# Properties

 Modulus $980$ Structure $$C_{84}\times C_{2}\times C_{2}$$ Order $336$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(980)

pari: g = idealstar(,980,2)

## Character group

 sage: G.order()  pari: g.no Order = 336 sage: H.invariants()  pari: g.cyc Structure = $$C_{84}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{980}(491,\cdot)$, $\chi_{980}(197,\cdot)$, $\chi_{980}(101,\cdot)$

## First 32 of 336 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{980}(1,\cdot)$$ 980.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{980}(3,\cdot)$$ 980.bt 84 yes $$-1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(9,\cdot)$$ 980.bn 42 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{980}(11,\cdot)$$ 980.bm 42 no $$-1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{980}(13,\cdot)$$ 980.bi 28 no $$1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$
$$\chi_{980}(17,\cdot)$$ 980.bu 84 no $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{980}(19,\cdot)$$ 980.s 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{980}(23,\cdot)$$ 980.bs 84 yes $$1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(27,\cdot)$$ 980.bj 28 yes $$-1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$-1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$
$$\chi_{980}(29,\cdot)$$ 980.bd 14 no $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$
$$\chi_{980}(31,\cdot)$$ 980.o 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(33,\cdot)$$ 980.bu 84 no $$1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(37,\cdot)$$ 980.bv 84 no $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{980}(39,\cdot)$$ 980.bq 42 yes $$-1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{980}(41,\cdot)$$ 980.bc 14 no $$-1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$
$$\chi_{980}(43,\cdot)$$ 980.bk 28 yes $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$
$$\chi_{980}(47,\cdot)$$ 980.bt 84 yes $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{980}(51,\cdot)$$ 980.bm 42 no $$-1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(53,\cdot)$$ 980.bv 84 no $$-1$$ $$1$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(57,\cdot)$$ 980.bh 28 no $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$-1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$
$$\chi_{980}(59,\cdot)$$ 980.bl 42 yes $$1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(61,\cdot)$$ 980.bo 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(67,\cdot)$$ 980.x 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{980}(69,\cdot)$$ 980.z 14 no $$-1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$-1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$-1$$
$$\chi_{980}(71,\cdot)$$ 980.be 14 no $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$
$$\chi_{980}(73,\cdot)$$ 980.bu 84 no $$1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{980}(79,\cdot)$$ 980.p 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(81,\cdot)$$ 980.bg 21 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(83,\cdot)$$ 980.bj 28 yes $$-1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$-1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$1$$
$$\chi_{980}(87,\cdot)$$ 980.bt 84 yes $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{980}(89,\cdot)$$ 980.br 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{980}(93,\cdot)$$ 980.bv 84 no $$-1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$