Frank Lübeck   

Conjugacy Classes and Character Degrees of E7(2)

[Classes][Characters]

The complex character table of the finite simple Chevalley group E7(2) is not known. This page contains part of the information. These data are obtained with computer programs using the theory of connected reductive algebraic groups, Deligne-Lusztig theory and Lusztig's classification of characters of finite groups of Lie type. A detailed description of this background is in preparation.

Actually, the information given below was computed generically, that is for all groups of type E7(q), q an arbitrary prime power, and then specialized for the case q=2.

Conjugacy Classes and Centralizer Orders

The following table lists a parameterization of the conjugacy classes of E7(2). It is obtained by considering the group as group of fixed points under a Frobenius morphism inside a connected reductive algebraic group G. Here we chose G to be of simply connected type (we could also have taken G of adjoint type, but this leads to an isomorphic group). Each element g in G has a Jordan decomposition g=su=us with s semisimple and u unipotent.

We give the following information: each row stands for a set of classes which have representatives with the same centralizer in G. The column "# classes" tells how many classes are in this set. The column "|C(su)(q)|, q=2" tells the order of the centralizer of elements in these classes. The next two columns describe the centralizer of the semisimple part s of an element in these classes; "type of C(s)" gives the semisimple part of the centralizer of s in G under the restricted Frobenius morphism, and "|Z0(C(s))(q)|" gives the number of rational points in the radical of the centralizer of s (generically, as polynomial in q (= 2), the polynomials are factorized into cyclotomic polynomials, phiN means the evaluation of the N-th cyclotomic polynomial at q). Finally, in column "type of u" a label for the class of the unipotent part u is given; we don't give precise explanations of that labeling here.

(Here is a GAP-readable file containing the group order and the sequence of centralizer orders (with multiplicities) as given below.)

There are 531 conjugacy classes.

