# Properties

 Modulus $1045$ Structure $$C_{2}\times C_{2}\times C_{180}$$ Order $720$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1045)

pari: g = idealstar(,1045,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{180}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1045}(837,\cdot)$, $\chi_{1045}(761,\cdot)$, $\chi_{1045}(496,\cdot)$

## First 32 of 720 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$12$$ $$13$$ $$14$$
$$\chi_{1045}(1,\cdot)$$ 1045.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1045}(2,\cdot)$$ 1045.cq 180 yes $$-1$$ $$1$$ $$e\left(\frac{73}{180}\right)$$ $$e\left(\frac{49}{180}\right)$$ $$e\left(\frac{73}{90}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{31}{45}\right)$$
$$\chi_{1045}(3,\cdot)$$ 1045.cr 180 yes $$1$$ $$1$$ $$e\left(\frac{49}{180}\right)$$ $$e\left(\frac{7}{180}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{43}{45}\right)$$
$$\chi_{1045}(4,\cdot)$$ 1045.ck 90 yes $$1$$ $$1$$ $$e\left(\frac{73}{90}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{17}{45}\right)$$
$$\chi_{1045}(6,\cdot)$$ 1045.cj 90 no $$-1$$ $$1$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$
$$\chi_{1045}(7,\cdot)$$ 1045.cf 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$i$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1045}(8,\cdot)$$ 1045.cg 60 yes $$-1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$i$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1045}(9,\cdot)$$ 1045.ck 90 yes $$1$$ $$1$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{41}{45}\right)$$
$$\chi_{1045}(12,\cdot)$$ 1045.bd 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1045}(13,\cdot)$$ 1045.cq 180 yes $$-1$$ $$1$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{11}{45}\right)$$
$$\chi_{1045}(14,\cdot)$$ 1045.cl 90 yes $$-1$$ $$1$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{11}{90}\right)$$
$$\chi_{1045}(16,\cdot)$$ 1045.ce 45 no $$1$$ $$1$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$
$$\chi_{1045}(17,\cdot)$$ 1045.cs 180 yes $$1$$ $$1$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{31}{180}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{77}{180}\right)$$ $$e\left(\frac{53}{90}\right)$$
$$\chi_{1045}(18,\cdot)$$ 1045.br 20 yes $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1045}(21,\cdot)$$ 1045.bm 18 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1045}(23,\cdot)$$ 1045.ca 36 no $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{1045}(24,\cdot)$$ 1045.cp 90 yes $$-1$$ $$1$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$
$$\chi_{1045}(26,\cdot)$$ 1045.bh 15 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1045}(27,\cdot)$$ 1045.ci 60 yes $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$-i$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1045}(28,\cdot)$$ 1045.cs 180 yes $$1$$ $$1$$ $$e\left(\frac{17}{180}\right)$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{73}{90}\right)$$
$$\chi_{1045}(29,\cdot)$$ 1045.cn 90 yes $$1$$ $$1$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{19}{90}\right)$$
$$\chi_{1045}(31,\cdot)$$ 1045.bt 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$-1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1045}(32,\cdot)$$ 1045.cd 36 yes $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{1045}(34,\cdot)$$ 1045.bl 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{1045}(36,\cdot)$$ 1045.ce 45 no $$1$$ $$1$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$
$$\chi_{1045}(37,\cdot)$$ 1045.bp 20 yes $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1045}(39,\cdot)$$ 1045.x 10 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1045}(41,\cdot)$$ 1045.cm 90 no $$1$$ $$1$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{73}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{41}{90}\right)$$
$$\chi_{1045}(42,\cdot)$$ 1045.ct 180 yes $$-1$$ $$1$$ $$e\left(\frac{173}{180}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{163}{180}\right)$$ $$e\left(\frac{7}{90}\right)$$
$$\chi_{1045}(43,\cdot)$$ 1045.cb 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1045}(46,\cdot)$$ 1045.by 30 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$-1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1045}(47,\cdot)$$ 1045.ct 180 yes $$-1$$ $$1$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{167}{180}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{1}{90}\right)$$