12n
0877
(K12n
0877
)
A knot diagram
1
Linearized knot diagam
4 8 6 11 1 2 10 2 12 5 7 8
Solving Sequence
2,8 4,9
1 12 10 7 6 3 5 11
c
8
c
1
c
12
c
9
c
7
c
6
c
3
c
5
c
11
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.35659 × 10
83
u
36
− 2.27819 × 10
84
u
35
+ ··· + 9.11104 × 10
86
b + 1.23806 × 10
87
,
− 2.69779 × 10
87
u
36
− 1.19660 × 10
88
u
35
+ ··· + 1.76754 × 10
89
a − 1.89107 × 10
90
,
u
37
+ 5u
36
+ ··· + 2744u + 388i
I
u
2
= h3.32625 × 10
77
au
42
− 3.27571 × 10
78
u
42
+ ··· + 1.71826 × 10
79
a − 1.65861 × 10
80
,
5.05212 × 10
81
au
42
− 1.09660 × 10
82
u
42
+ ··· + 1.99839 × 10
83
a − 3.99060 × 10
83
,
u
43
− 3u
42
+ ··· + 110u − 17i
I
u
3
= h2.20191 × 10
25
u
39
+ 2.35786 × 10
25
u
38
+ ··· + 1.03004 × 10
24
b − 1.37061 × 10
27
,
− 7.73943 × 10
26
u
39
− 1.52201 × 10
26
u
38
+ ··· + 1.95708 × 10
25
a + 9.28110 × 10
27
,
u
40
− 6u
38
+ ··· − 255u
2
− 19i
I
u
4
= hb, a
2
− a + 1, u + 1i
I
u
5
= hb − 2a, a
2
− a + 1, u − 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 169 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−9.36 × 10
83
u
36
− 2.28 × 10
84
u
35
+ · · · + 9.11 × 10
86
b + 1.24 ×
10
87
, −2.70 × 10
87
u
36
− 1.20 × 10
88
u
35
+ · · · + 1.77 × 10
89
a − 1.89 ×
10
90
, u
37
+ 5u
36
+ · · · + 2744u + 388i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
4
=
0.0152630u
36
+ 0.0676983u
35
+ ··· + 58.5223u + 10.6989
0.00102695u
36
+ 0.00250048u
35
+ ··· − 1.09050u − 1.35885
a
9
=
1
−u
2
a
1
=
0.0180233u
36
+ 0.0813561u
35
+ ··· + 78.6888u + 17.0783
0.00546745u
36
+ 0.0219598u
35
+ ··· + 15.1454u + 2.22914
a
12
=
0.0125559u
36
+ 0.0593963u
35
+ ··· + 63.5435u + 14.8491
0.00546745u
36
+ 0.0219598u
35
+ ··· + 15.1454u + 2.22914
a
10
=
0.00350220u
36
+ 0.0185379u
35
+ ··· + 25.9914u + 8.51953
0.00861657u
36
+ 0.0375921u
35
+ ··· + 31.1827u + 5.92203
a
7
=
−0.00574521u
36
− 0.0232586u
35
+ ··· − 14.5732u − 0.619490
0.00876059u
36
+ 0.0373042u
35
+ ··· + 32.3778u + 6.99306
a
6
=
−0.00574521u
36
− 0.0232586u
35
+ ··· − 14.5732u − 0.619490
0.00338316u
36
+ 0.0164838u
35
+ ··· + 19.6043u + 4.87169
a
3
=
u
u
a
5
=
0.0216125u
36
+ 0.0975640u
35
+ ··· + 96.4003u + 24.3397
0.0235451u
36
+ 0.0984750u
35
+ ··· + 81.0110u + 16.7723
a
11
=
0.0432275u
36
+ 0.192592u
35
+ ··· + 178.923u + 37.6052
−0.0104986u
36
− 0.0434372u
35
+ ··· − 34.9650u − 8.38565
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0638114u
36
− 0.256490u
35
+ ··· − 174.364u − 30.2157
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
37
− u
36
+ ··· + 8u − 1
c
2
, c
8
u
37
+ 5u
36
+ ··· + 2744u + 388
c
3
, c
9
u
37
+ u
36
+ ··· + 2u + 1
c
4
, c
10
u
37
+ 5u
36
+ ··· + 184u + 52
c
5
, c
11
u
37
+ u
36
+ ··· − 4u + 4
c
6
, c
12
u
37
− u
36
+ ··· − 104u − 47
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
37
− 11y
36
+ ··· + 32y −1
c
2
, c
8
y
37
− 23y
36
+ ··· + 3132720y −150544
c
3
, c
9
y
37
− 37y
36
+ ··· + 30y −1
c
4
, c
10
y
37
+ 13y
36
+ ··· − 5872y −2704
c
5
, c
11
y
37
− 5y
36
+ ··· − 976y −16
c
6
, c
12
y
37
− 31y
36
+ ··· + 16456y −2209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.023680 + 0.207468I
a = −0.224911 + 0.827302I
b = 0.956147 + 0.338744I
5.14523 − 0.88050I 13.89731 − 1.40909I
u = −1.023680 − 0.207468I
a = −0.224911 − 0.827302I
b = 0.956147 − 0.338744I
5.14523 + 0.88050I 13.89731 + 1.40909I
u = −0.513603 + 0.927764I
a = −0.362915 + 1.130270I
b = −0.266581 + 1.169590I
−2.71819 − 6.93203I 1.49325 + 6.38376I
u = −0.513603 − 0.927764I
a = −0.362915 − 1.130270I
b = −0.266581 − 1.169590I
−2.71819 + 6.93203I 1.49325 − 6.38376I
u = −0.203243 + 0.874057I
