731I
0.34008 + 3.38661I 0
u = −2.09503 − 0.56369I
a = −0.029412 − 0.377289I
b = 0.190855 + 0.638731I
0.34008 − 3.38661I 0
6
II. I
u
2
= h−55u
25
− 1474u
24
+ · · · + b − 140189, −1.70 × 10
4
u
25
− 3.62 ×
10
5
u
24
+ · · · + 2239a + 7.54 × 10
7
, u
26
+ 27u
25
+ · · · + 29107u + 2239i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
6
=
7.61233u
25
+ 161.533u
24
+ ··· − 386377.u − 33674
55u
25
+ 1474u
24
+ ··· + 1715942u + 140189
a
10
=
1
u
2
a
5
=
62.6123u
25
+ 1635.53u
24
+ ··· + 1.32957 × 10
6
u + 106515
55u
25
+ 1474u
24
+ ··· + 1715942u + 140189
a
1
=
−1.49978u
25
− 39.4940u
24
+ ··· − 40819.5u − 3351
−u
25
− 27u
24
+ ··· − 40302u − 3358
a
4
=
18.6123u
25
+ 533.533u
24
+ ··· + 1.07432 × 10
6
u + 89471
−62u
25
− 1572u
24
+ ··· − 688744u − 52365
a
7
=
129.612u
25
+ 3364.53u
24
+ ··· + 2.48091 × 10
6
u + 197811
29u
25
+ 900u
24
+ ··· + 2630825u + 220793
a
8
=
4.25011u
25
+ 105.753u
24
+ ··· − 539.268u − 555
9u
25
+ 233u
24
+ ··· + 150013u + 11755
a
11
=
0.500223u
25
+ 13.5060u
24
+ ··· + 14037.5u + 1126
−u
25
− 26u
24
+ ··· − 14553u − 1119
a
3
=
43.4185u
25
+ 1199.30u
24
+ ··· + 1.88287 × 10
6
u + 155911
−113u
25
− 2859u
24
+ ··· − 1150846u − 86384
a
2
=
−41.1867u
25
− 1062.04u
24
+ ··· − 628304.u − 48954
−3u
25
− 119u
24
+ ··· − 642593u − 54154
(ii) Obstruction class = −1
(iii) Cusp Shapes = 115u
25
+ 2941u
24
+ ··· + 1504608u + 115595
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
+ 6u
12
+ ··· + 12u + 16)
2
c
2
, c
7
(u
13
− 4u
12
+ ··· − 14u + 4)
2
c
3
, c
5
, c
10
c
12
u
26
+ u
25
+ ··· + u + 1
c
4
, c
11
(u
13
+ u
11
+ u
10
− 2u
7
− u
6
− u
5
− 2u
4
+ u
3
+ u
2
+ u + 1)
2
c
6
, c
9
u
26
− 27u
25
+ ··· − 29107u + 2239
c
8
(u
13
− 12u
12
+ ··· + 210u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 2y
12
+ ··· − 656y −256)
2
c
2
, c
7
(y
13
− 6y
12
+ ··· + 12y −16)
2
c
3
, c
5
, c
10
c
12
y
26
− 3y
25
+ ··· − y + 1
c
4
, c
11
(y
13
+ 2y
12
+ ··· − y −1)
2
c
6
, c
9
y
26
− 13y
25
+ ··· + 24344647y + 5013121
c
8
(y
13
+ 2y
12
+ ··· + 52908y −16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666943 + 0.686087I
a = 0.512939 + 0.892142I
b = 0.833119 − 0.986335I
2.19583 + 5.62038I 0
u = −0.666943 − 0.686087I
a = 0.512939 − 0.892142I
b = 0.833119 + 0.986335I
2.19583 − 5.62038I 0
u = −0.570390 + 0.767585I
a = −0.523314 − 0.899263I
b = −0.659342 + 0.919109I
3.66757 + 0.92622I 0
u = −0.570390 − 0.767585I
a = −0.523314 + 0.899263I
b = −0.659342 − 0.919109I
3.66757 − 0.92622I 0
u = −0.444770 + 0.992031I
a = −0.465440 − 0.788020I
b = −0.339390 + 0.806743I
3.66757 − 0.92622I 0
u = −0.444770 − 0.992031I
a = −0.465440 + 0.788020I
b = −0.339390 − 0.806743I
3.66757 + 0.92622I 0
u = −0.427386 + 1.179570I
a = 0.441249 + 0.649055I
b = 0.151020 − 0.735618I
2.19583 − 5.62038I 0
u = −0.427386 − 1.179570I
a = 0.441249 − 0.649055I
b = 0.151020 + 0.735618I
2.19583 + 5.62038I 0
u = −1.132080 + 0.739477I
a = 0.070245 − 0.895176I
b = −1.25982 + 1.01265I
−7.7321 + 12.4192I 0
u = −1.132080 − 0.739477I
a = 0.070245 + 0.895176I
b = −1.25982 − 1.01265I
−7.7321 − 12.4192I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.164030 + 0.702554I
a = −0.062452 + 0.817215I
b = 1.18521 − 0.99046I
−4.61821 + 6.97339I 0
u = −1.164030 − 0.702554I
a = −0.062452 − 0.817215I
b = 1.18521 + 0.99046I
−4.61821 − 6.97339I 0
u = −0.184678 + 0.579008I
a = 0.391553 + 1.227610I
b = 0.638483 − 0.453424I
−0.986461 −7.57792 + 0.I
u = −0.184678 − 0.579008I
a = 0.391553 − 1.227610I
b = 0.638483 + 0.453424I
−0.986461 −7.57792 + 0.I
u = −1.23786 + 0.75067I
a = 0.176474 − 0.765518I
b = −1.17090 + 0.84552I
−9.61879 + 2.75258I 0
u = −1.23786 − 0.75067I
a = 0.176474 + 0.765518I
b = −1.17090 − 0.84552I
−9.61879 − 2.75258I 0
u = −1.59354 + 0.40724I
a = −0.064942 + 0.451082I
b = 0.493879 − 0.916766I
0.14961 + 3.18230I 0
u = −1.59354 − 0.40724I
a = −0.064942 − 0.451082I
b = 0.493879 + 0.916766I
0.14961 − 3.18230I 0
u = −1.23407 + 1.31050I
a = −0.652684 + 0.170177I
b = 0.864731 + 0.289992I
−7.7321 − 12.4192I 0
u = −1.23407 − 1.31050I
a = −0.652684 − 0.170177I
b = 0.864731 − 0.289992I
−7.7321 + 12.4192I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38359 + 1.21059I
a = −0.532677 + 0.314559I
b = 0.895509 + 0.010486I
−9.61879 − 2.75258I 0
u = −1.38359 − 1.21059I
a = −0.532677 − 0.314559I
b = 0.895509 − 0.010486I
