# Properties

 Modulus $1380$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{44}$$ Order $352$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1380)

pari: g = idealstar(,1380,2)

## Character group

 sage: G.order()  pari: g.no Order = 352 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{44}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1380}(691,\cdot)$, $\chi_{1380}(461,\cdot)$, $\chi_{1380}(277,\cdot)$, $\chi_{1380}(1201,\cdot)$

## First 32 of 352 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{1380}(1,\cdot)$$ 1380.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1380}(7,\cdot)$$ 1380.br 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$
$$\chi_{1380}(11,\cdot)$$ 1380.bc 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{1380}(13,\cdot)$$ 1380.bq 44 no $$-1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$
$$\chi_{1380}(17,\cdot)$$ 1380.bo 44 no $$-1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$
$$\chi_{1380}(19,\cdot)$$ 1380.bi 22 no $$1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{1380}(29,\cdot)$$ 1380.bm 22 no $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{1380}(31,\cdot)$$ 1380.bk 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1380}(37,\cdot)$$ 1380.bs 44 no $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{1380}(41,\cdot)$$ 1380.bd 22 no $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{1380}(43,\cdot)$$ 1380.br 44 no $$-1$$ $$1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$
$$\chi_{1380}(47,\cdot)$$ 1380.w 4 no $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$i$$
$$\chi_{1380}(49,\cdot)$$ 1380.bj 22 no $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1380}(53,\cdot)$$ 1380.bo 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$
$$\chi_{1380}(59,\cdot)$$ 1380.ba 22 yes $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{1380}(61,\cdot)$$ 1380.bl 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1380}(67,\cdot)$$ 1380.br 44 no $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{1380}(71,\cdot)$$ 1380.bh 22 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{1380}(73,\cdot)$$ 1380.bq 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$
$$\chi_{1380}(77,\cdot)$$ 1380.bu 44 no $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$
$$\chi_{1380}(79,\cdot)$$ 1380.bi 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{1380}(83,\cdot)$$ 1380.bv 44 yes $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{1380}(89,\cdot)$$ 1380.bb 22 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{1380}(91,\cdot)$$ 1380.p 2 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$
$$\chi_{1380}(97,\cdot)$$ 1380.bs 44 no $$1$$ $$1$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$
$$\chi_{1380}(101,\cdot)$$ 1380.bd 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{1380}(103,\cdot)$$ 1380.br 44 no $$-1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$
$$\chi_{1380}(107,\cdot)$$ 1380.bv 44 yes $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$
$$\chi_{1380}(109,\cdot)$$ 1380.be 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{1380}(113,\cdot)$$ 1380.bo 44 no $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{1380}(119,\cdot)$$ 1380.ba 22 yes $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{1380}(121,\cdot)$$ 1380.y 11 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$