a = 0.21000 + 1.77056I
b = −0.05883 + 1.53025I
−5.67964 + 1.01449I 4.29448 − 6.92334I
u = −0.203243 − 0.874057I
a = 0.21000 − 1.77056I
b = −0.05883 − 1.53025I
−5.67964 − 1.01449I 4.29448 + 6.92334I
u = 0.393345 + 0.759798I
a = 0.341465 + 0.953652I
b = 0.130643 + 0.919943I
−0.18355 + 2.03501I 3.27155 − 3.11294I
u = 0.393345 − 0.759798I
a = 0.341465 − 0.953652I
b = 0.130643 − 0.919943I
−0.18355 − 2.03501I 3.27155 + 3.11294I
u = −0.259763 + 1.213030I
a = 0.172358 + 0.907964I
b = 0.13042 + 1.58902I
−5.01261 + 1.59452I −0.74857 − 4.14264I
u = −0.259763 − 1.213030I
a = 0.172358 − 0.907964I
b = 0.13042 − 1.58902I
−5.01261 − 1.59452I −0.74857 + 4.14264I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.255890 + 0.068162I
a = −0.132967 + 0.395325I
b = −1.177290 + 0.087112I
3.63356 + 3.81297I 10.07806 − 5.49647I
u = 1.255890 − 0.068162I
a = −0.132967 − 0.395325I
b = −1.177290 − 0.087112I
3.63356 − 3.81297I 10.07806 + 5.49647I
u = −0.452009 + 0.440661I
a = 1.136500 + 0.492247I
b = −0.989885 − 0.684757I
−1.67227 + 2.60991I −2.01632 − 5.81175I
u = −0.452009 − 0.440661I
a = 1.136500 − 0.492247I
b = −0.989885 + 0.684757I
−1.67227 − 2.60991I −2.01632 + 5.81175I
u = −1.381620 + 0.001380I
a = −0.716115 + 0.134351I
b = −0.596037 + 0.248959I
0.77318 + 3.37059I −2.04958 − 4.00982I
u = −1.381620 − 0.001380I
a = −0.716115 − 0.134351I
b = −0.596037 − 0.248959I
0.77318 − 3.37059I −2.04958 + 4.00982I
u = 1.45601
a = 0.621894
b = 0.272503
3.33967 2.87470
u = 0.473903 + 0.174617I
a = 0.614985 + 0.716675I
b = 0.514605 + 0.316308I
1.022900 + 0.779663I 7.50935 − 3.53502I
u = 0.473903 − 0.174617I
a = 0.614985 − 0.716675I
b = 0.514605 − 0.316308I
1.022900 − 0.779663I 7.50935 + 3.53502I
u = −0.04479 + 1.52449I
a = −0.568234 + 0.602533I
b = 0.29065 + 1.60332I
2.46403 − 4.84771I 7.83065 + 5.43608I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04479 − 1.52449I
a = −0.568234 − 0.602533I
b = 0.29065 − 1.60332I
2.46403 + 4.84771I 7.83065 − 5.43608I
u = −1.53849 + 0.44250I
a = −0.509830 − 0.453544I
b = 1.61671 − 1.81990I
−0.30645 − 7.70638I 0. + 7.90475I
u = −1.53849 − 0.44250I
a = −0.509830 + 0.453544I
b = 1.61671 + 1.81990I
−0.30645 + 7.70638I 0. − 7.90475I
u = −0.353652 + 0.059931I
a = −1.80596 + 0.93479I
b = −0.562272 − 0.178009I
−0.91481 + 3.77913I 5.64104 − 2.45174I
u = −0.353652 − 0.059931I
a = −1.80596 − 0.93479I
b = −0.562272 + 0.178009I
−0.91481 − 3.77913I 5.64104 + 2.45174I
u = −1.67250
a = −0.101046
b = 2.66187
8.44157 14.5320
u = −1.45646 + 0.84376I
a = −0.737564 + 0.407660I
b = 0.303225 + 0.408038I
6.74334 − 2.70316I 0
u = −1.45646 − 0.84376I
a = −0.737564 − 0.407660I
b = 0.303225 − 0.408038I
6.74334 + 2.70316I 0
u = 1.74832
a = 0.405395
b = −3.70278
7.10544 0
u = −0.00849 + 1.76143I
a = 0.643665 + 0.717640I
b = −0.11867 + 1.49405I
−0.02411 + 10.88880I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00849 − 1.76143I
a = 0.643665 − 0.717640I
b = −0.11867 − 1.49405I
−0.02411 − 10.88880I 0
u = 1.66398 + 0.63157I
a = 0.300742 − 0.721731I
b = −0.84961 − 2.41654I
8.0218 + 12.6732I 0
u = 1.66398 − 0.63157I
a = 0.300742 + 0.721731I
b = −0.84961 + 2.41654I
8.0218 − 12.6732I 0
u = −1.66761 + 0.70883I
a = −0.330845 − 0.831651I
b = 0.67399 − 2.28474I
5.3307 − 19.4688I 0
u = −1.66761 − 0.70883I
a = −0.330845 + 0.831651I
b = 0.67399 + 2.28474I
5.3307 + 19.4688I 0
u = 1.85036 + 0.61716I
a = 0.769394 + 0.240989I
b = −0.113001 + 0.215300I
6.00980 − 1.88404I 0
u = 1.85036 − 0.61716I
a = 0.769394 − 0.240989I
b = −0.113001 − 0.215300I
6.00980 + 1.88404I 0
8
II. I
u
2
= h3.33 × 10
77
au
42