−9.61879 + 2.75258I 0
u = −1.31515 + 1.34980I
a = 0.563894 − 0.177924I
b = −0.781390 − 0.189057I
−4.61821 − 6.97339I 0
u = −1.31515 − 1.34980I
a = 0.563894 + 0.177924I
b = −0.781390 + 0.189057I
−4.61821 + 6.97339I 0
u = −2.14553 + 0.78598I
a = 0.145155 − 0.294181I
b = −0.351114 + 0.409675I
0.14961 − 3.18230I 0
u = −2.14553 − 0.78598I
a = 0.145155 + 0.294181I
b = −0.351114 − 0.409675I
0.14961 + 3.18230I 0
12
III. I
u
3
= h−5.90 × 10
27
a
17
u
3
+ 2.02 × 10
27
a
16
u
3
+ · · · − 6.94 × 10
27
a −
7.67 × 10
27
, −a
17
u
3
− 3a
16
u
3
+ · · · − 143936a + 299131, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
6
=
a
10.8520a
17
u
3
− 3.71493a
16
u
3
+ ··· + 12.7566a + 14.0978
a
10
=
1
u
2
a
5
=
10.8520a
17
u
3
− 3.71493a
16
u
3
+ ··· + 13.7566a + 14.0978
10.8520a
17
u
3
− 3.71493a
16
u
3
+ ··· + 12.7566a + 14.0978
a
1
=
−23.0597a
17
u
3
− 29.2653a
16
u
3
+ ··· + 0.121965a − 21.6421
−20.4865a
17
u
3
− 35.2837a
16
u
3
+ ··· + 10.9648a + 5.80110
a
4
=
−74.9828a
17
u
3
+ 65.3497a
16
u
3
+ ··· + 8.99494a + 9.62933
2.66737a
17
u
3
− 28.8131a
16
u
3
+ ··· + 12.7566a + 7.79364
a
7
=
−52.3563a
17
u
3
+ 43.0709a
16
u
3
+ ··· − 21.4565a − 11.4650
44.5851a
17
u
3
− 47.4784a
16
u
3
+ ··· − 15.4615a − 9.97553
a
8
=
−5.90924a
17
u
3
+ 13.5578a
16
u
3
+ ··· + 16.5792a − 1.55499
−12.6224a
17
u
3
− 41.2569a
16
u
3
+ ··· − 2.59196a + 20.6120
a
11
=
−a
2
u
−2.57314a
17
u
3
+ 6.01835a
16
u
3
+ ··· − 10.8428a − 27.4432
a
3
=
−17.6642a
17
u
3
+ 26.4376a
16
u
3
+ ··· − 1.06590a + 3.09641
−15.0877a
17
u
3
+ 16.6517a
16
u
3
+ ··· + 18.8899a + 17.1794
a
2
=
−19.7311a
17
u
3
− 69.4691a
16
u
3
+ ··· + 3.00101a − 43.6395
93.3569a
17
u
3
− 211.428a
16
u
3
+ ··· − 9.44918a + 38.6282
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
29740572986906423854681079856
181342292827965370567175275
a
17
u
3
+
10865978472972041002022452596
181342292827965370567175275
a
16
u
3
+ ··· −
13566665167909917554244015824
181342292827965370567175275
a +
358282414867692411042348754
181342292827965370567175275
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
8
c
2
, c
7
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
8
c
3
, c
5
, c
10
c
12
u
72
− u
71
+ ··· + 276774u + 52573
c
4
, c
11
(u
36
− u
35
+ ··· − 248u + 4921)
2
c
6
, c
9
(u
4
+ u
3
− 2u + 1)
18
c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
8
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
8
c
2
, c
7
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
8
c
3
, c
5
, c
10
c
12
y
72
− 27y
71
+ ··· − 85049384088y + 2763920329
c
4
, c
11
(y
36
+ 39y
35
+ ··· + 446076356y + 24216241)
2
c
6
, c
9
(y
4
− y
3
+ 6y
2
− 4y + 1)
18
c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
8
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = 0.243057 − 0.919495I
b = 1.38638 + 0.42505I
−1.50643 + 1.96639I −11.48501 − 2.76537I
u = −0.621964 + 0.187730I
a = 0.134471 + 1.161030I
b = −1.47915 − 0.89391I
−1.50643 + 6.15314I −11.4850 − 11.0910I
u = −0.621964 + 0.187730I
a = 0.007767 − 1.345090I
b = −1.50405 + 1.31508I
−6.88799 − 3.02516I −17.5768 − 1.0149I
u = −0.621964 + 0.187730I
a = 0.16894 + 1.46402I
b = 1.24189 − 1.23421I
−3.90681 + 1.60535I −14.3279 − 4.0152I
u = −0.621964 + 0.187730I
a = 0.42871 + 1.57754I
b = −1.36735 − 1.70981I
−3.90681 + 6.51418I −14.3279 − 9.8412I
u = −0.621964 + 0.187730I
a = −0.01568 − 1.64400I
b = −1.12952 + 1.59123I
−7.66122 + 5.39594I −19.2841 − 7.6300I
u = −0.621964 + 0.187730I
a = −0.55384 − 1.59587I
b = 1.55061 + 1.88028I
−6.88799 + 11.14470I −17.5768 − 12.8416I
u = −0.621964 + 0.187730I
a = −0.41384 − 1.74353I
b = 1.12745 + 1.97870I
−7.66122 + 2.72360I −19.2841 − 6.2265I
u = −0.621964 + 0.187730I
a = 1.45832 − 1.14441I
b = 0.920625 − 0.121920I
−3.90681 + 1.60535I −14.3279 − 4.0152I
u = −0.621964 + 0.187730I
a = 0.11177 + 1.88289I
b = −0.04479 − 1.46120I
−4.48831 + 4.05977I −20.6523 − 6.9282I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = 0.93323 + 1.85638I
b = 0.920630 − 0.613419I
−1.50643 + 1.96639I −11.48501 − 2.76537I
u = −0.621964 + 0.187730I
a = −1.86495 + 1.00666I
b = −0.936272 + 0.262230I
−6.88799 − 3.02516I −17.5768 + 0.I
u = −0.621964 + 0.187730I
a = −1.64997 + 1.66023I
b = −0.722178 + 0.182166I
−7.66122 + 5.39594I −19.2841 − 7.6300I
u = −0.621964 + 0.187730I
a = 0.46308 − 2.42279I
