Frank Lübeck   

Character Degrees and their Multiplicities for some Groups of Lie Type of Rank < 9

Here we list for certain groups of Lie type of semisimple rank at most 8 all degrees of irreducible complex representations, together with their multiplicities (i.e., the number of irreducible characters of each degree). The data are generic in the sense that for whole series of groups these numbers are given as polynomials in a parameter q, the order of the underlying field defining the group.

Which series of groups of Lie type are covered?

Our main notation refers to the Dynkin diagram describing connected reductive algebraic groups and the action of the Frobenius morphism on the diagram which defines the finite group of Lie type.

Currently, we consider those groups arising from simple algebraic groups. For a given Dynkin diagram there can be several isogeny types which must be considered separately.

Type Al (linear)

We cover the simply connected groups (sc), these are SLl+1(q), and the adjoint groups (ad), these are PGLl+1(q). For each non-trivial divisor d of l+1 there is another series (f<d>). Here d denotes the index of the lattice spanned by the coroots in the co-character group of a maximal torus of the algebraic group. (The trivial divisors 1 and l+1 correspond to sc and ad, respectively.)

Type 2Al (unitary)

For all cases of type Al there is a corresponding twisted type. Here the sc type corresponds to SUl+1(q), and ad corresponds to PGUl+1(q).

Type Bl (orthogonal in odd dimension)

We cover the simply connected groups (sc), these are the Spin2l+1(q), and the adjoint groups (ad).

Type Cl (symplectic)

We cover the simply connected groups (sc), these are the Sp2l(q), and the adjoint groups (ad), the PCSp2l(q).

Type Dl (orthogonal in even dimension)

We cover the simply connected groups (sc), these are the Spin2l(q), and the adjoint groups (ad). Then there is another type, denoted by (SO), these are the groups SO2l(q).

If l is even and at least 6, then there is a fourth type of groups, denoted by (HS), the half spin groups HSpin2l(q).

Type 2Dl (twisted orthogonal in even dimension)

For all groups of type Dl, except the HS case, there is a corresponding twisted group. These are also covered here.

Exceptional series

There are ten exceptional types, all covered by our results. Some have only one isogeny type: 2B2(q2) (the Suzuki groups), G2(q), 2G2(q2) (the Ree groups), F4(q), 2F4(q2) (also called Ree groups), E8(q).

For each of the other series we consider the simply connected (sc) and the adjoint (ad) type: 3D4(q), E6(q), 2E6(q), E7(q).

How to read the tables?

For a fixed series of groups, that is a fixed isogeny type and action of the Frobenius on the Dynkin diagram, but varying over finite fields with q elements, it is necessary to distinguish a finite number of cases, which are described by congruence classes modulo some number. For example for type A1(q)sc = SL2(q) the list of character degrees can be uniformly described for all odd q and for all even q, that is the congruence classes of q modulo 2 must be distiguished.

For each isogeny type, twisting and congruence class, we link to one page containing two polynomials per row: the first is a character degree and the second is the multiplicity of this degree.

Since many of these tables are quite large, it does not seem useful to display them in a formatted form on Web pages. Instead we link to text files. They can be viewed in a Web browser, but can also be downloaded and fed into some computer program. For example, the files can be read directly into GAP or Maple.

The polynomial and the Phi-variant

The polynomials in the parameter q describing the character degrees are always products of a rational number, a power of q and some cyclotomic polynomials in the variable q. We provide each table in a format where the degrees are given as factorized polynomials and in a format where the i-th cyclotomic polynomial in q is abbreviated by Phi<i>. Here is an explicit list showing the Phi<i>; this can also be read by GAP or Maple.

The .gz variant

If you want to download some of the tables you can save network bandwidth by using versions of the files which are compressed with the GNU gzip utility. (So, alltogether, each file is available in four formats.)