 # classes|C(su)(q)|, q=2 type of C(s) |Z0(C(s))(q)|type of u
1 1 2^63*3^11*5^2*7^3*11*13*17*19*31*43*73*127 E7(q) 1 -
2 1 2^63*3^8*5^2*7^2*11*17*31 E7(q) 1 A1
3 1 2^59*3^6*5^2*7*17 E7(q) 1 2A1
4 1 2^51*3^6*5^2*7^2*13*17 E7(q) 1 3A1''
5 1 2^55*3^5*5*7 E7(q) 1 3A1'
6 1 2^48*3^4*5*7^2*31 E7(q) 1 A2
7 1 2^48*3^7*5*7*11 E7(q) 1 A2
8 1 2^51*3^4*5*7 E7(q) 1 4A1
9 1 2^48*3^2*5*7 E7(q) 1 A2+A1
10 1 2^48*3^5*5 E7(q) 1 A2+A1
11 1 2^45*3^3 E7(q) 1 A2+2A1
12 1 2^41*3^3*7 E7(q) 1 A2+3A1
13 1 2^39*3^4*7 E7(q) 1 2A2
14 1 2^35*3^5*5*7 E7(q) 1 A3
15 1 2^35*3^4*5*7 E7(q) 1 (A3+A1)''
16 1 2^39*3^2 E7(q) 1 2A2+A1
17 1 2^35*3^3 E7(q) 1 (A3+A1)'
18 1 2^34*3^4 E7(q) 1 D4(a1)
19 1 2^34*3^2*5 E7(q) 1 D4(a1)
20 1 2^33*3^3*7 E7(q) 1 D4(a1)
21 1 2^35*3^2 E7(q) 1 A3+2A1
22 1 2^34*3^2 E7(q) 1 D4(a1)+A1
23 1 2^34*3*5 E7(q) 1 D4(a1)+A1
24 1 2^26*3^4*5*7 E7(q) 1 D4
25 1 2^26*3^4*5*7 E7(q) 1 D4
26 1 2^33*3^2 E7(q) 1 (A3+A2)2
27 1 2^33*3 E7(q) 1 A3+A2
28 1 2^31*3 E7(q) 1 A3+A2+A1
29 1 2^28*3*7 E7(q) 1 A4
30 1 2^28*3^4 E7(q) 1 A4
31 1 2^26*3^2*5 E7(q) 1 D4+A1
32 1 2^26*3^2*5 E7(q) 1 D4+A1
33 1 2^23*3^3*7 E7(q) 1 A5''
34 1 2^28 E7(q) 1 A4+A1
35 1 2^28*3^2 E7(q) 1 A4+A1
36 1 2^25*3 E7(q) 1 A4+A2
37 1 2^25*3 E7(q) 1 D5(a1)
38 1 2^25*3^2 E7(q) 1 D5(a1)
39 1 2^23*3 E7(q) 1 D5(a1)+A1
40 1 2^21*3^2 E7(q) 1 A5'
41 1 2^23*3 E7(q) 1 (A5+A1)''
42 1 2^21*3 E7(q) 1 D6(a2)
43 1 2^22*3 E7(q) 1 (A5+A1)'
44 1 2^22*3 E7(q) 1 (A5+A1)'
45 1 2^18*3^2 E7(q) 1 D5
46 1 2^18*3^2 E7(q) 1 D5
47 1 2^22*3 E7(q) 1 D6(a2)+A1
48 1 2^22 E7(q) 1 D6(a2)+A1
49 1 2^21*3 E7(q) 1 D6(a2)+A1
50 1 2^18*3 E7(q) 1 D5+A1
51 1 2^18*3 E7(q) 1 D5+A1
52 1 2^18*3 E7(q) 1 D6(a1)
53 1 2^18*3 E7(q) 1 D6(a1)
54 1 2^19 E7(q) 1 A6
55 1 2^19*3 E7(q) 1 A6
56 1 2^17 E7(q) 1 D6(a1)+A1
57 1 2^14*3 E7(q) 1 D6
58 1 2^14*3 E7(q) 1 D6
59 1 2^15 E7(q) 1 E6(a1)
60 1 2^15*3 E7(q) 1 E6(a1)
61 1 2^12*3 E7(q) 1 E6
62 1 2^12*3 E7(q) 1 E6
63 1 2^14 E7(q) 1 D6+A1
64 1 2^14 E7(q) 1 D6+A1
65 1 2^12 E7(q) 1 E7(a2)
66 1 2^12 E7(q) 1 E7(a2)
67 1 2^10 E7(q) 1 E7(a1)
68 1 2^10 E7(q) 1 E7(a1)
69 1 2^9 E7(q) 1 E7
70 1 2^9 E7(q) 1 E7
71 1 2^9 E7(q) 1 E7
72 1 2^9 E7(q) 1 E7
73 1 2^18*3^10*5*7*11 2A5(q) + 2A2(q) 1 [ [ 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1 ] ]
74 1 2^18*3^8*5*7*11 2A5(q) + 2A2(q) 1 [ [ 1, 1, 1, 1, 1, 1 ], [ 2, 1 ] ]
75 1 2^17*3^7*5*7*11 2A5(q) + 2A2(q) 1 [ [ 1, 1, 1, 1, 1, 1 ], [ 3 ] ]
76 1 2^18*3^8*5 2A5(q) + 2A2(q) 1 [ [ 2, 1, 1, 1, 1 ], [ 1, 1, 1 ] ]
77 1 2^18*3^6*5 2A5(q) + 2A2(q) 1 [ [ 2, 1, 1, 1, 1 ], [ 2, 1 ] ]
78 1 2^17*3^5*5 2A5(q) + 2A2(q) 1 [ [ 2, 1, 1, 1, 1 ], [ 3 ] ]
79 1 2^17*3^6 2A5(q) + 2A2(q) 1 [ [ 2, 2, 1, 1 ], [ 1, 1, 1 ] ]
80 1 2^17*3^4 2A5(q) + 2A2(q) 1 [ [ 2, 2, 1, 1 ], [ 2, 1 ] ]
81 1 2^16*3^3 2A5(q) + 2A2(q) 1 [ [ 2, 2, 1, 1 ], [ 3 ] ]
82 1 2^15*3^6 2A5(q) + 2A2(q) 1 [ [ 2, 2, 2 ], [ 1, 1, 1 ] ]
83 1 2^15*3^4 2A5(q) + 2A2(q) 1 [ [ 2, 2, 2 ], [ 2, 1 ] ]
84 1 2^14*3^3 2A5(q) + 2A2(q) 1 [ [ 2, 2, 2 ], [ 3 ] ]
85 1 2^14*3^7 2A5(q) + 2A2(q) 1 [ [ 3, 1, 1, 1 ], [ 1, 1, 1 ] ]
86 1 2^14*3^5 2A5(q) + 2A2(q) 1 [ [ 3, 1, 1, 1 ], [ 2, 1 ] ]
87 1 2^13*3^4 2A5(q) + 2A2(q) 1 [ [ 3, 1, 1, 1 ], [ 3 ] ]
88 1 2^14*3^5 2A5(q) + 2A2(q) 1 [ [ 3, 2, 1 ], [ 1, 1, 1 ] ]
89 1 2^14*3^3 2A5(q) + 2A2(q) 1 [ [ 3, 2, 1 ], [ 2, 1 ] ]
90 1 2^13*3^2 2A5(q) + 2A2(q) 1 [ [ 3, 2, 1 ], [ 3 ] ]
91 1 2^12*3^4 2A5(q) + 2A2(q) 1 [ [ 3, 3 ], [ 1, 1, 1 ] ]
92 1 2^12*3^2 2A5(q) + 2A2(q) 1 [ [ 3, 3 ], [ 2, 1 ] ]
93 1 2^11*3^2 2A5(q) + 2A2(q) 1 [ [ 3, 3 ], [ 3 ] ]
94 1 2^11*3^2 2A5(q) + 2A2(q) 1 [ [ 3, 3 ], [ 3 ] ]
95 1 2^11*3^2 2A5(q) + 2A2(q) 1 [ [ 3, 3 ], [ 3 ] ]
96 1 2^11*3^5 2A5(q) + 2A2(q) 1 [ [ 4, 1, 1 ], [ 1, 1, 1 ] ]
97 1 2^11*3^3 2A5(q) + 2A2(q) 1 [ [ 4, 1, 1 ], [ 2, 1 ] ]
98 1 2^10*3^2 2A5(q) + 2A2(q) 1 [ [ 4, 1, 1 ], [ 3 ] ]
99 1 2^11*3^4 2A5(q) + 2A2(q) 1 [ [ 4, 2 ], [ 1, 1, 1 ] ]
100 1 2^11*3^2 2A5(q) + 2A2(q) 1 [ [ 4, 2 ], [ 2, 1 ] ]
101 1 2^10*3 2A5(q) + 2A2(q) 1 [ [ 4, 2 ], [ 3 ] ]
102 1 2^9*3^4 2A5(q) + 2A2(q) 1 [ [ 5, 1 ], [ 1, 1, 1 ] ]
103 1 2^9*3^2 2A5(q) + 2A2(q) 1 [ [ 5, 1 ], [ 2, 1 ] ]
104 1 2^8*3 2A5(q) + 2A2(q) 1 [ [ 5, 1 ], [ 3 ] ]
105 1 2^8*3^3 2A5(q) + 2A2(q) 1 [ [ 6 ], [ 1, 1, 1 ] ]
106 1 2^8*3 2A5(q) + 2A2(q) 1 [ [ 6 ], [ 2, 1 ] ]