b = 0.120823 + 0.249703I
−4.48831 + 4.05977I 0
u = −0.621964 + 0.187730I
a = −0.99584 − 2.39369I
b = −0.786199 + 0.418575I
−1.50643 + 6.15314I 0
u = −0.621964 + 0.187730I
a = −0.64577 − 3.22161I
b = −0.608633 + 0.093941I
−3.90681 + 6.51418I 0
u = −0.621964 + 0.187730I
a = 0.29331 + 3.40489I
b = 0.487989 + 0.012299I
−7.66122 + 2.72360I 0
u = −0.621964 + 0.187730I
a = 0.77528 + 3.47061I
b = 0.673351 − 0.010234I
−6.88799 + 11.14470I 0
u = −0.621964 − 0.187730I
a = 0.243057 + 0.919495I
b = 1.38638 − 0.42505I
−1.50643 − 1.96639I −11.48501 + 2.76537I
u = −0.621964 − 0.187730I
a = 0.134471 − 1.161030I
b = −1.47915 + 0.89391I
−1.50643 − 6.15314I −11.4850 + 11.0910I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 − 0.187730I
a = 0.007767 + 1.345090I
b = −1.50405 − 1.31508I
−6.88799 + 3.02516I −17.5768 + 1.0149I
u = −0.621964 − 0.187730I
a = 0.16894 − 1.46402I
b = 1.24189 + 1.23421I
−3.90681 − 1.60535I −14.3279 + 4.0152I
u = −0.621964 − 0.187730I
a = 0.42871 − 1.57754I
b = −1.36735 + 1.70981I
−3.90681 − 6.51418I −14.3279 + 9.8412I
u = −0.621964 − 0.187730I
a = −0.01568 + 1.64400I
b = −1.12952 − 1.59123I
−7.66122 − 5.39594I −19.2841 + 7.6300I
u = −0.621964 − 0.187730I
a = −0.55384 + 1.59587I
b = 1.55061 − 1.88028I
−6.88799 − 11.14470I −17.5768 + 12.8416I
u = −0.621964 − 0.187730I
a = −0.41384 + 1.74353I
b = 1.12745 − 1.97870I
−7.66122 − 2.72360I −19.2841 + 6.2265I
u = −0.621964 − 0.187730I
a = 1.45832 + 1.14441I
b = 0.920625 + 0.121920I
−3.90681 − 1.60535I −14.3279 + 4.0152I
u = −0.621964 − 0.187730I
a = 0.11177 − 1.88289I
b = −0.04479 + 1.46120I
−4.48831 − 4.05977I −20.6523 + 6.9282I
u = −0.621964 − 0.187730I
a = 0.93323 − 1.85638I
b = 0.920630 + 0.613419I
−1.50643 − 1.96639I −11.48501 + 2.76537I
u = −0.621964 − 0.187730I
a = −1.86495 − 1.00666I
b = −0.936272 − 0.262230I
−6.88799 + 3.02516I −17.5768 + 0.I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 − 0.187730I
a = −1.64997 − 1.66023I
b = −0.722178 − 0.182166I
−7.66122 − 5.39594I −19.2841 + 7.6300I
u = −0.621964 − 0.187730I
a = 0.46308 + 2.42279I
b = 0.120823 − 0.249703I
−4.48831 − 4.05977I 0
u = −0.621964 − 0.187730I
a = −0.99584 + 2.39369I
b = −0.786199 − 0.418575I
−1.50643 − 6.15314I 0
u = −0.621964 − 0.187730I
a = −0.64577 + 3.22161I
b = −0.608633 − 0.093941I
−3.90681 − 6.51418I 0
u = −0.621964 − 0.187730I
a = 0.29331 − 3.40489I
b = 0.487989 − 0.012299I
−7.66122 − 2.72360I 0
u = −0.621964 − 0.187730I
a = 0.77528 − 3.47061I
b = 0.673351 + 0.010234I
−6.88799 − 11.14470I 0
u = 1.12196 + 1.05376I
a = 0.935424 + 0.317876I
b = −1.352910 + 0.093439I
−7.66122 − 5.39594I −19.2841 + 7.6300I
u = 1.12196 + 1.05376I
a = −0.629892 − 0.828967I
b = 1.34287 + 0.48468I
−4.48831 − 4.05977I −20.6523 + 6.9282I
u = 1.12196 + 1.05376I
a = −0.072905 − 1.091850I
b = 0.773356 + 0.936297I
−1.50643 − 6.15314I −11.4850 + 11.0910I
u = 1.12196 + 1.05376I
a = 0.893999 + 0.030444I
b = −1.131990 + 0.328604I
−6.88799 + 3.02516I −17.5768 + 1.0149I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 + 1.05376I
a = −0.004295 + 0.876976I
b = −0.558649 − 0.685116I
−1.50643 − 1.96639I −11.48501 + 2.76537I
u = 1.12196 + 1.05376I
a = 0.311224 + 0.732782I
b = −1.162730 − 0.365037I
−4.48831 − 4.05977I −20.6523 + 6.9282I
u = 1.12196 + 1.05376I
a = −0.766136 − 0.158857I
b = 1.102540 − 0.125636I
−3.90681 − 1.60535I −14.3279 + 4.0152I
u = 1.12196 + 1.05376I
a = −0.170868 − 0.736807I
b = 1.30660 + 0.60299I
−7.66122 − 2.72360I −19.2841 + 6.2265I
u = 1.12196 + 1.05376I
a = −0.090223 − 0.707270I
b = 1.24928 + 0.73115I
−6.88799 − 11.14470I −17.5768 + 12.8416I
u = 1.12196 + 1.05376I
a = −0.302703 − 0.624434I
b = 0.901831 − 0.021552I
−7.66122 − 5.39594I −19.2841 + 7.6300I
u = 1.12196 + 1.05376I
a = 0.134083 + 0.676847I
b = −1.209800 − 0.658356I
−3.90681 − 6.51418I −14.3279 + 9.8412I
u = 1.12196 + 1.05376I
a = 0.210978 + 0.585167I
b = −0.677217 − 0.035293I
−3.90681 − 1.60535I −14.3279 + 4.0152I
u = 1.12196 + 1.05376I
a = −0.360671 − 1.339120I
b = 1.22641 + 1.11280I
−3.90681 − 6.51418I −14.3279 + 9.8412I
u = 1.12196 + 1.05376I
a = −0.255451 − 0.507035I
b = 0.645364 − 0.152056I
−6.88799 + 3.02516I −17.5768 + 1.0149I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 + 1.05376I
a = 0.52832 + 1.34223I
b = −1.41527 − 1.04664I
−7.66122 − 2.72360I −19.2841 + 6.2265I
u = 1.12196 + 1.05376I