Reading files into GAP or Maple

Before reading the files you need to tell GAP what q means. You can set it to some indeterminate, say by q := Indeterminate(Rationals, "q");; in GAP 4 or by q := Indeterminate(Rationals);; q.name := "q";; in GAP 3. Before reading the Phi-variant of a table, also read this file with GAP. Of course, you can also set q to some prime power, such that reading the table gives the degrees for this particular q (but only use a q in the appropriate congruence class!).

Almost the same comments apply to reading the files into Maple. If nothing is assigned to the variable q then you don't need to first define it, otherwise unassign by q := 'q':.

Further remarks

The degrees are ordered by increasing size for sufficiently large q. But note that for small special values of q the ordering can be slightly different. Also for some small q some of the degrees may not occur (when the polynomial describing the multiplicity specializes to zero).

References

These results were computed by the author of this page, using Deligne-Lusztig theory and self-written GAP 3 programs. A detailed reference for the mathematical and algorithmic background will hopefully be available soon. Section 2 of this article (Lübeck, F., Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math., 4 (2001), p. 135--169) contains a short description. Of course, for some of the groups of rank at most 3 the degrees were known before. Such cases are collected in the Maple part of CHEVIE; each table in that collection contains references to its origin.

Acknowledgement

Large parts of this presentation were prepared during a stay at Centre Bernoulli, EPFL, Lausanne, within the program Group representation theory (2005). I would like to thank the organizers and the institute for the possibility of participating in the program.

The tables, sorted by rank

Quick links: A1(q)ad A1(q)sc A2(q)ad A2(q)sc 2A2(q)ad 2A2(q)sc C2(q)ad C2(q)sc G2(q) 2B2(q2) 2G2(q2) A3(q)ad A3(q)sc A3(q)f2 2A3(q)ad 2A3(q)sc 2A3(q)f2 B3(q)ad B3(q)sc C3(q)ad C3(q)sc A4(q)ad A4(q)sc 2A4(q)ad 2A4(q)sc B4(q)ad B4(q)sc C4(q)ad C4(q)sc D4(q)ad D4(q)sc D4(q)SO 2D4(q)ad 2D4(q)sc 2D4(q)SO 3D4(q)ad 3D4(q)sc F4(q) 2F4(q2) A5(q)ad A5(q)sc A5(q)f2 A5(q)f3 2A5(q)ad 2A5(q)sc 2A5(q)f2 2A5(q)f3 B5(q)ad B5(q)sc C5(q)ad C5(q)sc D5(q)ad D5(q)sc D5(q)SO 2D5(q)ad 2D5(q)sc 2D5(q)SO A6(q)ad A6(q)sc 2A6(q)ad 2A6(q)sc B6(q)ad B6(q)sc C6(q)ad C6(q)sc D6(q)ad D6(q)sc D6(q)SO D6(q)HS 2D6(q)ad 2D6(q)sc 2D6(q)SO E6(q)ad E6(q)sc 2E6(q)ad 2E6(q)sc A7(q)ad A7(q)sc A7(q)f2 A7(q)f4 2A7(q)ad 2A7(q)sc 2A7(q)f2 2A7(q)f4 B7(q)ad B7(q)sc C7(q)ad C7(q)sc D7(q)ad D7(q)sc D7(q)SO 2D7(q)ad 2D7(q)sc 2D7(q)SO E7(q)ad E7(q)sc A8(q)ad A8(q)sc A8(q)f3 2A8(q)ad 2A8(q)sc 2A8(q)f3 B8(q)ad B8(q)sc C8(q)ad C8(q)sc D8(q)ad D8(q)SO D8(q)HS E8(q)

A1(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesA1ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesA1ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

A1(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesA1sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesA1sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

A2(q)ad

for q = 0, 2 mod 3: table name DegreesAndMultiplicitiesA2ad_0or2mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 3: table name DegreesAndMultiplicitiesA2ad_1mod3,
     polynomial version (.gz), Phi version (.gz)

A2(q)sc

for q = 0, 2 mod 3: table name DegreesAndMultiplicitiesA2sc_0or2mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 3: table name DegreesAndMultiplicitiesA2sc_1mod3,
     polynomial version (.gz), Phi version (.gz)

