# Properties

 Modulus $1960$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{84}$$ Order $672$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1960)

pari: g = idealstar(,1960,2)

## Character group

 sage: G.order()  pari: g.no Order = 672 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{84}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1960}(1471,\cdot)$, $\chi_{1960}(981,\cdot)$, $\chi_{1960}(1177,\cdot)$, $\chi_{1960}(1081,\cdot)$

## First 32 of 672 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{1960}(1,\cdot)$$ 1960.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1960}(3,\cdot)$$ 1960.do 84 yes $$-1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(9,\cdot)$$ 1960.db 42 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1960}(11,\cdot)$$ 1960.di 42 no $$-1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1960}(13,\cdot)$$ 1960.cr 28 yes $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$-1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-1$$
$$\chi_{1960}(17,\cdot)$$ 1960.dp 84 no $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1960}(19,\cdot)$$ 1960.ba 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1960}(23,\cdot)$$ 1960.dl 84 no $$1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(27,\cdot)$$ 1960.cp 28 yes $$-1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$1$$
$$\chi_{1960}(29,\cdot)$$ 1960.ca 14 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$1$$
$$\chi_{1960}(31,\cdot)$$ 1960.bc 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(33,\cdot)$$ 1960.dp 84 no $$1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(37,\cdot)$$ 1960.dk 84 yes $$-1$$ $$1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1960}(39,\cdot)$$ 1960.dg 42 no $$-1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1960}(41,\cdot)$$ 1960.cg 14 no $$-1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$
$$\chi_{1960}(43,\cdot)$$ 1960.cn 28 yes $$1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$-1$$
$$\chi_{1960}(47,\cdot)$$ 1960.dn 84 no $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1960}(51,\cdot)$$ 1960.di 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(53,\cdot)$$ 1960.dk 84 yes $$-1$$ $$1$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(57,\cdot)$$ 1960.co 28 no $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$-1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$
$$\chi_{1960}(59,\cdot)$$ 1960.dj 42 yes $$1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(61,\cdot)$$ 1960.dd 42 no $$-1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(67,\cdot)$$ 1960.bs 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1960}(69,\cdot)$$ 1960.cl 14 yes $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$
$$\chi_{1960}(71,\cdot)$$ 1960.ci 14 no $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$
$$\chi_{1960}(73,\cdot)$$ 1960.dp 84 no $$1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1960}(79,\cdot)$$ 1960.bd 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(81,\cdot)$$ 1960.cm 21 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(83,\cdot)$$ 1960.cp 28 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$1$$
$$\chi_{1960}(87,\cdot)$$ 1960.dn 84 no $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1960}(89,\cdot)$$ 1960.dh 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1960}(93,\cdot)$$ 1960.dk 84 yes $$-1$$ $$1$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$
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