a = 0.35846 + 1.45756I
b = −1.27526 − 1.24816I
−6.88799 − 11.14470I −17.5768 + 12.8416I
u = 1.12196 + 1.05376I
a = 0.167125 + 0.464153I
b = −0.949795 − 0.563580I
−1.50643 − 6.15314I −11.4850 + 11.0910I
u = 1.12196 + 1.05376I
a = −0.264501 − 0.301973I
b = 0.833776 + 0.377946I
−1.50643 − 1.96639I −11.48501 + 2.76537I
u = 1.12196 − 1.05376I
a = 0.935424 − 0.317876I
b = −1.352910 − 0.093439I
−7.66122 + 5.39594I −19.2841 − 7.6300I
u = 1.12196 − 1.05376I
a = −0.629892 + 0.828967I
b = 1.34287 − 0.48468I
−4.48831 + 4.05977I −20.6523 − 6.9282I
u = 1.12196 − 1.05376I
a = −0.072905 + 1.091850I
b = 0.773356 − 0.936297I
−1.50643 + 6.15314I −11.4850 − 11.0910I
u = 1.12196 − 1.05376I
a = 0.893999 − 0.030444I
b = −1.131990 − 0.328604I
−6.88799 − 3.02516I −17.5768 − 1.0149I
u = 1.12196 − 1.05376I
a = −0.004295 − 0.876976I
b = −0.558649 + 0.685116I
−1.50643 + 1.96639I −11.48501 − 2.76537I
u = 1.12196 − 1.05376I
a = 0.311224 − 0.732782I
b = −1.162730 + 0.365037I
−4.48831 + 4.05977I −20.6523 − 6.9282I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 − 1.05376I
a = −0.766136 + 0.158857I
b = 1.102540 + 0.125636I
−3.90681 + 1.60535I −14.3279 − 4.0152I
u = 1.12196 − 1.05376I
a = −0.170868 + 0.736807I
b = 1.30660 − 0.60299I
−7.66122 + 2.72360I −19.2841 − 6.2265I
u = 1.12196 − 1.05376I
a = −0.090223 + 0.707270I
b = 1.24928 − 0.73115I
−6.88799 + 11.14470I −17.5768 − 12.8416I
u = 1.12196 − 1.05376I
a = −0.302703 + 0.624434I
b = 0.901831 + 0.021552I
−7.66122 + 5.39594I −19.2841 − 7.6300I
u = 1.12196 − 1.05376I
a = 0.134083 − 0.676847I
b = −1.209800 + 0.658356I
−3.90681 + 6.51418I −14.3279 − 9.8412I
u = 1.12196 − 1.05376I
a = 0.210978 − 0.585167I
b = −0.677217 + 0.035293I
−3.90681 + 1.60535I −14.3279 − 4.0152I
u = 1.12196 − 1.05376I
a = −0.360671 + 1.339120I
b = 1.22641 − 1.11280I
−3.90681 + 6.51418I −14.3279 − 9.8412I
u = 1.12196 − 1.05376I
a = −0.255451 + 0.507035I
b = 0.645364 + 0.152056I
−6.88799 − 3.02516I −17.5768 − 1.0149I
u = 1.12196 − 1.05376I
a = 0.52832 − 1.34223I
b = −1.41527 + 1.04664I
−7.66122 + 2.72360I −19.2841 − 6.2265I
u = 1.12196 − 1.05376I
a = 0.35846 − 1.45756I
b = −1.27526 + 1.24816I
−6.88799 + 11.14470I −17.5768 − 12.8416I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12196 − 1.05376I
a = 0.167125 − 0.464153I
b = −0.949795 + 0.563580I
−1.50643 + 6.15314I −11.4850 − 11.0910I
u = 1.12196 − 1.05376I
a = −0.264501 + 0.301973I
b = 0.833776 − 0.377946I
−1.50643 + 1.96639I −11.48501 − 2.76537I
23
IV. I
u
4
= h8.05 × 10
32
a
17
u + 5.01 × 10
32
a
16
u + · · · − 7.33 × 10
32
a − 5.03 ×
10
33
, −2a
17
u + 3a
16
u + · · · + 36a + 9, u
2
− u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
6
=
a
−0.385900a
17
u − 0.240472a
16
u + ··· + 0.351634a + 2.41369
a
10
=
1
u − 1
a
5
=
−0.385900a
17
u − 0.240472a
16
u + ··· + 1.35163a + 2.41369
−0.385900a
17
u − 0.240472a
16
u + ··· + 0.351634a + 2.41369
a
1
=
0.171431a
17
u + 0.264717a
16
u + ··· − 21.2084a + 1.58429
0.218698a
17
u + 0.742566a
16
u + ··· − 33.7196a − 2.09684
a
4
=
0.398902a
17
u − 0.497063a
16
u + ··· + 6.40875a − 1.34451
−0.797803a
17
u + 0.994126a
16
u + ··· − 12.8175a + 2.68902
a
7
=
−0.385900a
17
u − 0.240472a
16
u + ··· + 2.35163a + 2.41369
0.385900a
17
u + 0.240472a
16
u + ··· − 1.35163a − 2.41369
a
8
=
0.115010a
17
u − 0.353110a
16
u + ··· + 15.4897a + 2.23782
0.185024a
17
u + 0.460788a
16
u + ··· + 9.03962a − 9.84163
a
11
=
−a
2
u
−0.0472669a
17
u − 0.477849a
16
u + ··· + 12.5112a + 3.68113
a
3
=
0.216648a
17
u − 0.531277a
16
u + ··· + 2.78395a − 2.13112
−0.232474a
17
u + 0.00880116a
16
u + ··· + 11.3610a + 3.70600
a
2
=
0.0834056a
17
u + 0.277553a
16
u + ··· − 43.0081a + 1.20610
−0.572218a
17
u + 0.212244a
16
u + ··· + 38.3797a − 9.86400
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00962865a
17
u − 0.477998a
16
u + ··· − 45.3429a + 35.5487
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
c
2
, c
7
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
4
c
3
, c
5
, c
10
c
12
u
36
+ u
35
+ ··· + 2u
2
+ 1
c
4
, c
11
u
36
+ 3u
35
+ ··· + 948u + 193
c
6
, c
9
(u
2
+ u + 1)
18
c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
4
c
2
, c
7
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
4
c
3
, c
5
, c
10
c
12
y
36
− 9y
35
+ ··· + 4y + 1
c
4
, c
11
y
36
− 21y
35
+ ··· + 837524y + 37249