2A2(q)ad

for q = 0, 1 mod 3: table name DegreesAndMultiplicities2A2ad_0or1mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 3: table name DegreesAndMultiplicities2A2ad_2mod3,
     polynomial version (.gz), Phi version (.gz)

2A2(q)sc

for q = 0, 1 mod 3: table name DegreesAndMultiplicities2A2sc_0or1mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 3: table name DegreesAndMultiplicities2A2sc_2mod3,
     polynomial version (.gz), Phi version (.gz)

C2(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesC2ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC2ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

C2(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC2sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC2sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

G2(q)

for q = 1 mod 6: table name DegreesAndMultiplicitiesG2_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesG2_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 6: table name DegreesAndMultiplicitiesG2_3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesG2_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicitiesG2_5mod6,
     polynomial version (.gz), Phi version (.gz)

2B2(q2) (Suzuki groups)

(polynomial coefficients contain Sqrt(2))

for q2 = 22m+1: table name DegreesAndMultiplicities2B2,
     polynomial version (.gz), Phi version (.gz)

2G2(q2) (Ree groups)

(polynomial coefficients contain Sqrt(3))

for q2 = 32m+1: table name DegreesAndMultiplicities2G2,
     polynomial version (.gz), Phi version (.gz)

A3(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesA3ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesA3ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesA3ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

A3(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesA3sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesA3sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesA3sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

A3(q)f2

for q = 0 mod 2: table name DegreesAndMultiplicitiesA3f2_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesA3f2_1mod2,
     polynomial version (.gz), Phi version (.gz)

2A3(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2A3ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2A3ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2A3ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

2A3(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2A3sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2A3sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2A3sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

2A3(q)f2

for q = 0 mod 2: table name DegreesAndMultiplicities2A3f2_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2A3f2_1mod2,
     polynomial version (.gz), Phi version (.gz)

B3(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB3ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB3ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B3(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB3sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB3sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB3sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C3(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC3ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC3ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC3ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C3(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC3sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC3sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

A4(q)ad

for q = 0, 2, 3, 4 mod 5: table name DegreesAndMultiplicitiesA4ad_0or2or3or4mod5,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 5: table name DegreesAndMultiplicitiesA4ad_1mod5,
     polynomial version (.gz), Phi version (.gz)

A4(q)sc

for q = 0, 2, 3, 4 mod 5: table name DegreesAndMultiplicitiesA4sc_0or2or3or4mod5,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 5: table name DegreesAndMultiplicitiesA4sc_1mod5,
     polynomial version (.gz), Phi version (.gz)

2A4(q)ad

for q = 0, 1, 2, 3 mod 5: table name DegreesAndMultiplicities2A4ad_0or1or2or3mod5,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 5: table name DegreesAndMultiplicities2A4ad_4mod5,
     polynomial version (.gz), Phi version (.gz)

2A4(q)sc

for q = 0, 1, 2, 3 mod 5: table name DegreesAndMultiplicities2A4sc_0or1or2or3mod5,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 5: table name DegreesAndMultiplicities2A4sc_4mod5,
     polynomial version (.gz), Phi version (.gz)

B4(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB4ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB4ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B4(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB4sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB4sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB4sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C4(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC4ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC4ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC4ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C4(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC4sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC4sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

D4(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesD4ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD4ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

D4(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD4sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD4sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD4sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

D4(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicitiesD4SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD4SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

2D4(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicities2D4ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2D4ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

2D4(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D4sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 3 mod 4: table name DegreesAndMultiplicities2D4sc_1or3mod4,
     polynomial version (.gz), Phi version (.gz)

2D4(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicities2D4SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2D4SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

3D4(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicities3D4ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities3D4ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

3D4(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities3D4sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 3 mod 4: table name DegreesAndMultiplicities3D4sc_1or3mod4,
     polynomial version (.gz), Phi version (.gz)