107 1 2^7*3 2A5(q) + 2A2(q) 1 [ [ 6 ], [ 3 ] ]
108 1 2^7*3 2A5(q) + 2A2(q) 1 [ [ 6 ], [ 3 ] ]
109 1 2^7*3 2A5(q) + 2A2(q) 1 [ [ 6 ], [ 3 ] ]
110 1 2^36*3^11*5^2*7^2*11*13*17*19 2E6(q) phi2 -
111 1 2^36*3^8*5*7*11 2E6(q) phi2 A1
112 1 2^33*3^6*5*7 2E6(q) phi2 2A1
113 1 2^31*3^5 2E6(q) phi2 3A1
114 1 2^27*3^7 2E6(q) phi2 A2
115 1 2^27*3^4*5*7 2E6(q) phi2 A2
116 1 2^26*3^5 2E6(q) phi2 A2+A1
117 1 2^22*3^4*7 2E6(q) phi2 2A2
118 1 2^25*3^3 2E6(q) phi2 A2+2A1
119 1 2^19*3^4*5 2E6(q) phi2 A3
120 1 2^22*3^2 2E6(q) phi2 2A2+A1
121 1 2^19*3^3 2E6(q) phi2 A3+A1
122 1 2^19*3^4 2E6(q) phi2 D4(a1)
123 1 2^19*3^2 2E6(q) phi2 D4(a1)
124 1 2^18*3^3 2E6(q) phi2 D4(a1)
125 1 2^15*3^3 2E6(q) phi2 A4
126 1 2^14*3^4 2E6(q) phi2 D4
127 1 2^14*3^4 2E6(q) phi2 D4
128 1 2^15*3^2 2E6(q) phi2 A4+A1
129 1 2^13*3^2 2E6(q) phi2 D5(a1)
130 1 2^12*3^2 2E6(q) phi2 A5
131 1 2^13*3 2E6(q) phi2 A5+A1
132 1 2^13*3 2E6(q) phi2 A5+A1
133 1 2^10*3^2 2E6(q) phi2 D5
134 1 2^10*3^2 2E6(q) phi2 D5
135 1 2^8*3 2E6(q) phi2 E6(a1)
136 1 2^7*3 2E6(q) phi2 E6
137 1 2^7*3 2E6(q) phi2 E6
138 1 2^21*3^8*5^2*7*11*17 2D5(q) + A1(q) phi2 [ [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ], [ 1, 1 ] ]
139 1 2^21*3^7*5^2*7*11*17 2D5(q) + A1(q) phi2 [ [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ], [ 2 ] ]
140 1 2^21*3^7*5 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 1, 1, 1, 1, 1, 1 ], [ -1, 0 ] ], [ 1, 1 ] ]
141 1 2^21*3^6*5 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 1, 1, 1, 1, 1, 1 ], [ -1, 0 ] ], [ 2 ] ]
142 1 2^18*3^6*5*7 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 1, 1, 1, 1, 1, 1 ], [ -1, 1 ] ], [ 1, 1 ] ]
143 1 2^18*3^5*5*7 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 1, 1, 1, 1, 1, 1 ], [ -1, 1 ] ], [ 2 ] ]
144 1 2^19*3^5*5 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 2, 2, 1, 1 ], [ -1, 0 ] ], [ 1, 1 ] ]
145 1 2^19*3^4*5 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 2, 2, 1, 1 ], [ -1, 0 ] ], [ 2 ] ]
146 1 2^18*3^4 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 2, 2, 1, 1 ], [ -1, 1 ] ], [ 1, 1 ] ]
147 1 2^18*3^3 2D5(q) + A1(q) phi2 [ [ [ 2, 2, 2, 2, 1, 1 ], [ -1, 1 ] ], [ 2 ] ]
148 1 2^16*3^5 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 1, 1, 1, 1 ], [ -1, -1, -1 ] ], [ 1, 1 ] ]
149 1 2^16*3^3*5 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 1, 1, 1, 1 ], [ -1, -1, -1 ] ], [ 1, 1 ] ]
150 1 2^16*3^4 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 1, 1, 1, 1 ], [ -1, -1, -1 ] ], [ 2 ] ]
151 1 2^16*3^2*5 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 1, 1, 1, 1 ], [ -1, -1, -1 ] ], [ 2 ] ]
152 1 2^15*3^4 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 2, 2 ], [ -1, 0, -1 ] ], [ 1, 1 ] ]
153 1 2^15*3^3 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 2, 2 ], [ -1, 0, -1 ] ], [ 2 ] ]
154 1 2^12*3^4*5 2D5(q) + A1(q) phi2 [ [ [ 4, 2, 1, 1, 1, 1 ], [ -1, 1, -1, 1 ] ], [ 1, 1 ] ]
155 1 2^12*3^3*5 2D5(q) + A1(q) phi2 [ [ [ 4, 2, 1, 1, 1, 1 ], [ -1, 1, -1, 1 ] ], [ 2 ] ]
156 1 2^14*3^3 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 2, 2 ], [ -1, 1, -1 ] ], [ 1, 1 ] ]
157 1 2^14*3^2 2D5(q) + A1(q) phi2 [ [ [ 3, 3, 2, 2 ], [ -1, 1, -1 ] ], [ 2 ] ]
158 1 2^12*3^3 2D5(q) + A1(q) phi2 [ [ [ 4, 2, 2, 2 ], [ -1, 1, -1, 1 ] ], [ 1, 1 ] ]
159 1 2^12*3^2 2D5(q) + A1(q) phi2 [ [ [ 4, 2, 2, 2 ], [ -1, 1, -1, 1 ] ], [ 2 ] ]
160 1 2^11*3^4 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 0 ] ], [ 1, 1 ] ]
161 1 2^11*3^3 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 0 ] ], [ 2 ] ]
162 1 2^12*3^2 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 1 ] ], [ 1, 1 ] ]
163 1 2^12*3^3 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 1 ] ], [ 1, 1 ] ]
164 1 2^12*3 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 1 ] ], [ 2 ] ]
165 1 2^12*3^2 2D5(q) + A1(q) phi2 [ [ [ 4, 4, 1, 1 ], [ -1, -1, -1, 1 ] ], [ 2 ] ]
166 1 2^9*3^3 2D5(q) + A1(q) phi2 [ [ [ 5, 5 ], [ -1, -1, -1, -1, -1 ] ], [ 1, 1 ] ]
167 1 2^9*3^2 2D5(q) + A1(q) phi2 [ [ [ 5, 5 ], [ -1, -1, -1, -1, -1 ] ], [ 2 ] ]
168 1 2^9*3^3 2D5(q) + A1(q) phi2 [ [ [ 6, 2, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
169 1 2^9*3^3 2D5(q) + A1(q) phi2 [ [ [ 6, 2, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