c
6
, c
9
(y
2
+ y + 1)
18
c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.541983 + 0.836491I
b = −1.62386 − 0.82399I
−0.61694 − 6.51418I −2.32792 + 9.84118I
u = 0.500000 + 0.866025I
a = −0.603976 − 0.851109I
b = 1.76804 + 0.88879I
−3.59813 − 11.14470I −5.57680 + 12.84155I
u = 0.500000 + 0.866025I
a = −0.409962 − 0.969381I
b = 0.90415 + 1.09651I
1.78344 − 1.96639I 0.51499 + 2.76537I
u = 0.500000 + 0.866025I
a = 0.438782 + 0.957848I
b = −1.18925 − 1.06578I
1.78344 − 6.15314I 0.51499 + 11.09103I
u = 0.500000 + 0.866025I
a = −0.561919 − 0.738983I
b = 1.71694 + 0.61600I
−4.37135 − 2.72360I −7.28409 + 6.22645I
u = 0.500000 + 0.866025I
a = −0.992366 − 0.445735I
b = 0.253752 + 0.238566I
−0.61694 − 1.60535I −2.32792 + 4.01523I
u = 0.500000 + 0.866025I
a = −0.523373 − 0.642770I
b = 0.189893 + 0.743243I
−0.61694 − 1.60535I −2.32792 + 4.01523I
u = 0.500000 + 0.866025I
a = 0.257489 + 0.650379I
b = 0.036976 − 1.088490I
−3.59813 + 3.02516I −5.57680 + 1.01485I
u = 0.500000 + 0.866025I
a = 0.109500 + 0.594369I
b = −1.081850 − 0.202354I
−1.19845 − 4.05977I −8.65235 + 6.92820I
u = 0.500000 + 0.866025I
a = −1.26468 + 0.72630I
b = −0.136996 − 0.491540I
1.78344 − 1.96639I 0.51499 + 2.76537I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.10950 − 1.48180I
b = 0.825668 + 0.646069I
−1.19845 − 4.05977I −8.65235 + 6.92820I
u = 0.500000 + 0.866025I
a = 1.06039 + 1.13009I
b = −0.712881 − 0.379867I
−4.37135 − 5.39594I −7.28409 + 7.62995I
u = 0.500000 + 0.866025I
a = 1.45082 + 0.61223I
b = −0.526650 − 0.035958I
−3.59813 + 3.02516I −5.57680 + 1.01485I
u = 0.500000 + 0.866025I
a = 0.209456 + 0.248628I
b = 0.475959 − 0.676068I
−4.37135 − 5.39594I −7.28409 + 7.62995I
u = 0.500000 + 0.866025I
a = 1.23586 − 1.20093I
b = 0.281762 + 0.703896I
1.78344 − 6.15314I 0.51499 + 11.09103I
u = 0.500000 + 0.866025I
a = 0.97376 − 1.92500I
b = 0.551769 + 0.930683I
−0.61694 − 6.51418I −2.32792 + 9.84118I
u = 0.500000 + 0.866025I
a = −0.70793 + 2.11771I
b = −0.684016 − 0.938790I
−4.37135 − 2.72360I −7.28409 + 6.22645I
u = 0.500000 + 0.866025I
a = −1.10434 + 2.11371I
b = −0.549397 − 1.026950I
−3.59813 − 11.14470I −5.57680 + 12.84155I
u = 0.500000 − 0.866025I
a = 0.541983 − 0.836491I
b = −1.62386 + 0.82399I
−0.61694 + 6.51418I −2.32792 − 9.84118I
u = 0.500000 − 0.866025I
a = −0.603976 + 0.851109I
b = 1.76804 − 0.88879I
−3.59813 + 11.14470I −5.57680 − 12.84155I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −0.409962 + 0.969381I
b = 0.90415 − 1.09651I
1.78344 + 1.96639I 0.51499 − 2.76537I
u = 0.500000 − 0.866025I
a = 0.438782 − 0.957848I
b = −1.18925 + 1.06578I
1.78344 + 6.15314I 0.51499 − 11.09103I
u = 0.500000 − 0.866025I
a = −0.561919 + 0.738983I
b = 1.71694 − 0.61600I
−4.37135 + 2.72360I −7.28409 − 6.22645I
u = 0.500000 − 0.866025I
a = −0.992366 + 0.445735I
b = 0.253752 − 0.238566I
−0.61694 + 1.60535I −2.32792 − 4.01523I
u = 0.500000 − 0.866025I
a = −0.523373 + 0.642770I
b = 0.189893 − 0.743243I
−0.61694 + 1.60535I −2.32792 − 4.01523I
u = 0.500000 − 0.866025I
a = 0.257489 − 0.650379I
b = 0.036976 + 1.088490I
−3.59813 − 3.02516I −5.57680 − 1.01485I
u = 0.500000 − 0.866025I
a = 0.109500 − 0.594369I
b = −1.081850 + 0.202354I
−1.19845 + 4.05977I −8.65235 − 6.92820I
u = 0.500000 − 0.866025I
a = −1.26468 − 0.72630I
b = −0.136996 + 0.491540I
1.78344 + 1.96639I 0.51499 − 2.76537I
u = 0.500000 − 0.866025I
a = −0.10950 + 1.48180I
b = 0.825668 − 0.646069I
−1.19845 + 4.05977I −8.65235 − 6.92820I
u = 0.500000 − 0.866025I
a = 1.06039 − 1.13009I
b = −0.712881 + 0.379867I
−4.37135 + 5.39594I −7.28409 − 7.62995I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 1.45082 − 0.61223I
b = −0.526650 + 0.035958I
−3.59813 − 3.02516I −5.57680 − 1.01485I
u = 0.500000 − 0.866025I
a = 0.209456 − 0.248628I
b = 0.475959 + 0.676068I
−4.37135 + 5.39594I −7.28409 − 7.62995I
u = 0.500000 − 0.866025I
a = 1.23586 + 1.20093I
b = 0.281762 − 0.703896I
1.78344 + 6.15314I 0.51499 − 11.09103I
u = 0.500000 − 0.866025I
a = 0.97376 + 1.92500I
b = 0.551769 − 0.930683I
−0.61694 + 6.51418I −2.32792 − 9.84118I
u = 0.500000 − 0.866025I
a = −0.70793 − 2.11771I
b = −0.684016 + 0.938790I
−4.37135 + 2.72360I −7.28409 − 6.22645I
u = 0.500000 − 0.866025I
a = −1.10434 − 2.11371I
b = −0.549397 + 1.026950I
−3.59813 + 11.14470I −5.57680 − 12.84155I
30
V.