F4(q)

for q = 11 mod 12: table name DegreesAndMultiplicitiesF4_11mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 12: table name DegreesAndMultiplicitiesF4_1mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 8 mod 12: table name DegreesAndMultiplicitiesF4_2or8mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 12: table name DegreesAndMultiplicitiesF4_3mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 12: table name DegreesAndMultiplicitiesF4_4mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 12: table name DegreesAndMultiplicitiesF4_5mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 7 mod 12: table name DegreesAndMultiplicitiesF4_7mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 9 mod 12: table name DegreesAndMultiplicitiesF4_9mod12,
     polynomial version (.gz), Phi version (.gz)

2F4(q2) (Ree groups)

(polynomial coefficients contain Sqrt(2))

for q2 = 22m+1: table name DegreesAndMultiplicities2F4,
     polynomial version (.gz), Phi version (.gz)

A5(q)ad

for q = 1 mod 6: table name DegreesAndMultiplicitiesA5ad_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesA5ad_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 5 mod 6: table name DegreesAndMultiplicitiesA5ad_3or5mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesA5ad_4mod6,
     polynomial version (.gz), Phi version (.gz)

A5(q)sc

for q = 1 mod 6: table name DegreesAndMultiplicitiesA5sc_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesA5sc_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 5 mod 6: table name DegreesAndMultiplicitiesA5sc_3or5mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesA5sc_4mod6,
     polynomial version (.gz), Phi version (.gz)

A5(q)f2

for q = 1 mod 6: table name DegreesAndMultiplicitiesA5f2_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesA5f2_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 5 mod 6: table name DegreesAndMultiplicitiesA5f2_3or5mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesA5f2_4mod6,
     polynomial version (.gz), Phi version (.gz)

A5(q)f3

for q = 1 mod 6: table name DegreesAndMultiplicitiesA5f3_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesA5f3_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 5 mod 6: table name DegreesAndMultiplicitiesA5f3_3or5mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesA5f3_4mod6,
     polynomial version (.gz), Phi version (.gz)

2A5(q)ad

for q = 1, 3 mod 6: table name DegreesAndMultiplicities2A5ad_1or3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2A5ad_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2A5ad_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2A5ad_5mod6,
     polynomial version (.gz), Phi version (.gz)

2A5(q)sc

for q = 1, 3 mod 6: table name DegreesAndMultiplicities2A5sc_1or3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2A5sc_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2A5sc_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2A5sc_5mod6,
     polynomial version (.gz), Phi version (.gz)

2A5(q)f2

for q = 1, 3 mod 6: table name DegreesAndMultiplicities2A5f2_1or3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2A5f2_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2A5f2_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2A5f2_5mod6,
     polynomial version (.gz), Phi version (.gz)

2A5(q)f3

for q = 1, 3 mod 6: table name DegreesAndMultiplicities2A5f3_1or3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2A5f3_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2A5f3_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2A5f3_5mod6,
     polynomial version (.gz), Phi version (.gz)

B5(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB5ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB5ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B5(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB5sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB5sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB5sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C5(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC5ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC5ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC5ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C5(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC5sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC5sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

D5(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD5ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD5ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD5ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

D5(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD5sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD5sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD5sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

D5(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicitiesD5SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD5SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

2D5(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D5ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2D5ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2D5ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

2D5(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D5sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2D5sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2D5sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

2D5(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicities2D5SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2D5SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

A6(q)ad

for q = 0, 2, 3, 4, 5, 6 mod 7: table name DegreesAndMultiplicitiesA6ad_0or2or3or4or5or6mod7,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 7: table name DegreesAndMultiplicitiesA6ad_1mod7,
     polynomial version (.gz), Phi version (.gz)

A6(q)sc

for q = 0, 2, 3, 4, 5, 6 mod 7: table name DegreesAndMultiplicitiesA6sc_0or2or3or4or5or6mod7,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 7: table name DegreesAndMultiplicitiesA6sc_1mod7,
     polynomial version (.gz), Phi version (.gz)

2A6(q)ad

for q = 0, 1, 2, 3, 4, 5 mod 7: table name DegreesAndMultiplicities2A6ad_0or1or2or3or4or5mod7,
     polynomial version (.gz), Phi version (.gz)

for q = 6 mod 7: table name DegreesAndMultiplicities2A6ad_6mod7,
     polynomial version (.gz), Phi version (.gz)