170 1 2^9*3^2 2D5(q) + A1(q) phi2 [ [ [ 6, 2, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 2 ] ]
171 1 2^9*3^2 2D5(q) + A1(q) phi2 [ [ [ 6, 2, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 2 ] ]
172 1 2^8*3^2 2D5(q) + A1(q) phi2 [ [ [ 6, 4 ], [ -1, -1, -1, 1, -1, 1 ] ], [ 1, 1 ] ]
173 1 2^8*3 2D5(q) + A1(q) phi2 [ [ [ 6, 4 ], [ -1, -1, -1, 1, -1, 1 ] ], [ 2 ] ]
174 1 2^7*3^2 2D5(q) + A1(q) phi2 [ [ [ 8, 2 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
175 1 2^7*3^2 2D5(q) + A1(q) phi2 [ [ [ 8, 2 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
176 1 2^7*3 2D5(q) + A1(q) phi2 [ [ [ 8, 2 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ], [ 2 ] ]
177 1 2^7*3 2D5(q) + A1(q) phi2 [ [ [ 8, 2 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ], [ 2 ] ]
178 1 2^9*3^6*7*19 2A2(q3) phi2 [ 1, 1, 1 ]
179 1 2^9*3^3 2A2(q3) phi2 [ 2, 1 ]
180 1 2^6*3^2 2A2(q3) phi2 [ 3 ]
181 1 2^6*3^2 2A2(q3) phi2 [ 3 ]
182 1 2^6*3^2 2A2(q3) phi2 [ 3 ]
183 1 2^21*3^9*5*7*11*43 2A6(q) phi2 [ 1, 1, 1, 1, 1, 1, 1 ]
184 1 2^21*3^7*5*11 2A6(q) phi2 [ 2, 1, 1, 1, 1, 1 ]
185 1 2^20*3^6 2A6(q) phi2 [ 2, 2, 1, 1, 1 ]
186 1 2^16*3^6*5 2A6(q) phi2 [ 3, 1, 1, 1, 1 ]
187 1 2^18*3^5 2A6(q) phi2 [ 2, 2, 2, 1 ]
188 1 2^16*3^4 2A6(q) phi2 [ 3, 2, 1, 1 ]
189 1 2^15*3^3 2A6(q) phi2 [ 3, 2, 2 ]
190 1 2^12*3^5 2A6(q) phi2 [ 4, 1, 1, 1 ]
191 1 2^13*3^3 2A6(q) phi2 [ 3, 3, 1 ]
192 1 2^12*3^3 2A6(q) phi2 [ 4, 2, 1 ]
193 1 2^11*3^2 2A6(q) phi2 [ 4, 3 ]
194 1 2^9*3^3 2A6(q) phi2 [ 5, 1, 1 ]
195 1 2^9*3^2 2A6(q) phi2 [ 5, 2 ]
196 1 2^7*3^2 2A6(q) phi2 [ 6, 1 ]
197 1 2^6*3 2A6(q) phi2 [ 7 ]
198 1 2^30*3^9*5^2*7^2*11*17*31 D6(q) phi2 [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ]
199 1 2^30*3^7*5^2*7 D6(q) phi2 [ [ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1, 0 ] ]
200 1 2^26*3^6*5^2*7*17 D6(q) phi2 [ [ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1, 1 ] ]
201 1 2^28*3^5*5 D6(q) phi2 [ [ 2, 2, 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ]
202 1 2^24*3^5*5*7 D6(q) phi2 [ [ 2, 2, 2, 2, 2, 2 ], [ -1, 0 ], '+' ]
203 1 2^24*3^5*5*7 D6(q) phi2 [ [ 2, 2, 2, 2, 2, 2 ], [ -1, 0 ], '-' ]
204 1 2^26*3^4*5 D6(q) phi2 [ [ 2, 2, 2, 2, 1, 1, 1, 1 ], [ -1, 1 ] ]
205 1 2^23*3^3*5*7 D6(q) phi2 [ [ 3, 3, 1, 1, 1, 1, 1, 1 ], [ -1, -1, -1 ] ]
206 1 2^23*3^6*5 D6(q) phi2 [ [ 3, 3, 1, 1, 1, 1, 1, 1 ], [ -1, -1, -1 ] ]
207 1 2^24*3^3*5 D6(q) phi2 [ [ 2, 2, 2, 2, 2, 2 ], [ -1, 1 ] ]
208 1 2^18*3^5*5*7 D6(q) phi2 [ [ 4, 2, 1, 1, 1, 1, 1, 1 ], [ -1, 1, -1, 1 ] ]
209 1 2^23*3^2 D6(q) phi2 [ [ 3, 3, 2, 2, 1, 1 ], [ -1, 0, -1 ] ]
210 1 2^23*3^4 D6(q) phi2 [ [ 3, 3, 2, 2, 1, 1 ], [ -1, 0, -1 ] ]
211 1 2^20*3^3 D6(q) phi2 [ [ 3, 3, 2, 2, 1, 1 ], [ -1, 1, -1 ] ]
212 1 2^18*3^3 D6(q) phi2 [ [ 3, 3, 3, 3 ], [ -1, -1, -1 ] ]
213 1 2^18*3^3 D6(q) phi2 [ [ 4, 2, 2, 2, 1, 1 ], [ -1, 1, -1, 1 ] ]
214 1 2^16*3^4 D6(q) phi2 [ [ 4, 4, 1, 1, 1, 1 ], [ -1, -1, -1, 0 ] ]
215 1 2^17*3^3 D6(q) phi2 [ [ 4, 4, 1, 1, 1, 1 ], [ -1, -1, -1, 1 ] ]
216 1 2^17*3^2*5 D6(q) phi2 [ [ 4, 4, 1, 1, 1, 1 ], [ -1, -1, -1, 1 ] ]
217 1 2^16*3^3 D6(q) phi2 [ [ 4, 4, 2, 2 ], [ -1, 0, -1, 0 ], '+' ]
218 1 2^16*3^3 D6(q) phi2 [ [ 4, 4, 2, 2 ], [ -1, 0, -1, 0 ], '-' ]
219 1 2^16*3^2 D6(q) phi2 [ [ 4, 3, 3, 2 ], [ -1, 1, -1, 1 ] ]
220 1 2^16*3^2 D6(q) phi2 [ [ 4, 4, 2, 2 ], [ -1, 0, -1, 1 ] ]
221 1 2^16*3^2 D6(q) phi2 [ [ 4, 4, 2, 2 ], [ -1, 1, -1, 0 ] ]
222 1 2^13*3^3*5 D6(q) phi2 [ [ 6, 2, 1, 1, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ]
223 1 2^13*3^3*5 D6(q) phi2 [ [ 6, 2, 1, 1, 1, 1 ], [ -1, 1, -1, -1, -1, 1 ] ]
224 1 2^16*3 D6(q) phi2 [ [ 4, 4, 2, 2 ], [ -1, 1, -1, 1 ] ]
225 1 2^13*3 D6(q) phi2 [ [ 5, 5, 1, 1 ], [ -1, -1, -1, -1, -1 ] ]
226 1 2^13*3^3 D6(q) phi2 [ [ 5, 5, 1, 1 ], [ -1, -1, -1, -1, -1 ] ]
227 1 2^13*3^2 D6(q) phi2 [ [ 6, 2, 2, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
228 1 2^13*3^2 D6(q) phi2 [ [ 6, 2, 2, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
229 1 2^12*3 D6(q) phi2 [ [ 6, 4, 1, 1 ], [ -1, -1, -1, 1, -1, 1 ] ]
230 1 2^12*3^2 D6(q) phi2 [ [ 6, 4, 1, 1 ], [ -1, -1, -1, 1, -1, 1 ] ]
231 1 2^10*3^2 D6(q) phi2 [ [ 6, 6 ], [ -1, -1, -1, -1, -1, 0 ], '+' ]