− 3.28 × 10
78
u
42
+ · · · + 1.72 × 10
79
a − 1.66 ×
10
80
, 5.05 × 10
81
au
42
− 1.10 × 10
82
u
42
+ · · · + 2.00 × 10
83
a − 3.99 ×
10
83
, u
43
− 3u
42
+ · · · + 110u − 17i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
4
=
a
−0.00287322au
42
+ 0.0282956u
42
+ ··· − 0.148423a + 1.43271
a
9
=
1
−u
2
a
1
=
−0.0460162au
42
+ 0.106090u
42
+ ··· − 2.56707a + 5.57201
0.00293218au
42
− 0.0252712u
42
+ ··· + 0.473351a − 0.516706
a
12
=
−0.0489483au
42
+ 0.131361u
42
+ ··· − 3.04042a + 6.08871
0.00293218au
42
− 0.0252712u
42
+ ··· + 0.473351a − 0.516706
a
10
=
0.00873077au
42
+ 0.106037u
42
+ ··· − 1.17990a + 5.44946
0.0460162u
42
− 0.137175u
41
+ ··· − 10.6374u + 2.56707
a
7
=
−0.0278442au
42
− 0.0717915u
42
+ ··· − 1.80262a − 7.63595
−0.000873541au
42
− 0.0982682u
42
+ ··· − 0.782275a − 4.47485
a
6
=
−0.0278442au
42
− 0.0717915u
42
+ ··· − 1.80262a − 7.63595
−0.00293545au
42
− 0.0837892u
42
+ ··· − 0.832122a − 3.94930
a
3
=
u
u
a
5
=
0.00984394au
42
− 0.125943u
42
+ ··· + 1.79971a − 5.22417
0.00422200au
42
− 0.0543645u
42
+ ··· − 0.723111a − 3.46387
a
11
=
−0.0425359au
42
− 0.0109791u
42
+ ··· − 3.72010a + 0.0400840
−0.00613998au
42
− 0.0134470u
42
+ ··· − 0.167347a − 0.720202
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.260099u
42
− 0.756964u
41
+ ··· − 62.4522u + 23.1375
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
86
− 7u
85
+ ··· − 55u + 3
c
2
, c
8
(u
43
− 3u
42
+ ··· + 110u − 17)
2
c
3
, c
9
u
86
+ 4u
85
+ ··· + 3742879u + 515187
c
4
, c
10
(u
43
− 2u
42
+ ··· + 8u − 5)
2
c
5
, c
11
u
86
+ 2u
85
+ ··· − 1380u + 529
c
6
, c
12
u
86
− 2u
85
+ ··· + 2676206273u + 339660187
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
86
− 7y
85
+ ··· − 31y + 9
c
2
, c
8
(y
43
− 39y
42
+ ··· + 4960y −289)
2
c
3
, c
9
y
86
− 28y
85
+ ··· − 1722726646621y + 265417644969
c
4
, c
10
(y
43
+ 20y
42
+ ··· − 446y −25)
2
c
5
, c
11
y
86
+ 32y
85
+ ··· + 34272852y + 279841
c
6
, c
12
y
86
− 10y
85
+ ··· − 3384577457419862375y + 115369042632874969
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.115680 + 0.088438I
a = −0.530621 − 0.816347I
b = −0.36669 − 1.40614I
2.05988 − 4.53064I 6.07841 + 4.88354I
u = −1.115680 + 0.088438I
a = 0.016420 + 0.564275I
b = −0.685045 − 0.446535I
2.05988 − 4.53064I 6.07841 + 4.88354I
u = −1.115680 − 0.088438I
a = −0.530621 + 0.816347I
b = −0.36669 + 1.40614I
2.05988 + 4.53064I 6.07841 − 4.88354I
u = −1.115680 − 0.088438I
a = 0.016420 − 0.564275I
b = −0.685045 + 0.446535I
2.05988 + 4.53064I 6.07841 − 4.88354I
u = 1.194820 + 0.508478I
a = 0.529082 + 0.865996I
b = −0.128273 + 0.357532I
3.19067 + 2.37658I 0. − 11.61854I
u = 1.194820 + 0.508478I
a = 0.127113 − 0.366982I
b = −2.67295 − 2.83110I
3.19067 + 2.37658I 0. − 11.61854I
u = 1.194820 − 0.508478I
a = 0.529082 − 0.865996I
b = −0.128273 − 0.357532I
3.19067 − 2.37658I 0. + 11.61854I
u = 1.194820 − 0.508478I
a = 0.127113 + 0.366982I
b = −2.67295 + 2.83110I
3.19067 − 2.37658I 0. + 11.61854I
u = 1.337540 + 0.195957I
a = 0.751109 − 0.509623I
b = 0.64184 − 1.29054I
0.786358 + 1.135550I 0
u = 1.337540 + 0.195957I
a = −0.162295 − 0.099306I
b = 0.298914 − 0.668145I
0.786358 + 1.135550I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.337540 − 0.195957I
a = 0.751109 + 0.509623I
b = 0.64184 + 1.29054I
0.786358 − 1.135550I 0
u = 1.337540 − 0.195957I
a = −0.162295 + 0.099306I
b = 0.298914 + 0.668145I
0.786358 − 1.135550I 0
u = 0.294990 + 0.528224I
a = −0.435664 − 0.275251I
b = −0.033816 + 0.763184I
1.43197 + 1.52483I 4.77881 − 4.92385I
u = 0.294990 + 0.528224I
a = 1.39558 + 0.81111I