2A6(q)sc

for q = 0, 1, 2, 3, 4, 5 mod 7: table name DegreesAndMultiplicities2A6sc_0or1or2or3or4or5mod7,
     polynomial version (.gz), Phi version (.gz)

for q = 6 mod 7: table name DegreesAndMultiplicities2A6sc_6mod7,
     polynomial version (.gz), Phi version (.gz)

B6(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB6ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB6ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B6(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB6sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB6sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB6sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C6(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC6ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC6ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC6ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C6(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC6sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC6sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

D6(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD6ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD6ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD6ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

D6(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD6sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD6sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD6sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

D6(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicitiesD6SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD6SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

D6(q)HS

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD6HS_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD6HS_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD6HS_3mod4,
     polynomial version (.gz), Phi version (.gz)

2D6(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D6ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 3 mod 4: table name DegreesAndMultiplicities2D6ad_1or3mod4,
     polynomial version (.gz), Phi version (.gz)

2D6(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D6sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 3 mod 4: table name DegreesAndMultiplicities2D6sc_1or3mod4,
     polynomial version (.gz), Phi version (.gz)

2D6(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicities2D6SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2D6SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

E6(q)ad

for q = 1 mod 6: table name DegreesAndMultiplicitiesE6ad_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesE6ad_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 6: table name DegreesAndMultiplicitiesE6ad_3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesE6ad_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicitiesE6ad_5mod6,
     polynomial version (.gz), Phi version (.gz)

E6(q)sc

for q = 1 mod 6: table name DegreesAndMultiplicitiesE6sc_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicitiesE6sc_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 6: table name DegreesAndMultiplicitiesE6sc_3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicitiesE6sc_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicitiesE6sc_5mod6,
     polynomial version (.gz), Phi version (.gz)

2E6(q)ad

for q = 1 mod 6: table name DegreesAndMultiplicities2E6ad_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2E6ad_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 6: table name DegreesAndMultiplicities2E6ad_3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2E6ad_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2E6ad_5mod6,
     polynomial version (.gz), Phi version (.gz)

2E6(q)sc

for q = 1 mod 6: table name DegreesAndMultiplicities2E6sc_1mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 6: table name DegreesAndMultiplicities2E6sc_2mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 6: table name DegreesAndMultiplicities2E6sc_3mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 6: table name DegreesAndMultiplicities2E6sc_4mod6,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 6: table name DegreesAndMultiplicities2E6sc_5mod6,
     polynomial version (.gz), Phi version (.gz)

A7(q)ad

for q = 0, 2, 4 mod 8: table name DegreesAndMultiplicitiesA7ad_0or2or4mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 8: table name DegreesAndMultiplicitiesA7ad_1mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 7 mod 8: table name DegreesAndMultiplicitiesA7ad_3or7mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 8: table name DegreesAndMultiplicitiesA7ad_5mod8,
     polynomial version (.gz), Phi version (.gz)

A7(q)sc

for q = 0, 2, 4 mod 8: table name DegreesAndMultiplicitiesA7sc_0or2or4mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 8: table name DegreesAndMultiplicitiesA7sc_1mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 7 mod 8: table name DegreesAndMultiplicitiesA7sc_3or7mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 8: table name DegreesAndMultiplicitiesA7sc_5mod8,
     polynomial version (.gz), Phi version (.gz)

A7(q)f2

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesA7f2_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesA7f2_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesA7f2_3mod4,
     polynomial version (.gz), Phi version (.gz)

A7(q)f4

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesA7f4_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesA7f4_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesA7f4_3mod4,
     polynomial version (.gz), Phi version (.gz)

2A7(q)ad

for q = 0, 2, 4 mod 8: table name DegreesAndMultiplicities2A7ad_0or2or4mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 5 mod 8: table name DegreesAndMultiplicities2A7ad_1or5mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 8: table name DegreesAndMultiplicities2A7ad_3mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 7 mod 8: table name DegreesAndMultiplicities2A7ad_7mod8,
     polynomial version (.gz), Phi version (.gz)