232 1 2^10*3^2 D6(q) phi2 [ [ 6, 6 ], [ -1, -1, -1, -1, -1, 0 ], '-' ]
233 1 2^10*3 D6(q) phi2 [ [ 6, 6 ], [ -1, -1, -1, -1, -1, 1 ] ]
234 1 2^9*3^2 D6(q) phi2 [ [ 8, 2, 1, 1 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ]
235 1 2^9*3^2 D6(q) phi2 [ [ 8, 2, 1, 1 ], [ -1, 1, -1, -1, -1, -1, -1, 1 ] ]
236 1 2^9*3 D6(q) phi2 [ [ 8, 4 ], [ -1, -1, -1, 1, -1, -1, -1, 1 ] ]
237 1 2^9*3 D6(q) phi2 [ [ 8, 4 ], [ -1, -1, -1, 1, -1, -1, -1, 1 ] ]
238 1 2^7*3 D6(q) phi2 [ [ 10, 2 ], [ -1, 1, -1, -1, -1, -1, -1, -1, -1, 1 ] ]
239 1 2^7*3 D6(q) phi2 [ [ 10, 2 ], [ -1, 1, -1, -1, -1, -1, -1, -1, -1, 1 ] ]
240 1 2^6*3^3*7^3 A2(q) + A1(q3) phi3 [ [ 1, 1, 1 ], [ 1, 1 ] ]
241 1 2^6*3*7^2 A2(q) + A1(q3) phi3 [ [ 1, 1, 1 ], [ 2 ] ]
242 1 2^6*3^2*7^2 A2(q) + A1(q3) phi3 [ [ 2, 1 ], [ 1, 1 ] ]
243 1 2^6*7 A2(q) + A1(q3) phi3 [ [ 2, 1 ], [ 2 ] ]
244 1 2^5*3^2*7^2 A2(q) + A1(q3) phi3 [ [ 3 ], [ 1, 1 ] ]
245 1 2^5*7 A2(q) + A1(q3) phi3 [ [ 3 ], [ 2 ] ]
246 1 2^13*3^5*5^2*7*17 2D4(q) + A1(q) phi4 [ [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ], [ 1, 1 ] ]
247 1 2^13*3^4*5^2*7*17 2D4(q) + A1(q) phi4 [ [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ], [ 2 ] ]
248 1 2^13*3^3*5^2 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ], [ 1, 1 ] ]
249 1 2^13*3^2*5^2 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ], [ 2 ] ]
250 1 2^11*3^3*5^2 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 1 ] ], [ 1, 1 ] ]
251 1 2^11*3^2*5^2 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 1 ] ], [ 2 ] ]
252 1 2^11*3^2*5 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 2, 2 ], [ -1, 1 ] ], [ 1, 1 ] ]
253 1 2^11*3*5 2D4(q) + A1(q) phi4 [ [ [ 2, 2, 2, 2 ], [ -1, 1 ] ], [ 2 ] ]
254 1 2^10*3^2*5 2D4(q) + A1(q) phi4 [ [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ], [ 1, 1 ] ]
255 1 2^10*3^2*5 2D4(q) + A1(q) phi4 [ [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ], [ 1, 1 ] ]
256 1 2^10*3*5 2D4(q) + A1(q) phi4 [ [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ], [ 2 ] ]
257 1 2^10*3*5 2D4(q) + A1(q) phi4 [ [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ], [ 2 ] ]
258 1 2^7*3^2*5 2D4(q) + A1(q) phi4 [ [ [ 4, 2, 1, 1 ], [ -1, 1, -1, 1 ] ], [ 1, 1 ] ]
259 1 2^7*3*5 2D4(q) + A1(q) phi4 [ [ [ 4, 2, 1, 1 ], [ -1, 1, -1, 1 ] ], [ 2 ] ]
260 1 2^7*3*5 2D4(q) + A1(q) phi4 [ [ [ 4, 4 ], [ -1, -1, -1, 1 ] ], [ 1, 1 ] ]
261 1 2^7*5 2D4(q) + A1(q) phi4 [ [ [ 4, 4 ], [ -1, -1, -1, 1 ] ], [ 2 ] ]
262 1 2^6*3*5 2D4(q) + A1(q) phi4 [ [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
263 1 2^6*3*5 2D4(q) + A1(q) phi4 [ [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 1, 1 ] ]
264 1 2^6*5 2D4(q) + A1(q) phi4 [ [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 2 ] ]
265 1 2^6*5 2D4(q) + A1(q) phi4 [ [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ], [ 2 ] ]
266 1 2^15*3^4*5*7^3*31 A5(q) phi3 [ 1, 1, 1, 1, 1, 1 ]
267 1 2^15*3^2*5*7^2 A5(q) phi3 [ 2, 1, 1, 1, 1 ]
268 1 2^14*3^2*7 A5(q) phi3 [ 2, 2, 1, 1 ]
269 1 2^12*3*7^2 A5(q) phi3 [ 2, 2, 2 ]
270 1 2^11*3*7^2 A5(q) phi3 [ 3, 1, 1, 1 ]
271 1 2^11*7 A5(q) phi3 [ 3, 2, 1 ]
272 1 2^9*3*7 A5(q) phi3 [ 3, 3 ]
273 1 2^8*3*7 A5(q) phi3 [ 4, 1, 1 ]
274 1 2^8*7 A5(q) phi3 [ 4, 2 ]
275 1 2^6*7 A5(q) phi3 [ 5, 1 ]
276 1 2^5*7 A5(q) phi3 [ 6 ]
277 1 2^10*3^7*5*11 2A4(q) phi2 phi6 [ 1, 1, 1, 1, 1 ]
278 1 2^10*3^6 2A4(q) phi2 phi6 [ 2, 1, 1, 1 ]
279 1 2^9*3^4 2A4(q) phi2 phi6 [ 2, 2, 1 ]
280 1 2^7*3^4 2A4(q) phi2 phi6 [ 3, 1, 1 ]
281 1 2^7*3^3 2A4(q) phi2 phi6 [ 3, 2 ]
282 1 2^5*3^3 2A4(q) phi2 phi6 [ 4, 1 ]
283 1 2^4*3^2 2A4(q) phi2 phi6 [ 5 ]
284 1 2^4*3^4*5^2 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 1, 1 ], [ 1, 1 ], [ 1, 1 ] ]
285 1 2^4*3^3*5 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 1, 1 ], [ 1, 1 ], [ 2 ] ]
286 1 2^4*3^3*5^2 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 1, 1 ], [ 2 ], [ 1, 1 ] ]
287 1 2^4*3^2*5 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 1, 1 ], [ 2 ], [ 2 ] ]
288 1 2^4*3^3*5^2 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 2 ], [ 1, 1 ], [ 1, 1 ] ]
289 1 2^4*3^2*5 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 2 ], [ 1, 1 ], [ 2 ] ]
