# Properties

 Modulus $1375$ Structure $$C_{100}\times C_{10}$$ Order $1000$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1375)

pari: g = idealstar(,1375,2)

## Character group

 sage: G.order()  pari: g.no Order = 1000 sage: H.invariants()  pari: g.cyc Structure = $$C_{100}\times C_{10}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1375}(1002,\cdot)$, $\chi_{1375}(376,\cdot)$

## First 32 of 1000 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$12$$ $$13$$ $$14$$
$$\chi_{1375}(1,\cdot)$$ 1375.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1375}(2,\cdot)$$ 1375.cm 100 yes $$1$$ $$1$$ $$e\left(\frac{11}{100}\right)$$ $$e\left(\frac{87}{100}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{9}{100}\right)$$ $$e\left(\frac{49}{100}\right)$$ $$e\left(\frac{33}{50}\right)$$
$$\chi_{1375}(3,\cdot)$$ 1375.ck 100 yes $$-1$$ $$1$$ $$e\left(\frac{87}{100}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{21}{50}\right)$$
$$\chi_{1375}(4,\cdot)$$ 1375.cf 50 yes $$1$$ $$1$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{8}{25}\right)$$
$$\chi_{1375}(6,\cdot)$$ 1375.cc 50 yes $$-1$$ $$1$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{2}{25}\right)$$
$$\chi_{1375}(7,\cdot)$$ 1375.bn 20 no $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1375}(8,\cdot)$$ 1375.cm 100 yes $$1$$ $$1$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{99}{100}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{49}{50}\right)$$
$$\chi_{1375}(9,\cdot)$$ 1375.ci 50 yes $$1$$ $$1$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$
$$\chi_{1375}(12,\cdot)$$ 1375.cq 100 no $$-1$$ $$1$$ $$e\left(\frac{9}{100}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{37}{50}\right)$$
$$\chi_{1375}(13,\cdot)$$ 1375.ct 100 yes $$1$$ $$1$$ $$e\left(\frac{49}{100}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{17}{50}\right)$$
$$\chi_{1375}(14,\cdot)$$ 1375.cb 50 yes $$1$$ $$1$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{21}{50}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{9}{25}\right)$$
$$\chi_{1375}(16,\cdot)$$ 1375.br 25 yes $$1$$ $$1$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{16}{25}\right)$$
$$\chi_{1375}(17,\cdot)$$ 1375.co 100 yes $$1$$ $$1$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{57}{100}\right)$$ $$e\left(\frac{37}{100}\right)$$ $$e\left(\frac{49}{50}\right)$$
$$\chi_{1375}(18,\cdot)$$ 1375.bg 20 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-1$$
$$\chi_{1375}(19,\cdot)$$ 1375.by 50 yes $$-1$$ $$1$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{22}{25}\right)$$
$$\chi_{1375}(21,\cdot)$$ 1375.ch 50 yes $$-1$$ $$1$$ $$e\left(\frac{21}{50}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{3}{25}\right)$$
$$\chi_{1375}(23,\cdot)$$ 1375.cq 100 no $$-1$$ $$1$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{17}{100}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{93}{100}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{79}{100}\right)$$ $$e\left(\frac{9}{100}\right)$$ $$e\left(\frac{33}{50}\right)$$
$$\chi_{1375}(24,\cdot)$$ 1375.o 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1375}(26,\cdot)$$ 1375.j 5 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{1375}(27,\cdot)$$ 1375.ck 100 yes $$-1$$ $$1$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{67}{100}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{59}{100}\right)$$ $$e\left(\frac{13}{50}\right)$$
$$\chi_{1375}(28,\cdot)$$ 1375.cl 100 yes $$1$$ $$1$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{29}{100}\right)$$ $$e\left(\frac{27}{50}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$i$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{1}{50}\right)$$
$$\chi_{1375}(29,\cdot)$$ 1375.by 50 yes $$-1$$ $$1$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$
$$\chi_{1375}(31,\cdot)$$ 1375.bu 25 yes $$1$$ $$1$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$1$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$
$$\chi_{1375}(32,\cdot)$$ 1375.bo 20 no $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1375}(34,\cdot)$$ 1375.ce 50 no $$1$$ $$1$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{16}{25}\right)$$
$$\chi_{1375}(36,\cdot)$$ 1375.bt 25 yes $$1$$ $$1$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{1}{25}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{1}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$
$$\chi_{1375}(37,\cdot)$$ 1375.cs 100 yes $$-1$$ $$1$$ $$e\left(\frac{49}{100}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{27}{50}\right)$$
$$\chi_{1375}(38,\cdot)$$ 1375.cr 100 yes $$-1$$ $$1$$ $$e\left(\frac{59}{100}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{27}{50}\right)$$
$$\chi_{1375}(39,\cdot)$$ 1375.bx 50 yes $$-1$$ $$1$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{21}{50}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{19}{25}\right)$$
$$\chi_{1375}(41,\cdot)$$ 1375.bw 50 yes $$-1$$ $$1$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$-1$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{6}{25}\right)$$
$$\chi_{1375}(42,\cdot)$$ 1375.cp 100 yes $$-1$$ $$1$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$i$$ $$e\left(\frac{59}{100}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{37}{100}\right)$$ $$e\left(\frac{87}{100}\right)$$ $$e\left(\frac{39}{50}\right)$$
$$\chi_{1375}(43,\cdot)$$ 1375.bo 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$