2A7(q)sc

for q = 0, 2, 4 mod 8: table name DegreesAndMultiplicities2A7sc_0or2or4mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 1, 5 mod 8: table name DegreesAndMultiplicities2A7sc_1or5mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 8: table name DegreesAndMultiplicities2A7sc_3mod8,
     polynomial version (.gz), Phi version (.gz)

for q = 7 mod 8: table name DegreesAndMultiplicities2A7sc_7mod8,
     polynomial version (.gz), Phi version (.gz)

2A7(q)f2

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2A7f2_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2A7f2_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2A7f2_3mod4,
     polynomial version (.gz), Phi version (.gz)

2A7(q)f4

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2A7f4_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2A7f4_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2A7f4_3mod4,
     polynomial version (.gz), Phi version (.gz)

B7(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB7ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB7ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B7(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB7sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB7sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB7sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C7(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC7ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC7ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC7ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C7(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC7sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC7sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

D7(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD7ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD7ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD7ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

D7(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD7sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD7sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD7sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

D7(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicitiesD7SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD7SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

2D7(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D7ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2D7ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2D7ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

2D7(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicities2D7sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicities2D7sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicities2D7sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

2D7(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicities2D7SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicities2D7SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

E7(q)ad

for q = 11 mod 12: table name DegreesAndMultiplicitiesE7ad_11mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 12: table name DegreesAndMultiplicitiesE7ad_1mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 8 mod 12: table name DegreesAndMultiplicitiesE7ad_2or8mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 12: table name DegreesAndMultiplicitiesE7ad_3mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 12: table name DegreesAndMultiplicitiesE7ad_4mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 12: table name DegreesAndMultiplicitiesE7ad_5mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 7 mod 12: table name DegreesAndMultiplicitiesE7ad_7mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 9 mod 12: table name DegreesAndMultiplicitiesE7ad_9mod12,
     polynomial version (.gz), Phi version (.gz)

E7(q)sc

for q = 11 mod 12: table name DegreesAndMultiplicitiesE7sc_11mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 12: table name DegreesAndMultiplicitiesE7sc_1mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 8 mod 12: table name DegreesAndMultiplicitiesE7sc_2or8mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 12: table name DegreesAndMultiplicitiesE7sc_3mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 12: table name DegreesAndMultiplicitiesE7sc_4mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 12: table name DegreesAndMultiplicitiesE7sc_5mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 7 mod 12: table name DegreesAndMultiplicitiesE7sc_7mod12,
     polynomial version (.gz), Phi version (.gz)

for q = 9 mod 12: table name DegreesAndMultiplicitiesE7sc_9mod12,
     polynomial version (.gz), Phi version (.gz)

A8(q)ad

for q = 0, 2, 3, 5, 8 mod 9: table name DegreesAndMultiplicitiesA8ad_0or2or3or5or8mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 9: table name DegreesAndMultiplicitiesA8ad_1mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 4, 7 mod 9: table name DegreesAndMultiplicitiesA8ad_4or7mod9,
     polynomial version (.gz), Phi version (.gz)

A8(q)sc

for q = 0, 2, 3, 5, 8 mod 9: table name DegreesAndMultiplicitiesA8sc_0or2or3or5or8mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 9: table name DegreesAndMultiplicitiesA8sc_1mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 4, 7 mod 9: table name DegreesAndMultiplicitiesA8sc_4or7mod9,
     polynomial version (.gz), Phi version (.gz)

A8(q)f3

for q = 0, 2 mod 3: table name DegreesAndMultiplicitiesA8f3_0or2mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 3: table name DegreesAndMultiplicitiesA8f3_1mod3,
     polynomial version (.gz), Phi version (.gz)

2A8(q)ad

for q = 0, 1, 3, 4, 7 mod 9: table name DegreesAndMultiplicities2A8ad_0or1or3or4or7mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 5 mod 9: table name DegreesAndMultiplicities2A8ad_2or5mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 8 mod 9: table name DegreesAndMultiplicities2A8ad_8mod9,
     polynomial version (.gz), Phi version (.gz)