290 1 2^4*3^2*5^2 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 2 ], [ 2 ], [ 1, 1 ] ]
291 1 2^4*3*5 A1(q) + A1(q) + A1(q2) phi2 phi4 [ [ 2 ], [ 2 ], [ 2 ] ]
292 1 2^4*3^5*7 A1(q) + A1(q3) phi2 phi6 [ [ 1, 1 ], [ 1, 1 ] ]
293 1 2^4*3^3 A1(q) + A1(q3) phi2 phi6 [ [ 1, 1 ], [ 2 ] ]
294 1 2^4*3^4*7 A1(q) + A1(q3) phi2 phi6 [ [ 2 ], [ 1, 1 ] ]
295 1 2^4*3^2 A1(q) + A1(q3) phi2 phi6 [ [ 2 ], [ 2 ] ]
296 1 2^6*3^4*5*7^2 A2(q2) phi2 phi3 [ 1, 1, 1 ]
297 1 2^6*3^2*7 A2(q2) phi2 phi3 [ 2, 1 ]
298 1 2^4*3*7 A2(q2) phi2 phi3 [ 3 ]
299 1 2^12*3^5*5^2*7*17 2D4(q) phi2 phi4 [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ]
300 1 2^12*3^3*5^2 2D4(q) phi2 phi4 [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ]
301 1 2^10*3^3*5^2 2D4(q) phi2 phi4 [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 1 ] ]
302 1 2^10*3^2*5 2D4(q) phi2 phi4 [ [ 2, 2, 2, 2 ], [ -1, 1 ] ]
303 1 2^9*3^2*5 2D4(q) phi2 phi4 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
304 1 2^9*3^2*5 2D4(q) phi2 phi4 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
305 1 2^6*3^2*5 2D4(q) phi2 phi4 [ [ 4, 2, 1, 1 ], [ -1, 1, -1, 1 ] ]
306 1 2^6*3*5 2D4(q) phi2 phi4 [ [ 4, 4 ], [ -1, -1, -1, 1 ] ]
307 1 2^5*3*5 2D4(q) phi2 phi4 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
308 1 2^5*3*5 2D4(q) phi2 phi4 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
309 1 2^12*3^4*7^3*13 3D4(q) phi1 phi3 [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ]
310 1 2^12*3^2*7^2 3D4(q) phi1 phi3 [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ]
311 1 2^10*3*7 3D4(q) phi1 phi3 [ [ 2, 2, 2, 2 ], [ -1, 1 ] ]
312 1 2^9*7^2 3D4(q) phi1 phi3 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
313 1 2^9*3*7 3D4(q) phi1 phi3 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
314 1 2^6*7 3D4(q) phi1 phi3 [ [ 4, 4 ], [ -1, -1, -1, 1 ] ]
315 1 2^5*7 3D4(q) phi1 phi3 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
316 1 2^5*7 3D4(q) phi1 phi3 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
317 1 2^12*3^6*7^2*13 3D4(q) phi2 phi6 [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ]
318 1 2^12*3^4*7 3D4(q) phi2 phi6 [ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ]
319 1 2^10*3^3 3D4(q) phi2 phi6 [ [ 2, 2, 2, 2 ], [ -1, 1 ] ]
320 1 2^9*3^2*7 3D4(q) phi2 phi6 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
321 1 2^9*3^3 3D4(q) phi2 phi6 [ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ]
322 1 2^6*3^2 3D4(q) phi2 phi6 [ [ 4, 4 ], [ -1, -1, -1, 1 ] ]
323 1 2^5*3^2 3D4(q) phi2 phi6 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
324 1 2^5*3^2 3D4(q) phi2 phi6 [ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ]
325 1 2^7*3^4*5^2*7 A3(q) + A1(q) phi2 phi4 [ [ 1, 1, 1, 1 ], [ 1, 1 ] ]
326 1 2^7*3^3*5^2*7 A3(q) + A1(q) phi2 phi4 [ [ 1, 1, 1, 1 ], [ 2 ] ]
327 1 2^7*3^3*5 A3(q) + A1(q) phi2 phi4 [ [ 2, 1, 1 ], [ 1, 1 ] ]
328 1 2^7*3^2*5 A3(q) + A1(q) phi2 phi4 [ [ 2, 1, 1 ], [ 2 ] ]
329 1 2^6*3^3*5 A3(q) + A1(q) phi2 phi4 [ [ 2, 2 ], [ 1, 1 ] ]
330 1 2^6*3^2*5 A3(q) + A1(q) phi2 phi4 [ [ 2, 2 ], [ 2 ] ]
331 1 2^5*3^2*5 A3(q) + A1(q) phi2 phi4 [ [ 3, 1 ], [ 1, 1 ] ]
332 1 2^5*3*5 A3(q) + A1(q) phi2 phi4 [ [ 3, 1 ], [ 2 ] ]
333 1 2^4*3^2*5 A3(q) + A1(q) phi2 phi4 [ [ 4 ], [ 1, 1 ] ]
334 1 2^4*3*5 A3(q) + A1(q) phi2 phi4 [ [ 4 ], [ 2 ] ]
335 1 2^7*3^7*5 2A3(q) + A1(q) phi2 phi6 [ [ 1, 1, 1, 1 ], [ 1, 1 ] ]
336 1 2^7*3^6*5 2A3(q) + A1(q) phi2 phi6 [ [ 1, 1, 1, 1 ], [ 2 ] ]
337 1 2^7*3^5 2A3(q) + A1(q) phi2 phi6 [ [ 2, 1, 1 ], [ 1, 1 ] ]
338 1 2^7*3^4 2A3(q) + A1(q) phi2 phi6 [ [ 2, 1, 1 ], [ 2 ] ]
339 1 2^6*3^4 2A3(q) + A1(q) phi2 phi6 [ [ 2, 2 ], [ 1, 1 ] ]
340 1 2^6*3^3 2A3(q) + A1(q) phi2 phi6 [ [ 2, 2 ], [ 2 ] ]
341 1 2^5*3^4 2A3(q) + A1(q) phi2 phi6 [ [ 3, 1 ], [ 1, 1 ] ]
342 1 2^5*3^3 2A3(q) + A1(q) phi2 phi6 [ [ 3, 1 ], [ 2 ] ]
343 1 2^4*3^3 2A3(q) + A1(q) phi2 phi6 [ [ 4 ], [ 1, 1 ] ]
344 1 2^4*3^2 2A3(q) + A1(q) phi2 phi6 [ [ 4 ], [ 2 ] ]
345 1 2^4*3^7 2A2(q) + A1(q) phi2^2 phi6 [ [ 1, 1, 1 ], [ 1, 1 ] ]
346 1 2^4*3^6 2A2(q) + A1(q) phi2^2 phi6 [ [ 1, 1, 1 ], [ 2 ] ]
347 1 2^4*3^5 2A2(q) + A1(q) phi2^2 phi6 [ [ 2, 1 ], [ 1, 1 ] ]