b = 0.066598 + 0.867420I
1.43197 + 1.52483I 4.77881 − 4.92385I
u = 0.294990 − 0.528224I
a = −0.435664 + 0.275251I
b = −0.033816 − 0.763184I
1.43197 − 1.52483I 4.77881 + 4.92385I
u = 0.294990 − 0.528224I
a = 1.39558 − 0.81111I
b = 0.066598 − 0.867420I
1.43197 − 1.52483I 4.77881 + 4.92385I
u = 0.213109 + 1.378840I
a = 0.083822 + 1.308350I
b = 0.326802 + 1.369390I
−4.20801 + 3.81011I 0
u = 0.213109 + 1.378840I
a = −0.300600 − 0.256235I
b = 1.38339 − 1.96236I
−4.20801 + 3.81011I 0
u = 0.213109 − 1.378840I
a = 0.083822 − 1.308350I
b = 0.326802 − 1.369390I
−4.20801 − 3.81011I 0
u = 0.213109 − 1.378840I
a = −0.300600 + 0.256235I
b = 1.38339 + 1.96236I
−4.20801 − 3.81011I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.399740 + 0.139228I
a = 0.427844 − 0.842577I
b = −0.44234 − 3.01249I
4.07903 + 8.22022I 0
u = 1.399740 + 0.139228I
a = 0.090161 − 0.501687I
b = −0.299763 − 0.437113I
4.07903 + 8.22022I 0
u = 1.399740 − 0.139228I
a = 0.427844 + 0.842577I
b = −0.44234 + 3.01249I
4.07903 − 8.22022I 0
u = 1.399740 − 0.139228I
a = 0.090161 + 0.501687I
b = −0.299763 + 0.437113I
4.07903 − 8.22022I 0
u = −1.40247 + 0.29057I
a = −0.775681 + 0.883009I
b = −0.57870 + 1.57791I
2.64500 + 3.06546I 0
u = −1.40247 + 0.29057I
a = 0.660428 − 0.286945I
b = −0.316631 + 0.132705I
2.64500 + 3.06546I 0
u = −1.40247 − 0.29057I
a = −0.775681 − 0.883009I
b = −0.57870 − 1.57791I
2.64500 − 3.06546I 0
u = −1.40247 − 0.29057I
a = 0.660428 + 0.286945I
b = −0.316631 − 0.132705I
2.64500 − 3.06546I 0
u = −1.47287 + 0.24746I
a = −0.103512 − 0.862014I
b = 0.58468 − 2.98444I
6.94974 − 4.89323I 0
u = −1.47287 + 0.24746I
a = −0.159985 + 0.026947I
b = 0.243337 − 0.145539I
6.94974 − 4.89323I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47287 − 0.24746I
a = −0.103512 + 0.862014I
b = 0.58468 + 2.98444I
6.94974 + 4.89323I 0
u = −1.47287 − 0.24746I
a = −0.159985 − 0.026947I
b = 0.243337 + 0.145539I
6.94974 + 4.89323I 0
u = 0.285156 + 0.399219I
a = 0.815991 + 0.837097I
b = 0.906247 − 0.313562I
0.47321 + 2.39024I 2.04869 − 4.02922I
u = 0.285156 + 0.399219I
a = 1.03908 + 2.24033I
b = −0.105611 + 0.731929I
0.47321 + 2.39024I 2.04869 − 4.02922I
u = 0.285156 − 0.399219I
a = 0.815991 − 0.837097I
b = 0.906247 + 0.313562I
0.47321 − 2.39024I 2.04869 + 4.02922I
u = 0.285156 − 0.399219I
a = 1.03908 − 2.24033I
b = −0.105611 − 0.731929I
0.47321 − 2.39024I 2.04869 + 4.02922I
u = 0.26091 + 1.49221I
a = −0.742276 + 0.668844I
b = 0.036986 + 1.190880I
1.47280 − 1.84076I 0
u = 0.26091 + 1.49221I
a = 0.864713 + 0.676358I
b = 0.100868 + 1.121450I
1.47280 − 1.84076I 0
u = 0.26091 − 1.49221I
a = −0.742276 − 0.668844I
b = 0.036986 − 1.190880I
1.47280 + 1.84076I 0
u = 0.26091 − 1.49221I
a = 0.864713 − 0.676358I
b = 0.100868 − 1.121450I
1.47280 + 1.84076I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473826 + 0.064283I
a = −1.54698 − 0.84528I
b = −0.25071 − 1.60585I
−5.62558 − 0.60241I 3.49360 + 2.24885I
u = −0.473826 + 0.064283I
a = 2.74140 − 0.91558I
b = −0.206993 + 0.451612I
−5.62558 − 0.60241I 3.49360 + 2.24885I
u = −0.473826 − 0.064283I
a = −1.54698 + 0.84528I
b = −0.25071 + 1.60585I
−5.62558 + 0.60241I 3.49360 − 2.24885I
u = −0.473826 − 0.064283I
a = 2.74140 + 0.91558I
b = −0.206993 − 0.451612I
−5.62558 + 0.60241I 3.49360 − 2.24885I
u = 0.169794 + 0.434125I
a = −2.23282 − 0.47524I
b = −0.511531 − 0.638166I
−0.38058 − 6.28025I 0.64015 + 9.26219I
u = 0.169794 + 0.434125I
a = −2.55925 + 1.01168I
b = 0.145150 + 1.155370I
−0.38058 − 6.28025I 0.64015 + 9.26219I
u = 0.169794 − 0.434125I
a = −2.23282 + 0.47524I
b = −0.511531 + 0.638166I