I
u
5
= h1.00 × 10
26
u
37
− 1.31 × 10
27
u
36
+ · · · + 8.88 × 10
25
b − 1.96 × 10
26
, 9.58 ×
10
25
u
37
−1.34×10
27
u
36
+· · ·+8.88×10
25
a−6.26×10
25
, u
38
−14u
37
+· · ·+u+1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
6
=
−1.07846u
37
+ 15.0328u
36
+ ··· − 1.32859u + 0.705098
−1.12838u
37
+ 14.7346u
36
+ ··· + 5.11878u + 2.20684
a
10
=
1
u
2
a
5
=
−2.20684u
37
+ 29.7674u
36
+ ··· + 3.79019u + 2.91194
−1.12838u
37
+ 14.7346u
36
+ ··· + 5.11878u + 2.20684
a
1
=
1.14500u
37
− 13.8852u
36
+ ··· − 5.28452u − 6.30863
2.14475u
37
− 29.3644u
36
+ ··· − 6.45362u − 1.14500
a
4
=
−2.14118u
37
+ 29.5971u
36
+ ··· + 2.00663u + 1.83348
0.711034u
37
− 7.98714u
36
+ ··· + 4.30409u + 1.45781
a
7
=
−1.29908u
37
+ 18.2134u
36
+ ··· + 3.34374u − 5.63126
−0.348895u
37
+ 4.27392u
36
+ ··· − 1.33584u + 1.26983
a
8
=
−2.04475u
37
+ 26.4077u
36
+ ··· − 8.11017u + 6.02040
−1.55656u
37
+ 20.0352u
36
+ ··· + 3.77539u − 0.100008
a
11
=
−2.48235u
37
+ 35.5630u
36
+ ··· + 6.33298u − 6.16339
1.48260u
37
− 20.0838u
36
+ ··· − 3.16387u + 0.999756
a
3
=
0.353686u
37
− 8.41298u
36
+ ··· + 2.42110u + 7.48022
−3.06937u
37
+ 42.9880u
36
+ ··· + 9.94450u + 2.74494
a
2
=
5.94574u
37
− 82.0649u
36
+ ··· − 3.71762u + 7.45689
0.912713u
37
− 8.80065u
36
+ ··· + 3.88952u − 2.58106
(ii) Obstruction class = 1
(iii) Cusp Shapes =
492727574785899921881516631
88808490307033734347531651
u
37
−
6194406854275124730621113225
88808490307033734347531651
u
36
+
··· −
3077658052047205031838876941
88808490307033734347531651
u −
1759778284097884737803921371
88808490307033734347531651
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
− 11u
18
+ ··· − 2u + 1)
2
c
2
, c
7
u
38
− 11u
36
+ ··· − 2u
2
+ 1
c
3
, c
10
u
38
− 2u
37
+ ··· − 5u + 1
c
4
, c
11
u
38
+ 11u
36
+ ··· + 39u
2
+ 1
c
5
, c
12
u
38
+ 2u
37
+ ··· + 5u + 1
c
6
u
38
+ 14u
37
+ ··· − u + 1
c
8
u
38
− 39u
34
+ ··· − 12u
2
+ 1
c
9
u
38
− 14u
37
+ ··· + u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ y
18
+ ··· + 34y − 1)
2
c
2
, c
7
(y
19
− 11y
18
+ ··· − 2y + 1)
2
c
3
, c
5
, c
10
c
12
y
38
− 14y
37
+ ··· + 31y + 1
c
4
, c
11
(y
19
+ 11y
18
+ ··· + 39y + 1)
2
c
6
, c
9
y
38
− 20y
37
+ ··· − 21y + 1
c
8
(y
19
− 39y
17
+ ··· − 12y + 1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968758 + 0.176842I
a = 0.033254 + 0.182169I
b = −0.999984 + 0.176661I
−3.32952 −11.83134 + 0.I
u = 0.968758 − 0.176842I
a = 0.033254 − 0.182169I
b = −0.999984 − 0.176661I
−3.32952 −11.83134 + 0.I
u = −0.579538 + 0.657340I
a = −0.943026 + 1.017610I
b = 0.205604 − 0.680250I
−6.22842 + 5.39858I −13.3102 − 7.2958I
u = −0.579538 − 0.657340I
a = −0.943026 − 1.017610I
b = 0.205604 + 0.680250I
−6.22842 − 5.39858I −13.3102 + 7.2958I
u = 0.989111 + 0.541052I
a = −0.374160 − 0.278889I
b = 0.875497 − 0.422743I
−6.16647 + 4.01607I −12.51721 − 5.30034I
u = 0.989111 − 0.541052I
a = −0.374160 + 0.278889I
b = 0.875497 + 0.422743I
−6.16647 − 4.01607I −12.51721 + 5.30034I
u = 0.754554 + 0.921192I
a = −0.130405 + 0.889071I
b = −0.805968 − 0.781140I
−0.09286 − 5.79250I 0. + 9.57133I
u = 0.754554 − 0.921192I
a = −0.130405 − 0.889071I
b = −0.805968 + 0.781140I
−0.09286 + 5.79250I 0. − 9.57133I
u = 0.689684 + 0.304524I
a = 0.009715 − 0.697784I
b = 1.130350 − 0.432057I
−6.16647 − 4.01607I −12.51721 + 5.30034I
u = 0.689684 − 0.304524I
a = 0.009715 + 0.697784I
b = 1.130350 + 0.432057I
−6.16647 + 4.01607I −12.51721 − 5.30034I
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206852 + 0.719847I
a = −0.36842 − 1.38031I
b = 0.979786 + 0.194884I
−0.09286 − 5.79250I −5.01784 + 9.57133I
u = 0.206852 − 0.719847I
a = −0.36842 + 1.38031I
b = 0.979786 − 0.194884I
−0.09286 + 5.79250I −5.01784 − 9.57133I
u = 0.450422 + 0.588996I
a = −0.260946 + 1.313780I
b = −1.152450 − 0.438017I
−0.21041 − 2.23415I −4.27004 + 3.35920I
u = 0.450422 − 0.588996I
a = −0.260946 − 1.313780I
b = −1.152450 + 0.438017I
−0.21041 + 2.23415I −4.27004 − 3.35920I
u = 0.648553 + 1.127180I
a = 0.049855 − 0.762092I
b = 0.578914 + 0.610276I
−0.21041 − 2.23415I 0
u = 0.648553 − 1.127180I
a = 0.049855 + 0.762092I
b = 0.578914 − 0.610276I
−0.21041 + 2.23415I 0
u = 1.023480 + 0.941692I
a = −0.104442 − 1.057930I
b = 1.22994 + 0.97508I
−6.07851 − 10.59750I 0
u = 1.023480 − 0.941692I
a = −0.104442 + 1.057930I
b = 1.22994 − 0.97508I
−6.07851 + 10.59750I 0
u = 1.051710 + 0.921697I
a = 0.127410 + 0.955311I
b = −1.16836 − 0.87547I
−3.13428 − 5.88725I 0
u = 1.051710 − 0.921697I
a = 0.127410 − 0.955311I
b = −1.16836 + 0.87547I
−3.13428 + 5.88725I 0
35
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05571 + 0.97125I
a = −0.276111 − 1.011390I
b = 1.33028 + 0.78757I
−6.96832 − 2.20792I 0
u = 1.05571 − 0.97125I
a = −0.276111 + 1.011390I
b = 1.33028 − 0.78757I
−6.96832 + 2.20792I 0
u = −0.450018 + 0.294282I
a = −2.30414 + 0.98679I