348 1 2^4*3^4 2A2(q) + A1(q) phi2^2 phi6 [ [ 2, 1 ], [ 2 ] ]
349 1 2^3*3^4 2A2(q) + A1(q) phi2^2 phi6 [ [ 3 ], [ 1, 1 ] ]
350 1 2^3*3^3 2A2(q) + A1(q) phi2^2 phi6 [ [ 3 ], [ 2 ] ]
351 1 2^4*3^5*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 1, 1, 1 ], [ 1, 1 ] ]
352 1 2^4*3^4*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 1, 1, 1 ], [ 2 ] ]
353 1 2^4*3^3*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 2, 1 ], [ 1, 1 ] ]
354 1 2^4*3^2*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 2, 1 ], [ 2 ] ]
355 1 2^3*3^2*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 3 ], [ 1, 1 ] ]
356 1 2^3*3*5 2A2(q) + A1(q) phi1 phi2 phi4 [ [ 3 ], [ 2 ] ]
357 1 2^3*3^4*5^2 A1(q) + A1(q2) phi2^2 phi4 [ [ 1, 1 ], [ 1, 1 ] ]
358 1 2^3*3^3*5 A1(q) + A1(q2) phi2^2 phi4 [ [ 1, 1 ], [ 2 ] ]
359 1 2^3*3^3*5^2 A1(q) + A1(q2) phi2^2 phi4 [ [ 2 ], [ 1, 1 ] ]
360 1 2^3*3^2*5 A1(q) + A1(q2) phi2^2 phi4 [ [ 2 ], [ 2 ] ]
361 1 2^3*3^3*7^2 A1(q3) phi1 phi2 phi3 [ 1, 1 ]
362 1 2^3*3*7 A1(q3) phi1 phi2 phi3 [ 2 ]
363 1 2^6*3^4*5^2*7 A3(q) phi2^2 phi4 [ 1, 1, 1, 1 ]
364 1 2^6*3^3*5 A3(q) phi2^2 phi4 [ 2, 1, 1 ]
365 1 2^5*3^3*5 A3(q) phi2^2 phi4 [ 2, 2 ]
366 1 2^4*3^2*5 A3(q) phi2^2 phi4 [ 3, 1 ]
367 1 2^3*3^2*5 A3(q) phi2^2 phi4 [ 4 ]
368 1 2^6*3^3*5*7^2 A3(q) phi1 phi2 phi3 [ 1, 1, 1, 1 ]
369 1 2^6*3^2*7 A3(q) phi1 phi2 phi3 [ 2, 1, 1 ]
370 1 2^5*3^2*7 A3(q) phi1 phi2 phi3 [ 2, 2 ]
371 1 2^4*3*7 A3(q) phi1 phi2 phi3 [ 3, 1 ]
372 1 2^3*3*7 A3(q) phi1 phi2 phi3 [ 4 ]
373 1 2^3*3^2*7*13 A1(q3) phi12 [ 1, 1 ]
374 1 2^3*13 A1(q3) phi12 [ 2 ]
375 1 2^3*3^3*5*7 A1(q) + A1(q2) phi1 phi2 phi3 [ [ 1, 1 ], [ 1, 1 ] ]
376 1 2^3*3^2*7 A1(q) + A1(q2) phi1 phi2 phi3 [ [ 1, 1 ], [ 2 ] ]
377 1 2^3*3^2*5*7 A1(q) + A1(q2) phi1 phi2 phi3 [ [ 2 ], [ 1, 1 ] ]
378 1 2^3*3*7 A1(q) + A1(q2) phi1 phi2 phi3 [ [ 2 ], [ 2 ] ]
379 1 2^3*3^3*7^2 A1(q3) phi1 phi2 phi3 [ 1, 1 ]
380 1 2^3*3*7 A1(q3) phi1 phi2 phi3 [ 2 ]
381 2 2^3*3^2*5*17 A1(q) + A1(q2) phi8 [ [ 1, 1 ], [ 1, 1 ] ]
382 2 2^3*3*17 A1(q) + A1(q2) phi8 [ [ 1, 1 ], [ 2 ] ]
383 2 2^3*3*5*17 A1(q) + A1(q2) phi8 [ [ 2 ], [ 1, 1 ] ]
384 2 2^3*17 A1(q) + A1(q2) phi8 [ [ 2 ], [ 2 ] ]
385 2 2^2*3^2*5*17 A1(q2) phi2 phi8 [ 1, 1 ]
386 2 2^2*3*17 A1(q2) phi2 phi8 [ 2 ]
387 3 2^3*3*7*31 A2(q) phi1 phi5 [ 1, 1, 1 ]
388 3 2^3*31 A2(q) phi1 phi5 [ 2, 1 ]
389 3 2^2*31 A2(q) phi1 phi5 [ 3 ]
390 3 2^3*3^4*11 2A2(q) phi2 phi10 [ 1, 1, 1 ]
391 3 2^3*3^2*11 2A2(q) phi2 phi10 [ 2, 1 ]
392 3 2^2*3*11 2A2(q) phi2 phi10 [ 3 ]
393 4 2^3*3^3*7^2 A2(q) phi2 phi3 phi6 [ 1, 1, 1 ]
394 4 2^3*3^2*7 A2(q) phi2 phi3 phi6 [ 2, 1 ]
395 4 2^2*3^2*7 A2(q) phi2 phi3 phi6 [ 3 ]
396 1 2^3*3^4*7 2A2(q) phi1 phi3 phi6 [ 1, 1, 1 ]
397 1 2^3*3^2*7 2A2(q) phi1 phi3 phi6 [ 2, 1 ]
398 1 2^2*3*7 2A2(q) phi1 phi3 phi6 [ 3 ]
399 1 2^3*3^5*5 2A2(q) phi1 phi2^2 phi4 [ 1, 1, 1 ]
400 1 2^3*3^3*5 2A2(q) phi1 phi2^2 phi4 [ 2, 1 ]
401 1 2^2*3^2*5 2A2(q) phi1 phi2^2 phi4 [ 3 ]
402 6 2*3^3*11 A1(q) phi2^2 phi10 [ 1, 1 ]
403 6 2*3^2*11 A1(q) phi2^2 phi10 [ 2 ]
404 3 2*3^2*5*7 A1(q) phi1 phi2 phi3 phi4 [ 1, 1 ]
405 3 2*3*5*7 A1(q) phi1 phi2 phi3 phi4 [ 2 ]
406 1 2*3^3*5 A1(q) phi1 phi2 phi4 phi6 [ 1, 1 ]
407 1 2*3^2*5 A1(q) phi1 phi2 phi4 phi6 [ 2 ]
408 3 2*3^3*7 A1(q) phi1 phi2 phi3 phi6 [ 1, 1 ]
409 3 2*3^2*7 A1(q) phi1 phi2 phi3 phi6 [ 2 ]
410 2 2*3^2*17 A1(q) phi1 phi2 phi8 [ 1, 1 ]
411 2 2*3*17 A1(q) phi1 phi2 phi8 [ 2 ]
412 4 2*3*5*17 A1(q) phi4 phi8 [ 1, 1 ]
413 4 2*5*17 A1(q) phi4 phi8 [ 2 ]
414 4 3^3*7 A0(q) phi1 phi2^2 phi3 phi6 [ [ 1 ], 1 ]
415 9 127 A0(q) phi1 phi7 [ [ 1 ], 1 ]
416 2 3^2*17 A0(q) phi1 phi2^2 phi8 [ [ 1 ], 1 ]
417 4 73 A0(q) phi1 phi9 [ [ 1 ], 1 ]
418 3 3^2*5*7 A0(q) phi1 phi2^2 phi3 phi4 [ [ 1 ], 1 ]
419 1 3^3*5 A0(q) phi1 phi2^2 phi4 phi6 [ [ 1 ], 1 ]
420 3 7*13 A0(q) phi1 phi3 phi12 [ [ 1 ], 1 ]
421 6 7*31 A0(q) phi1 phi3 phi5 [ [ 1 ], 1 ]
422 1 3^3*11 A0(q) phi2^3 phi10 [ [ 1 ], 1 ]
423 1 3^2*7^2 A0(q) phi2 phi3^2 phi6 [ [ 1 ], 1 ]
424 9 3*43 A0(q) phi2 phi14 [ [ 1 ], 1 ]
425 4 3*5*17 A0(q) phi2 phi4 phi8 [ [ 1 ], 1 ]
426 9 3^2*19 A0(q) phi2 phi18 [ [ 1 ], 1 ]
427 3 3*31 A0(q) phi1^2 phi2 phi5 [ [ 1 ], 1 ]
428 4 3^2*13 A0(q) phi2 phi6 phi12 [ [ 1 ], 1 ]
429 2 3^2*11 A0(q) phi2 phi6 phi10 [ [ 1 ], 1 ]