−0.38058 + 6.28025I 0.64015 − 9.26219I
u = 0.169794 − 0.434125I
a = −2.55925 − 1.01168I
b = 0.145150 − 1.155370I
−0.38058 + 6.28025I 0.64015 − 9.26219I
u = −0.03772 + 1.56297I
a = −0.120715 − 0.856591I
b = 0.05713 − 1.83396I
−8.16558 − 1.16224I 0
u = −0.03772 + 1.56297I
a = 0.11469 + 1.74498I
b = 0.04099 + 1.67869I
−8.16558 − 1.16224I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03772 − 1.56297I
a = −0.120715 + 0.856591I
b = 0.05713 + 1.83396I
−8.16558 + 1.16224I 0
u = −0.03772 − 1.56297I
a = 0.11469 − 1.74498I
b = 0.04099 − 1.67869I
−8.16558 + 1.16224I 0
u = 1.53711 + 0.31414I
a = 0.768268 + 0.635630I
b = −0.056706 + 0.707806I
4.44405 + 0.89151I 0
u = 1.53711 + 0.31414I
a = −0.062562 + 0.463261I
b = 1.15312 + 3.42175I
4.44405 + 0.89151I 0
u = 1.53711 − 0.31414I
a = 0.768268 − 0.635630I
b = −0.056706 − 0.707806I
4.44405 − 0.89151I 0
u = 1.53711 − 0.31414I
a = −0.062562 − 0.463261I
b = 1.15312 − 3.42175I
4.44405 − 0.89151I 0
u = −0.194415 + 0.346795I
a = −1.065970 − 0.131400I
b = −0.14265 + 2.22850I
−0.28736 + 3.36637I 11.88280 + 1.35996I
u = −0.194415 + 0.346795I
a = 3.21301 + 0.74244I
b = −0.589464 + 0.006918I
−0.28736 + 3.36637I 11.88280 + 1.35996I
u = −0.194415 − 0.346795I
a = −1.065970 + 0.131400I
b = −0.14265 − 2.22850I
−0.28736 − 3.36637I 11.88280 − 1.35996I
u = −0.194415 − 0.346795I
a = 3.21301 − 0.74244I
b = −0.589464 − 0.006918I
−0.28736 − 3.36637I 11.88280 − 1.35996I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60996 + 0.08161I
a = 0.884676 + 0.826488I
b = 0.66083 + 1.52938I
1.31869 − 7.19355I 0
u = 1.60996 + 0.08161I
a = −0.634090 − 0.080905I
b = 0.135911 + 0.270762I
1.31869 − 7.19355I 0
u = 1.60996 − 0.08161I
a = 0.884676 − 0.826488I
b = 0.66083 − 1.52938I
1.31869 + 7.19355I 0
u = 1.60996 − 0.08161I
a = −0.634090 + 0.080905I
b = 0.135911 − 0.270762I
1.31869 + 7.19355I 0
u = −1.62004 + 0.05900I
a = −0.169701 − 0.719649I
b = 0.24164 − 2.95574I
7.35319 − 4.35321I 0
u = −1.62004 + 0.05900I
a = −0.516824 − 0.337282I
b = 0.055828 − 0.398375I
7.35319 − 4.35321I 0
u = −1.62004 − 0.05900I
a = −0.169701 + 0.719649I
b = 0.24164 + 2.95574I
7.35319 + 4.35321I 0
u = −1.62004 − 0.05900I
a = −0.516824 + 0.337282I
b = 0.055828 + 0.398375I
7.35319 + 4.35321I 0
u = −1.63959 + 0.12969I
a = −0.629016 − 0.711882I
b = 0.62535 − 1.60664I
3.95952 − 9.14255I 0
u = −1.63959 + 0.12969I
a = 0.220903 + 0.413033I
b = −1.26345 + 3.62757I
3.95952 − 9.14255I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63959 − 0.12969I
a = −0.629016 + 0.711882I
b = 0.62535 + 1.60664I
3.95952 + 9.14255I 0
u = −1.63959 − 0.12969I
a = 0.220903 − 0.413033I
b = −1.26345 − 3.62757I
3.95952 + 9.14255I 0
u = 0.256452 + 0.097043I
a = 1.72057 − 2.43295I
b = −0.01397 − 1.83611I
−3.48797 + 8.65451I 10.96127 − 3.30272I
u = 0.256452 + 0.097043I
a = −1.71936 + 5.75556I
b = 0.717391 + 0.308677I
−3.48797 + 8.65451I 10.96127 − 3.30272I
u = 0.256452 − 0.097043I
a = 1.72057 + 2.43295I
b = −0.01397 + 1.83611I
−3.48797 − 8.65451I 10.96127 + 3.30272I
u = 0.256452 − 0.097043I
a = −1.71936 − 5.75556I
b = 0.717391 − 0.308677I
−3.48797 − 8.65451I 10.96127 + 3.30272I
u = −1.64625 + 0.57157I
a = −0.206383 − 0.751197I
b = 0.65091 − 2.37486I
7.57975 − 5.62049I 0
u = −1.64625 + 0.57157I
a = −0.731761 + 0.237535I
b = −0.1289710 + 0.0080917I
7.57975 − 5.62049I 0
u = −1.64625 − 0.57157I
a = −0.206383 + 0.751197I
b = 0.65091 + 2.37486I
7.57975 + 5.62049I 0
u = −1.64625 − 0.57157I
a = −0.731761 − 0.237535I
b = −0.1289710 − 0.0080917I
7.57975 + 5.62049I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.81032
a = 0.704212