b = 0.645307 − 0.642915I
−3.13428 − 5.88725I −6.10322 + 3.33579I
u = −0.450018 − 0.294282I
a = −2.30414 − 0.98679I
b = 0.645307 + 0.642915I
−3.13428 + 5.88725I −6.10322 − 3.33579I
u = −0.503149 + 0.186021I
a = 0.28442 − 2.60224I
b = 0.112954 + 0.920226I
−4.01271 + 3.94421I −0.80843 − 2.14732I
u = −0.503149 − 0.186021I
a = 0.28442 + 2.60224I
b = 0.112954 − 0.920226I
−4.01271 − 3.94421I −0.80843 + 2.14732I
u = 1.08335 + 1.05071I
a = 0.466233 + 0.805227I
b = −1.262780 − 0.424688I
−4.01271 − 3.94421I 0
u = 1.08335 − 1.05071I
a = 0.466233 − 0.805227I
b = −1.262780 + 0.424688I
−4.01271 + 3.94421I 0
u = −0.409291 + 0.110056I
a = 2.39251 − 2.62061I
b = −0.560795 + 0.904131I
−6.96832 − 2.20792I −9.88914 − 0.83240I
u = −0.409291 − 0.110056I
a = 2.39251 + 2.62061I
b = −0.560795 − 0.904131I
−6.96832 + 2.20792I −9.88914 + 0.83240I
36
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323511 + 0.265038I
a = 3.43477 − 0.83700I
b = −0.817872 + 0.728634I
−6.07851 − 10.59750I −8.79802 + 6.88476I
u = −0.323511 − 0.265038I
a = 3.43477 + 0.83700I
b = −0.817872 − 0.728634I
−6.07851 + 10.59750I −8.79802 − 6.88476I
u = 1.07221 + 1.23787I
a = −0.509379 − 0.540089I
b = 0.968129 + 0.155352I
−6.22842 − 5.39858I 0
u = 1.07221 − 1.23787I
a = −0.509379 + 0.540089I
b = 0.968129 − 0.155352I
−6.22842 + 5.39858I 0
u = 1.75690 + 0.41553I
a = 0.040049 + 0.451631I
b = −0.332418 − 0.887807I
0.01311 − 3.38613I 0
u = 1.75690 − 0.41553I
a = 0.040049 − 0.451631I
b = −0.332418 + 0.887807I
0.01311 + 3.38613I 0
u = −2.48579 + 0.15450I
a = −0.067185 + 0.321722I
b = 0.043866 − 0.230460I
0.01311 − 3.38613I 0
u = −2.48579 − 0.15450I
a = −0.067185 − 0.321722I
b = 0.043866 + 0.230460I
0.01311 + 3.38613I 0
37
VI. I
u
6
= hb
2
+ ba − a
2
− 1, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
6
=
a
b
a
10
=
1
1
a
5
=
b + a
b
a
1
=
−ba − 2a
2
− 1
−a
2
a
4
=
b + 2a
b + a
a
7
=
−b − a
−a
a
8
=
a
3
b + 2a
4
+ a
2
+ 1
a
4
a
11
=
−a
2
−ba + 1
a
3
=
a
2
b + a
3
+ b + 2a
a
3
+ a
a
2
=
−a
7
b − a
8
− 2a
5
b − 3a
6
− 2a
3
b − 3a
4
− 2ba − 4a
2
− 1
−a
8
− 2a
6
− 2a
4
− 2a
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4a
7
− 4a
6
+ 4a
5
− 4a
4
+ 8a
3
− 4a
2
− 18
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
2
c
2
, c
7
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
2
c
3
, c
5
, c
10
c
12
u
18
− u
17
+ ··· + 6u − 1
c
4
, c
11
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
2
c
6
, c
9
(u + 1)
18
c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
2
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
2
c
2
, c
7
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
2
c
3
, c
5
, c
10
c
12
y
18
− 9y
17
+ ··· − 36y + 1
c
4
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
2
c
6
, c
9
(y − 1)
18
c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
2
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.140343 + 0.966856I
b = 0.405278 − 0.989579I
−1.50643 + 2.09337I −11.48501 − 4.16283I
u = 1.00000
a = −0.140343 + 0.966856I
b = −0.264935 + 0.022723I
−1.50643 + 2.09337I −11.48501 − 4.16283I
u = 1.00000
a = −0.140343 − 0.966856I
b = 0.405278 + 0.989579I
−1.50643 − 2.09337I −11.48501 + 4.16283I
u = 1.00000
a = −0.140343 − 0.966856I
b = −0.264935 − 0.022723I
−1.50643 − 2.09337I −11.48501 + 4.16283I
u = 1.00000
a = −0.628449 + 0.875112I
b = −0.688833 + 0.247803I
−3.90681 + 2.45442I −14.3279 − 2.9130I
u = 1.00000
a = −0.628449 + 0.875112I
b = 1.31728 − 1.12291I
−3.90681 + 2.45442I −14.3279 − 2.9130I
u = 1.00000
a = −0.628449 − 0.875112I
b = −0.688833 − 0.247803I
−3.90681 − 2.45442I −14.3279 + 2.9130I
u = 1.00000
a = −0.628449 − 0.875112I
b = 1.31728 + 1.12291I
−3.90681 − 2.45442I −14.3279 + 2.9130I
u = 1.00000
a = 0.796005 + 0.733148I
b = 0.818454 + 0.233108I
−7.66122 + 1.33617I −19.2841 − 0.7017I
u = 1.00000
a = 0.796005 + 0.733148I
b = −1.61446 − 0.96626I
−7.66122 + 1.33617I −19.2841 − 0.7017I
41
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.796005 − 0.733148I
b = 0.818454 − 0.233108I
−7.66122 − 1.33617I −19.2841 + 0.7017I
u = 1.00000
a = 0.796005 − 0.733148I
b = −1.61446 + 0.96626I
−7.66122 − 1.33617I −19.2841 + 0.7017I
u = 1.00000
a = 0.728966 + 0.986295I
b = 0.708074 + 0.344774I
−6.88799 − 7.08493I −17.5768 + 5.9133I
u = 1.00000
a = 0.728966 + 0.986295I
b = −1.43704 − 1.33107I
−6.88799 − 7.08493I −17.5768 + 5.9133I
u = 1.00000
a = 0.728966 − 0.986295I
b = 0.708074 − 0.344774I
−6.88799 + 7.08493I −17.5768 − 5.9133I
u = 1.00000
a = 0.728966 − 0.986295I
b = −1.43704 + 1.33107I
−6.88799 + 7.08493I −17.5768 − 5.9133I
u = 1.00000
a = −0.512358
b = −0.896270
−4.48831 −20.6520
u = 1.00000
a = −0.512358
b = 1.40863
−4.48831 −20.6520
42
VII. I
u
7
= hb + 1, a, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
6
=
0
−1
a
10
=
1
1
a
5
=
−1
−1
a
1
=
−1
0
a
4
=
−1
−1
a
7
=
1
0
a
8
=
1
0
a
11
=
0