Character Degrees

The following table lists the degrees of the complex irreducible characters of E7(2).

The irreducible characters are parameterized via Lusztig-series and these correspond to classes of semisimple elements in the "dual group". The rows of the following table correspond to types of such Lusztig-series. The column "type of series" gives the Dynkin type of the centralizer of the semisimple element parameterizing the series. The column "# series" is the number of series of that type. The column "# chars in series " shows the number of characters in each series of that type and in "degrees" the corresponding character degrees are listed.

(Here is a GAP-readable file containing the sequence of character degrees (with multiplicities) as given below.)

There are 531 irreducible characters.

 type of series # series # chars in series degrees
1 E7(q) 1 76
1
141986
95420052
181785768
2422215628
3876501772
8530234908
9984521052
70638567384
107870529624
318594354936
355826317176
4168711231776
6446850476352
8034930945600
8430496776768
16674844927104
17304703910208
24616807459200
24616807459200
38794205498048
73064305398656
84149798818176
140508279612800
171651073642048
193140575229888
217548558235008
300432248772096
350959531418496
412598430486528
484358290835328
557717964876800
557717964876800
707073923212800
1133889455043072
1586021200068096
1753543329567744
1992662874508800
2403457990176768
3300787443892224
5656591385702400
8860008402026496
9007012855526400
9007012855526400
10771174248726528
12603805419110400
12603805419110400
12688169600544768
14028346636541952
15941302996070400
19862633215000576
27846215454081024
36284462561378304
37408924364111872
44922820021567488
61997861226921984
71940239161753600
87885349704728576
98887974517702656
136600329642835968
148139812866490368
211250396409102336
226220896942030848
263288617225420800
276250518381133824
325104278316253184
520295260425814016
546401318571343872
668140788642742272
746221872718282752
1144908748658049024
1340099730767609856
1561527856876486656
3278608021780955136
4995688255404900352
9223372036854775808
2 2A5(q) + 2A2(q) 1 33
38140812832395
76281625664790
305126502659160
839097882312690
1678195764625380
6712783058501520
9611484833763540
16781957646253800
19222969667527080
21358855186141200
23494740704755320
33563915292507600
42717710372282400
46989481409510640
76891878670108320
134255661170030400
134255661170030400
170870841489129600
187957925638042560
187957925638042560
268511322340060800
307567514680433280
375915851276085120
429618115744097280
615135029360866560
859236231488194560
1074045289360243200
1249798154891919360
1503663405104340480
2460540117443466240
2499596309783838720
3436944925952778240
9998385239135354880
3 2E6(q) 1 30
86507701
167651924538
4206004422620
47948450417868
70512427085100
158164797984732
180728774651964
255725068895296
374716757651600
1743580015195200
1917938016714720
5427662023772352
11871026882402688
12579188611651200
12579188611651200
19179380167147200
24097169953595200
25061056751739008
43020825051847104
86842592380357632
111589120972492800
122748033069742080
191854979917619200
196396852911587328
288818901340569600
647843012545462272
740265060974444544
1102578823363297280
2812732550789726208
5944763946354343936
4 2D5(q) + A1(q) 1 40
4038439005783
8076878011566
621919606890582
1243839213781164
1373069261966220
2746138523932440
3020752376325684
6041504752651368
9062257128977052
18124514257954104
21145266634279788
31095980344529100
42290533268559576
43178989849831836
60415047526513680
62191960689058200
86357979699663672
92270254404129984
120830095053027360
144996114063632832
169162133074238304
184540508808259968
241660190106054720
289992228127265664
338324266148476608
338324266148476608
483320380212109440
497535685512465600
676648532296953216
690863837597309376
773312608339375104
995071371024931200
1381727675194618752
1406022924253409280
1546625216678750208
2547382709823823872
2812045848506818560
4234610218927915008
5094765419647647744
8469220437855830016
5 2A2(q3) 1 3
8943016903595775
500808946601363400
4578824654641036800
6 2A6(q) 1 15
2660986941795
111761451555390
2288448769943700
4917503868437160
6407656555842360
20138349175504560
65566718245828800
76891878670108320
153783757340216640
161106793404036480
410090019573911040
629440495159956480
1171685770211174400
1831099622283509760
5580494086959267840
7 D6(q) 1 42
6203439333
4429255683762
8461491250212
113076292161924
177691316254452
287690702507208
287690702507208
682105375299348
823841557179732
829226142520776
1392870640317156
2301525620057664
2589216322564872
10252250489347776
12336854242809096
14096844422853192
24166019010605472
47076660410270400
48332038021210944
53070473121329664
54122973452323776
59704282261495872
90947383373246400
115076281002883200
115076281002883200
115790123173810176
147297639683690496
165709844644151808
193328152084843776
238817129045983488
386656304169687552
698475904306532352
789558671539782144
843613754552045568
902198043062604288
1178381117469523968
1178381117469523968
1426299535684767744
2218129162295574528
2911294525512941568
4644411207856422912
6660892264488763392
8 A2(q) + A1(q3) 1 6
93627911664176175
561767469985057050
749023293313409400
749023293313409400
4494139759880456400
5992186346507275200
9 2D4(q) + A1(q) 1 20
1199416384717551
2398832769435102
40780157080396734
81560314160793468
100750976316274284
201501952632548568
244680942482380404
244680942482380404
489361884964760808
489361884964760808
570922199125554276
570922199125554276
1141844398251108552
1141844398251108552
1612015621060388544
2609930053145390976
3224031242120777088
4912809511803088896
5219860106290781952
9825619023606177792
10 A5(q) 1 11
201350347664895
12483721555223490
118394004426958260
149804658662681880
249674431104469800
1198437269301455040
1304750252868519600
1997395448835758400
3788608141662664320
6391665436274426880
6597848192283279360
11 2A4(q) 1 7
7208613625322655
72086136253226550
317178999514196820
865033635038718600
1268715998056787280
2306756360103249600
7381620352330398720
12 A1(q) + A1(q) + A1(q2) 1 8
428191649344165707
856383298688331414
856383298688331414
1712766597376662828
1712766597376662828
3425533194753325656
3425533194753325656
6851066389506651312
13 A1(q) + A1(q3) 1 4
509751963504959175
1019503927009918350
4078015708039673400
8156031416079346800
14 A2(q2) 1 3
43693025443282215
873860508865644300
2796353628370061760
15 2D4(q) 1 10
1199416384717551
40780157080396734
100750976316274284
244680942482380404
244680942482380404
570922199125554276
570922199125554276
1612015621060388544
2609930053145390976
4912809511803088896
16 3D4(q) 1 8
2400715683696825
62418607776117450
124837215552234900
470540274004577700
777831881517771300
1123534939970114100
3994790897671516800
9833331440422195200
17 3D4(q) 1 8
1867223309541975
48547806048091350
97095612096182700
365975768670227100
604980352291599900
873860508865644300
3107059587077846400
7648146675883929600
18 A3(q) + A1(q) 1 10
61170235620595101
122340471241190202
856383298688331414
1223404712411902020
1712766597376662828
2446809424823804040
3425533194753325656
3914895079718086464
6851066389506651312
7829790159436172928
19 2A3(q) + A1(q) 1 10
79294749878549205
158589499757098410
475768499271295230
951536998542590460
1585894997570984100
1903073997085180920
3171789995141968200
3806147994170361840
5074863992227149120
10149727984454298240
20 2A2(q) + A1(q) 1 6
396473749392746025
792947498785492050
792947498785492050
1585894997570984100
3171789995141968200
6343579990283936400
21 2A2(q) + A1(q) 1 6
713652748906942845
1427305497813885690
1427305497813885690
2854610995627771380
5709221991255542760
11418443982511085520
22 A1(q) + A1(q2) 1 4
428191649344165707
856383298688331414
1712766597376662828
3425533194753325656
23 A1(q3) 1 2
655395381649233225
5243163053193865800
24 A3(q) 1 5
61170235620595101
856383298688331414
1223404712411902020
3425533194753325656
3914895079718086464
25 A3(q) 1 5
131079076329846645
1835107068617853030
2621581526596932900
7340428274471412120
8389060885110185280
26 A1(q3) 1 2
1058715616510299825
8469724932082398600
27 A1(q) + A1(q2) 1 4
917553534308926515
1835107068617853030
3670214137235706060
7340428274471412120
28 A1(q3) 1 2
655395381649233225
5243163053193865800
29 A1(q) + A1(q2) 2 4
1133448483558085695
2266896967116171390
4533793934232342780
9067587868464685560
30 A1(q2) 2 2
1133448483558085695
4533793934232342780
31 A2(q) 3 3
1331932549803280425
7991595298819682550
10655460398426243400
32 2A2(q) 3 3
973162839418558425
1946325678837116850
7785302715348467400
33 A2(q) 4 3
655395381649233225
3932372289895399350
5243163053193865800
34 2A2(q) 1 3
1529255890514877525
3058511781029755050
12234047124119020200
35 2A2(q) 1 3
713652748906942845
1427305497813885690
5709221991255542760
36 A1(q) 6 2
2919488518255675275
5838977036511350550
37 A1(q) 1 2
6422874740162485605
12845749480324971210
38 A1(q) 3 2
2752660602926779545
5505321205853559090
39 A1(q) 3 2
4587767671544632575
9175535343089265150
40 A1(q) 4 2
3400345450674257085
6800690901348514170
41 A1(q) 2 2
5667242417790428475
11334484835580856950
42 A0(q) 4 1
4587767671544632575
43 A0(q) 9 1
6827465274975870525
44 A0(q) 2 1
5667242417790428475
45 A0(q) 4 1
11877919040026514475
46 A0(q) 3 1
2752660602926779545
47 A0(q) 1 1
6422874740162485605
48 A0(q) 3 1
9528440548592698425
49 A0(q) 6 1
3995797649409841275
50 A0(q) 1 1
2919488518255675275
51 A0(q) 1 1
1966186144947699675
52 A0(q) 9 1
6721613100170043075
53 A0(q) 4 1
3400345450674257085
54 A0(q) 9 1
5070690584338804425
55 A0(q) 3 1
9323527848622962975
56 A0(q) 4 1
7411009315572098775
57 A0(q) 2 1
8758465554767025825

Last updated: Thu Aug 25 12:49:59 2005 (CET)