Properties

Modulus $3528$
Structure \(C_{42}\times C_{6}\times C_{2}\times C_{2}\)
Order $1008$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3528)
 
pari: g = idealstar(,3528,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1008
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{42}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3528}(2647,\cdot)$, $\chi_{3528}(1765,\cdot)$, $\chi_{3528}(785,\cdot)$, $\chi_{3528}(1081,\cdot)$

First 32 of 1008 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{3528}(1,\cdot)\) 3528.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3528}(5,\cdot)\) 3528.ex 42 yes \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(-1\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{3528}(11,\cdot)\) 3528.fe 42 yes \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(-1\) \(e\left(\frac{41}{42}\right)\)
\(\chi_{3528}(13,\cdot)\) 3528.fk 42 yes \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{3528}(17,\cdot)\) 3528.fm 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{3528}(19,\cdot)\) 3528.bk 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3528}(23,\cdot)\) 3528.ew 42 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(-1\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{3528}(25,\cdot)\) 3528.dv 21 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(1\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{3528}(29,\cdot)\) 3528.fr 42 yes \(-1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{3528}(31,\cdot)\) 3528.x 6 no \(1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3528}(37,\cdot)\) 3528.eo 42 no \(1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{3528}(41,\cdot)\) 3528.fd 42 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{3528}(43,\cdot)\) 3528.er 42 yes \(-1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{3528}(47,\cdot)\) 3528.dx 42 no \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{3528}(53,\cdot)\) 3528.fu 42 no \(-1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{42}\right)\)
\(\chi_{3528}(55,\cdot)\) 3528.dr 14 no \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{3528}(59,\cdot)\) 3528.gd 42 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{42}\right)\)
\(\chi_{3528}(61,\cdot)\) 3528.eb 42 yes \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{3528}(65,\cdot)\) 3528.gc 42 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{3528}(67,\cdot)\) 3528.ba 6 no \(-1\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3528}(71,\cdot)\) 3528.dl 14 no \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{3528}(73,\cdot)\) 3528.ez 42 no \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{3528}(79,\cdot)\) 3528.cv 6 no \(-1\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3528}(83,\cdot)\) 3528.ej 42 yes \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{3528}(85,\cdot)\) 3528.ef 42 yes \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{3528}(89,\cdot)\) 3528.fm 42 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{3528}(95,\cdot)\) 3528.fy 42 no \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{3528}(97,\cdot)\) 3528.cd 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{3528}(101,\cdot)\) 3528.ex 42 yes \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(-1\) \(e\left(\frac{11}{42}\right)\)
\(\chi_{3528}(103,\cdot)\) 3528.eg 42 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(1\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{3528}(107,\cdot)\) 3528.fl 42 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{3528}(109,\cdot)\) 3528.eo 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{42}\right)\)