b = −1.95016
7.04633 0
u = 1.81032
a = 0.137336
b = −10.9556
7.04633 0
u = 1.63813 + 0.86204I
a = 0.940907 + 0.346569I
b = 0.275684 + 0.126572I
5.43168 + 10.49420I 0
u = 1.63813 + 0.86204I
a = 0.314823 − 0.765184I
b = −0.60244 − 2.02673I
5.43168 + 10.49420I 0
u = 1.63813 − 0.86204I
a = 0.940907 − 0.346569I
b = 0.275684 − 0.126572I
5.43168 − 10.49420I 0
u = 1.63813 − 0.86204I
a = 0.314823 + 0.765184I
b = −0.60244 + 2.02673I
5.43168 − 10.49420I 0
20
III. I
u
3
= h2.20 × 10
25
u
39
+ 2.36 × 10
25
u
38
+ · · · + 1.03 × 10
24
b − 1.37 ×
10
27
, −7.74 × 10
26
u
39
− 1.52 × 10
26
u
38
+ · · · + 1.96 × 10
25
a + 9.28 ×
10
27
, u
40
− 6u
38
+ · · · − 255u
2
− 19i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
4
=
39.5458u
39
+ 7.77693u
38
+ ··· − 2324.41u − 474.232
−21.3768u
39
− 22.8909u
38
+ ··· + 1244.77u + 1330.64
a
9
=
1
−u
2
a
1
=
−58.1679u
39
+ 3.29014u
38
+ ··· + 3449.07u − 137.870
−5.80256u
39
+ 11.6925u
38
+ ··· + 359.869u − 685.518
a
12
=
−52.3653u
39
− 8.40239u
38
+ ··· + 3089.20u + 547.648
−5.80256u
39
+ 11.6925u
38
+ ··· + 359.869u − 685.518
a
10
=
−70.0334u
39
− 21.3768u
38
+ ··· + 4061.56u + 1244.77
7.77693u
39
+ 12.7669u
38
+ ··· − 474.232u − 751.370
a
7
=
36.0799u
39
− 5.80256u
38
+ ··· − 2110.89u + 359.869
3.29014u
39
− 18.6530u
38
+ ··· − 137.870u + 1105.19
a
6
=
36.0799u
39
− 5.80256u
38
+ ··· − 2110.89u + 359.869
−8.40239u
39
− 16.8892u
38
+ ··· + 547.648u + 994.941
a
3
=
u
u
a
5
=
−19.8101u
39
− 2.40796u
38
+ ··· + 1124.82u + 148.776
−21.0277u
39
− 13.7029u
38
+ ··· + 1259.48u + 794.359
a
11
=
−41.8084u
39
− 21.0277u
38
+ ··· + 2425.85u + 1259.48
−2.40796u
39
− 6.63080u
38
+ ··· + 148.776u + 376.393
(ii) Obstruction class = 1
(iii) Cusp Shapes =
149855023258607474000595971
515021663836420099366239
u
38
−
948392840239352276013737578
515021663836420099366239
u
36
+
··· −
89911988946080209745670467197
515021663836420099366239
u
2
−
8671019797870820314013476786
515021663836420099366239
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
40
− 12u
39
+ ··· + 15u + 1
c
2
, c
8
u
40
− 6u
38
+ ··· − 255u
2
− 19
c
3
, c
9
u
40
+ 5u
39
+ ··· − 3u + 1
c
4
, c
10
u
40
+ 8u
38
+ ··· − 297u
2
− 19
c
5
, c
11
u
40
− 5u
39
+ ··· − 36u − 36
c
6
, c
12
u
40
+ 5u
39
+ ··· − 81u + 27
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
40
− 24y
39
+ ··· − 235y + 1
c
2
, c
8
(y
20
− 6y
19
+ ··· − 255y −19)
2
c
3
, c
9
y
40
− 31y
39
+ ··· + 41y + 1
c
4
, c
10
(y
20
+ 8y
19
+ ··· − 297y −19)
2
c
5
, c
11
y
40
− y
39
+ ··· − 27216y + 1296
c
6
, c
12
y
40
+ 11y
39
+ ··· + 104247y + 729
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929042I
a = 1.008700 + 0.535913I
b = 0.116734 + 0.879504I
1.39660 4.42730
u = − 0.929042I
a = 1.008700 − 0.535913I
b = 0.116734 − 0.879504I
1.39660 4.42730
u = 1.178850 + 0.209458I
a = −0.703351 − 0.338282I
b = 0.022042 + 0.625498I
1.32275 − 5.63915I 0. + 7.01051I
u = 1.178850 − 0.209458I
a = −0.703351 + 0.338282I
b = 0.022042 − 0.625498I
1.32275 + 5.63915I 0. − 7.01051I
u = −1.178850 + 0.209458I
a = −0.749427 + 0.898373I
b = −0.72110 + 1.23469I
1.32275 + 5.63915I 0. − 7.01051I
u = −1.178850 − 0.209458I
a = −0.749427 − 0.898373I
b = −0.72110 − 1.23469I
1.32275 − 5.63915I 0. + 7.01051I
u = 1.199010 + 0.348364I
a = 0.137760 + 0.349959I
b = −2.07637 + 0.88877I
3.52609 + 1.74568I 0
u = 1.199010 − 0.348364I
a = 0.137760 − 0.349959I
b = −2.07637 − 0.88877I
3.52609 − 1.74568I 0
u = −1.199010 + 0.348364I
a = −0.548822 + 0.771359I
b = 0.239946 + 0.310271I
3.52609 − 1.74568I 0
u = −1.199010 − 0.348364I
a = −0.548822 − 0.771359I
b = 0.239946 − 0.310271I