2A8(q)sc

for q = 0, 1, 3, 4, 7 mod 9: table name DegreesAndMultiplicities2A8sc_0or1or3or4or7mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 5 mod 9: table name DegreesAndMultiplicities2A8sc_2or5mod9,
     polynomial version (.gz), Phi version (.gz)

for q = 8 mod 9: table name DegreesAndMultiplicities2A8sc_8mod9,
     polynomial version (.gz), Phi version (.gz)

2A8(q)f3

for q = 0, 1 mod 3: table name DegreesAndMultiplicities2A8f3_0or1mod3,
     polynomial version (.gz), Phi version (.gz)

for q = 2 mod 3: table name DegreesAndMultiplicities2A8f3_2mod3,
     polynomial version (.gz), Phi version (.gz)

B8(q)ad

for q = 0 mod 2: table name DegreesAndMultiplicitiesB8ad_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesB8ad_1mod2,
     polynomial version (.gz), Phi version (.gz)

B8(q)sc

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesB8sc_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesB8sc_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesB8sc_3mod4,
     polynomial version (.gz), Phi version (.gz)

C8(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesC8ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesC8ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesC8ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

C8(q)sc

for q = 0 mod 2: table name DegreesAndMultiplicitiesC8sc_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesC8sc_1mod2,
     polynomial version (.gz), Phi version (.gz)

D8(q)ad

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD8ad_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD8ad_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD8ad_3mod4,
     polynomial version (.gz), Phi version (.gz)

D8(q)SO

for q = 0 mod 2: table name DegreesAndMultiplicitiesD8SO_0mod2,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 2: table name DegreesAndMultiplicitiesD8SO_1mod2,
     polynomial version (.gz), Phi version (.gz)

D8(q)HS

for q = 0, 2 mod 4: table name DegreesAndMultiplicitiesD8HS_0or2mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 4: table name DegreesAndMultiplicitiesD8HS_1mod4,
     polynomial version (.gz), Phi version (.gz)

for q = 3 mod 4: table name DegreesAndMultiplicitiesD8HS_3mod4,
     polynomial version (.gz), Phi version (.gz)

E8(q)

for q = 11 mod 60: table name DegreesAndMultiplicitiesE8_11mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 13, 37 mod 60: table name DegreesAndMultiplicitiesE8_13or37mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 16 mod 60: table name DegreesAndMultiplicitiesE8_16mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 17, 53 mod 60: table name DegreesAndMultiplicitiesE8_17or53mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 19 mod 60: table name DegreesAndMultiplicitiesE8_19mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 1 mod 60: table name DegreesAndMultiplicitiesE8_1mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 21 mod 60: table name DegreesAndMultiplicitiesE8_21mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 23, 47 mod 60: table name DegreesAndMultiplicitiesE8_23or47mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 25 mod 60: table name DegreesAndMultiplicitiesE8_25mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 29 mod 60: table name DegreesAndMultiplicitiesE8_29mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 2, 8, 32 mod 60: table name DegreesAndMultiplicitiesE8_2or8or32mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 31 mod 60: table name DegreesAndMultiplicitiesE8_31mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 3, 27 mod 60: table name DegreesAndMultiplicitiesE8_3or27mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 41 mod 60: table name DegreesAndMultiplicitiesE8_41mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 49 mod 60: table name DegreesAndMultiplicitiesE8_49mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 4 mod 60: table name DegreesAndMultiplicitiesE8_4mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 59 mod 60: table name DegreesAndMultiplicitiesE8_59mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 5 mod 60: table name DegreesAndMultiplicitiesE8_5mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 7, 43 mod 60: table name DegreesAndMultiplicitiesE8_7or43mod60,
     polynomial version (.gz), Phi version (.gz)

for q = 9 mod 60: table name DegreesAndMultiplicitiesE8_9mod60,
     polynomial version (.gz), Phi version (.gz)


Zuletzt geändert: Mi 17.01.2007, 09:48:37 (UTC)