1
a
3
=
−1
0
a
2
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
11
u
c
3
, c
6
, c
10
u + 1
c
5
, c
9
, c
12
u − 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
11
y
c
3
, c
5
, c
6
c
9
, c
10
, c
12
y − 1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
46
VIII. I
v
1
= ha, b
9
+ b
8
+ 2b
7
+ b
6
+ 3b
5
+ b
4
+ 2b
3
+ b − 1, v − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
1
0
a
6
=
0
b
a
10
=
1
0
a
5
=
b
b
a
1
=
b
2
+ 1
b
2
a
4
=
0
b
a
7
=
0
b
a
8
=
b
4
+ b
2
+ 1
b
4
a
11
=
1
b
2
a
3
=
b
b
3
+ b
a
2
=
b
6
+ b
4
+ 2b
2
+ 1
b
8
+ 2b
6
+ 2b
4
+ 2b
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
7
− 4b
6
− 4b
5
− 4b
4
− 8b
3
− 4b
2
− 6
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
2
, c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
3
, c
4
, c
5
c
10
, c
11
, c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
, c
9
u
9
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
2
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
3
, c
4
, c
5
c
10
, c
11
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
6
, c
9
y
9
c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.140343 + 0.966856I
1.78344 − 2.09337I 0.51499 + 4.16283I
v = 1.00000
a = 0
b = 0.140343 − 0.966856I
1.78344 + 2.09337I 0.51499 − 4.16283I
v = 1.00000
a = 0
b = 0.628449 + 0.875112I
−0.61694 − 2.45442I −2.32792 + 2.91298I
v = 1.00000
a = 0
b = 0.628449 − 0.875112I
−0.61694 + 2.45442I −2.32792 − 2.91298I
v = 1.00000
a = 0
b = −0.796005 + 0.733148I
−4.37135 − 1.33617I −7.28409 + 0.70175I
v = 1.00000
a = 0
b = −0.796005 − 0.733148I
−4.37135 + 1.33617I −7.28409 − 0.70175I
v = 1.00000
a = 0
b = −0.728966 + 0.986295I
−3.59813 + 7.08493I −5.57680 − 5.91335I
v = 1.00000
a = 0
b = −0.728966 − 0.986295I
−3.59813 − 7.08493I −5.57680 + 5.91335I
v = 1.00000
a = 0
b = 0.512358
−1.19845 −8.65230
50
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
15
· ((u
13
+ 6u
12
+ ··· + 12u + 16)
2
)(u
19
− 11u
18
+ ··· − 2u + 1)
2
· (u
20
+ 10u
19
+ ··· − 160u + 64)
c
2
, c
7
u(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
14
· ((u
13
− 4u
12
+ ··· − 14u + 4)
2
)(u
20
− 6u
19
+ ··· − 40u + 8)
· (u
38
− 11u
36
+ ··· − 2u
2
+ 1)
c
3
, c
10
(u + 1)(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
18
− u
17
+ ··· + 6u − 1)(u
20
+ u
19
+ ··· − u + 1)(u
26
+ u
25
+ ··· + u + 1)
· (u
36
+ u
35
+ ··· + 2u
2
+ 1)(u
38
− 2u
37
+ ··· − 5u + 1)
· (u
72
− u
71
+ ··· + 276774u + 52573)
c
4
, c
11
u(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
· (u
13
+ u
11
+ u
10
− 2u
7
− u
6
− u
5
− 2u
4
+ u
3
+ u
2
+ u + 1)
2
· (u
20
+ u
19
+ ··· + 2u + 26)(u
36
− u
35
+ ··· − 248u + 4921)
2
· (u
36
+ 3u
35
+ ··· + 948u + 193)(u
38
+ 11u
36
+ ··· + 39u
2
+ 1)
c
5
, c
12
(u − 1)(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
18
− u
17
+ ··· + 6u − 1)(u
20
+ u
19
+ ··· − u + 1)(u
26
+ u
25
+ ··· + u + 1)
· (u
36
+ u
35
+ ··· + 2u
2
+ 1)(u
38
+ 2u
37
+ ··· + 5u + 1)
· (u
72
− u
71
+ ··· + 276774u + 52573)
c
6
u
9
(u + 1)
19
(u
2
+ u + 1)
18
(u
4
+ u
3
− 2u + 1)
18
· (u
20
− 19u
19
+ ··· − 4045u + 419)
· (u
26
− 27u
25
+ ··· − 29107u + 2239)(u
38
+ 14u
37
+ ··· − u + 1)
c
8
u(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
14
· ((u
13
− 12u
12
+ ··· + 210u + 4)
2
)(u
20
− 18u
19
+ ··· − 24920u + 3688)
· (u
38
− 39u
34
+ ··· − 12u
2
+ 1)
c
9
u
9
(u − 1)(u + 1)
18
(u
2
+ u + 1)
18
(u
4
+ u
3
− 2u + 1)
18
· (u
20
− 19u
19
+ ··· − 4045u + 419)
· (u
26
− 27u
25
+ ··· − 29107u + 2239)(u
38
− 14u
37
+ ··· + u + 1)
51
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
15
· ((y
13
+ 2y
12
+ ··· − 656y − 256)
2
)(y
19
+ y
18
+ ··· + 34y − 1)
2
· (y
20
− 2y
19
+ ··· − 23040y + 4096)
c
2
, c
7
y(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
15
· ((y
13
− 6y
12
+ ··· + 12y − 16)
2
)(y
19
− 11y
18
+ ··· − 2y + 1)
2
· (y
20
− 10y
19
+ ··· + 160y + 64)
c
3
, c
5
, c
10
c
12
(y − 1)(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
18
− 9y
17
+ ··· − 36y + 1)(y
20
− y
19
+ ··· + 11y + 1)
· (y
26
− 3y
25
+ ··· − y + 1)(y
36
− 9y
35
+ ··· + 4y + 1)
· (y
38
− 14y
37
+ ··· + 31y + 1)
· (y
72
− 27y
71
+ ··· − 85049384088y + 2763920329)
c
4
, c
11
y(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· ((y
13
+ 2y
12
+ ··· − y − 1)
2
)(y
19
+ 11y
18
+ ··· + 39y + 1)
2
· (y
20
+ 21y
19
+ ··· + 10448y + 676)
· (y
36
− 21y
35
+ ··· + 837524y + 37249)
· (y
36
+ 39y
35
+ ··· + 446076356y + 24216241)
2
c
6
, c
9
y
9
(y − 1)
19
(y
2
+ y + 1)
18
(y
4
− y
3
+ 6y
2
− 4y + 1)
18
· (y
20
− 9y
19
+ ··· − 853997y + 175561)
· (y
26
− 13y
25
+ ··· + 24344647y + 5013121)
· (y
38
− 20y
37
+ ··· − 21y + 1)
c
8
y(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
15
· ((y
13
+ 2y
12
+ ··· + 52908y − 16)
2
)(y
19
− 39y
17
+ ··· − 12y + 1)
2
· (y
20
− 4y
19
+ ··· + 14317984y + 13601344)
52