3.52609 + 1.74568I 0
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136984 + 1.302140I
a = −0.305822 − 0.314089I
b = 1.73222 − 1.78973I
−4.33120 + 3.94595I 0
u = 0.136984 − 1.302140I
a = −0.305822 + 0.314089I
b = 1.73222 + 1.78973I
−4.33120 − 3.94595I 0
u = −0.136984 + 1.302140I
a = −0.108453 + 1.343220I
b = −0.330792 + 1.302590I
−4.33120 − 3.94595I 0
u = −0.136984 − 1.302140I
a = −0.108453 − 1.343220I
b = −0.330792 − 1.302590I
−4.33120 + 3.94595I 0
u = 0.050813 + 0.653192I
a = 0.54749 + 2.31274I
b = −0.068034 + 1.252060I
−6.41705 − 0.11934I −5.06037 − 1.90424I
u = 0.050813 − 0.653192I
a = 0.54749 − 2.31274I
b = −0.068034 − 1.252060I
−6.41705 + 0.11934I −5.06037 + 1.90424I
u = −0.050813 + 0.653192I
a = 0.27250 + 1.80754I
b = −0.22773 + 1.58802I
−6.41705 + 0.11934I −5.06037 + 1.90424I
u = −0.050813 − 0.653192I
a = 0.27250 − 1.80754I
b = −0.22773 − 1.58802I
−6.41705 − 0.11934I −5.06037 − 1.90424I
u = −0.226986 + 0.550089I
a = −0.27141 + 1.59457I
b = 0.11892 + 1.82807I
−3.85848 − 8.80900I −7.98418 + 11.33270I
u = −0.226986 − 0.550089I
a = −0.27141 − 1.59457I
b = 0.11892 − 1.82807I
−3.85848 + 8.80900I −7.98418 − 11.33270I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.226986 + 0.550089I
a = 1.45723 + 2.48719I
b = 0.511984 + 0.415389I
−3.85848 + 8.80900I −7.98418 − 11.33270I
u = 0.226986 − 0.550089I
a = 1.45723 − 2.48719I
b = 0.511984 − 0.415389I
−3.85848 − 8.80900I −7.98418 + 11.33270I
u = −0.004800 + 0.571260I
a = −1.58528 + 1.61394I
b = 0.152978 + 0.082715I
−0.55712 − 3.66399I −1.27961 + 13.86053I
u = −0.004800 − 0.571260I
a = −1.58528 − 1.61394I
b = 0.152978 − 0.082715I
−0.55712 + 3.66399I −1.27961 − 13.86053I
u = 0.004800 + 0.571260I
a = 0.712428 + 0.739925I
b = −1.00518 + 2.26941I
−0.55712 + 3.66399I −1.27961 − 13.86053I
u = 0.004800 − 0.571260I
a = 0.712428 − 0.739925I
b = −1.00518 − 2.26941I
−0.55712 − 3.66399I −1.27961 + 13.86053I
u = 1.47284 + 0.15553I
a = 0.552345 − 0.801614I
b = −0.36950 − 2.22670I
3.28324 + 7.83214I 0
u = 1.47284 − 0.15553I
a = 0.552345 + 0.801614I
b = −0.36950 + 2.22670I
3.28324 − 7.83214I 0
u = −1.47284 + 0.15553I
a = −0.152691 + 0.262120I
b = −0.285395 + 0.888432I
3.28324 − 7.83214I 0
u = −1.47284 − 0.15553I
a = −0.152691 − 0.262120I
b = −0.285395 − 0.888432I
3.28324 + 7.83214I 0
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51156 + 0.26431I
a = 0.355371 + 0.035389I
b = 0.0104865 − 0.1040000I
6.77206 + 4.79490I 0
u = 1.51156 − 0.26431I
a = 0.355371 − 0.035389I
b = 0.0104865 + 0.1040000I
6.77206 − 4.79490I 0
u = −1.51156 + 0.26431I
a = −0.112338 − 0.872812I
b = 0.51658 − 2.86042I
6.77206 − 4.79490I 0
u = −1.51156 − 0.26431I
a = −0.112338 + 0.872812I
b = 0.51658 + 2.86042I
6.77206 + 4.79490I 0
u = 0.05303 + 1.61259I
a = −0.082693 − 0.843305I
b = 0.05758 − 1.82287I
−8.09446 − 1.28532I 0
u = 0.05303 − 1.61259I
a = −0.082693 + 0.843305I
b = 0.05758 + 1.82287I
−8.09446 + 1.28532I 0
u = −0.05303 + 1.61259I
a = −0.05806 + 1.72700I
b = −0.06640 + 1.70162I
−8.09446 + 1.28532I 0
u = −0.05303 − 1.61259I
a = −0.05806 − 1.72700I
b = −0.06640 − 1.70162I
−8.09446 − 1.28532I 0
u = 1.83596
a = 0.0349025
b = −14.4201
7.08706 0
u = −1.83596
a = −0.765863
b = 1.76221
7.08706 0
27
IV. I
u
4
= hb, a
2
− a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
8
=
1
0
a
4
=
a
0
a
9
=
1
−1
a
1
=
−a + 1
−1
a
12
=
−a + 2
−1
a
10
=
2a
−a
a
7
=
2a − 1
−a + 1
a
6
=
2a − 1
a
a
3
=
−1
−1
a
5
=
2a + 1
−a
a
11
=
−a + 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
u
2
− u + 1
c
2
, c
12
(u − 1)
2
c
3
, c
4
, c
7
u
2
+ u + 1
c
5
u
2
+ 2u + 4
c
