# Properties

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

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 $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{42}\right)$$