6
u
2
+ 3
c
8
(u + 1)
2
c
11
u
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
2
+ y + 1
c
2
, c
8
, c
12
(y −1)
2
c
5
y
2
+ 4y + 16
c
6
(y + 3)
2
c
11
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I 6.00000 + 3.46410I
u = −1.00000
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I 6.00000 − 3.46410I
31
V. I
u
5
= hb − 2a, a
2
− a + 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
8
=
1
0
a
4
=
a
2a
a
9
=
1
−1
a
1
=
a − 1
2a − 1
a
12
=
−a
2a − 1
a
10
=
0
a
a
7
=
1
−a + 1
a
6
=
1
−a + 2
a
3
=
1
1
a
5
=
1
−a + 2
a
11
=
a
2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 4
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
u
2
+ u + 1
c
2
(u + 1)
2
c
3
, c
4
, c
7
u
2
− u + 1
c
5
u
2
c
6
, c
8
(u − 1)
2
c
11
u
2
+ 2u + 4
c
12
u
2
+ 3
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
2
+ y + 1
c
2
, c
6
, c
8
(y −1)
2
c
5
y
2
c
11
y
2
+ 4y + 16
c
12
(y + 3)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 1.00000 + 1.73205I
1.64493 − 2.02988I 6.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 1.00000 − 1.73205I
1.64493 + 2.02988I 6.00000 − 3.46410I
35
VI. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
8
=
1
0
a
4
=
0
b
a
9
=
1
0
a
1
=
−1
−b − 1
a
12
=
b
−b − 1
a
10
=
0
−b
a
7
=
1
b + 1
a
6
=
−b
b + 1
a
3
=
−1
0
a
5
=
0
b
a
11
=
0
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8b − 4
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
2
− u + 1
c
2
, c
4
, c
8
c
10
u
2
c
3
, c
5
, c
9
c
11
u
2
+ u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
9
c
11
, c
12
y
2
+ y + 1
c
2
, c
4
, c
8
c
10
y
2
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
4.05977I 0. − 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
39
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
37
− u
36
+ ··· + 8u − 1)
· (u
40
− 12u
39
+ ··· + 15u + 1)(u
86
− 7u
85
+ ··· − 55u + 3)
c
2
, c
8
u
2
(u − 1)
2
(u + 1)
2
(u
37
+ 5u
36
+ ··· + 2744u + 388)
· (u
40
− 6u
38
+ ··· − 255u
2
− 19)(u
43
− 3u
42
+ ··· + 110u − 17)
2
c
3
, c
9
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
37
+ u
36
+ ··· + 2u + 1)
· (u
40
+ 5u
39
+ ··· − 3u + 1)(u
86
+ 4u
85
+ ··· + 3742879u + 515187)
c
4
, c
10
u
2
(u
2
− u + 1)(u
2
+ u + 1)(u
37
+ 5u
36
+ ··· + 184u + 52)
· (u
40
+ 8u
38
+ ··· − 297u
2
− 19)(u
43
− 2u
42
+ ··· + 8u − 5)
2
c
5
, c
11
u
2
(u
2
+ u + 1)(u
2
+ 2u + 4)(u
37
+ u
36
+ ··· − 4u + 4)
· (u
40
− 5u
39
+ ··· − 36u − 36)(u
86
+ 2u
85
+ ··· − 1380u + 529)
c
6
, c
12
((u − 1)
2
)(u
2
+ 3)(u
2
− u + 1)(u
37
− u
36
+ ··· − 104u − 47)
· (u
40
+ 5u
39
+ ··· − 81u + 27)
· (u
86
− 2u
85
+ ··· + 2676206273u + 339660187)
40
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
2
+ y + 1)
3
)(y
37
− 11y
36
+ ··· + 32y −1)
· (y
40
− 24y
39
+ ··· − 235y + 1)(y
86
− 7y
85
+ ··· − 31y + 9)
c
2
, c
8
y
2
(y −1)
4
(y
20
− 6y
19
+ ··· − 255y −19)
2
· (y
37
− 23y
36
+ ··· + 3132720y −150544)
· (y
43
− 39y
42
+ ··· + 4960y −289)
2
c
3
, c
9
((y
2
+ y + 1)
3
)(y
37
− 37y
36
+ ··· + 30y −1)
· (y
40
− 31y
39
+ ··· + 41y + 1)
· (y
86
− 28y
85
+ ··· − 1722726646621y + 265417644969)
c
4
, c
10
y
2
(y
2
+ y + 1)
2
(y
20
+ 8y
19
+ ··· − 297y −19)
2
· (y
37
+ 13y
36
+ ··· − 5872y −2704)(y
43
+ 20y
42
+ ··· − 446y −25)
2
c
5
, c
11
y
2
(y
2
+ y + 1)(y
2
+ 4y + 16)(y
37
− 5y
36
+ ··· − 976y −16)
· (y
40
− y
39
+ ··· − 27216y + 1296)
· (y
86
+ 32y
85
+ ··· + 34272852y + 279841)
c
6
, c
12
((y −1)
2
)(y + 3)
2
(y
2
+ y + 1)(y
37
− 31y
36
+ ··· + 16456y −2209)
· (y
40
+ 11y
39
+ ··· + 104247y + 729)
· (y
86
− 10y
85
+ ··· − 3384577457419862375y + 115369042632874969)
41
