# Properties

 Modulus $1425$ Structure $$C_{2}\times C_{2}\times C_{180}$$ Order $720$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1425)

pari: g = idealstar(,1425,2)

## 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 = $\chi_{1425}(476,\cdot)$, $\chi_{1425}(1027,\cdot)$, $\chi_{1425}(1351,\cdot)$

## 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$22$$
$$\chi_{1425}(1,\cdot)$$ 1425.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1425}(2,\cdot)$$ 1425.cq 180 yes $$-1$$ $$1$$ $$e\left(\frac{109}{180}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{103}{180}\right)$$
$$\chi_{1425}(4,\cdot)$$ 1425.cn 90 no $$1$$ $$1$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{13}{90}\right)$$
$$\chi_{1425}(7,\cdot)$$ 1425.bg 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$-i$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1425}(8,\cdot)$$ 1425.ch 60 yes $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$
$$\chi_{1425}(11,\cdot)$$ 1425.bw 30 yes $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1425}(13,\cdot)$$ 1425.cs 180 no $$1$$ $$1$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{79}{180}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{137}{180}\right)$$
$$\chi_{1425}(14,\cdot)$$ 1425.cm 90 yes $$1$$ $$1$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{7}{45}\right)$$
$$\chi_{1425}(16,\cdot)$$ 1425.ce 45 no $$1$$ $$1$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$
$$\chi_{1425}(17,\cdot)$$ 1425.cr 180 yes $$1$$ $$1$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{49}{180}\right)$$
$$\chi_{1425}(22,\cdot)$$ 1425.cs 180 no $$1$$ $$1$$ $$e\left(\frac{103}{180}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{137}{180}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{49}{180}\right)$$ $$e\left(\frac{151}{180}\right)$$
$$\chi_{1425}(23,\cdot)$$ 1425.cr 180 yes $$1$$ $$1$$ $$e\left(\frac{29}{180}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{137}{180}\right)$$ $$e\left(\frac{143}{180}\right)$$
$$\chi_{1425}(26,\cdot)$$ 1425.t 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1425}(28,\cdot)$$ 1425.ct 180 no $$-1$$ $$1$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{157}{180}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{131}{180}\right)$$
$$\chi_{1425}(29,\cdot)$$ 1425.cm 90 yes $$1$$ $$1$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{44}{45}\right)$$
$$\chi_{1425}(31,\cdot)$$ 1425.bv 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1425}(32,\cdot)$$ 1425.cd 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{1425}(34,\cdot)$$ 1425.cp 90 no $$-1$$ $$1$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{38}{45}\right)$$
$$\chi_{1425}(37,\cdot)$$ 1425.bp 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1425}(41,\cdot)$$ 1425.cl 90 yes $$1$$ $$1$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{71}{90}\right)$$
$$\chi_{1425}(43,\cdot)$$ 1425.ca 36 no $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$
$$\chi_{1425}(44,\cdot)$$ 1425.co 90 yes $$-1$$ $$1$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{37}{90}\right)$$
$$\chi_{1425}(46,\cdot)$$ 1425.bv 30 no $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1425}(47,\cdot)$$ 1425.cr 180 yes $$1$$ $$1$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{41}{180}\right)$$
$$\chi_{1425}(49,\cdot)$$ 1425.s 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1425}(52,\cdot)$$ 1425.cs 180 no $$1$$ $$1$$ $$e\left(\frac{79}{180}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{97}{180}\right)$$ $$e\left(\frac{163}{180}\right)$$
$$\chi_{1425}(53,\cdot)$$ 1425.cq 180 yes $$-1$$ $$1$$ $$e\left(\frac{83}{180}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{29}{180}\right)$$ $$e\left(\frac{161}{180}\right)$$
$$\chi_{1425}(56,\cdot)$$ 1425.y 10 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1425}(58,\cdot)$$ 1425.bq 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{1425}(59,\cdot)$$ 1425.cm 90 yes $$1$$ $$1$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{28}{45}\right)$$
$$\chi_{1425}(61,\cdot)$$ 1425.ce 45 no $$1$$ $$1$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{2}{45}\right)$$
$$\chi_{1425}(62,\cdot)$$ 1425.cr 180 yes $$1$$ $$1$$ $$e\left(\frac{151}{180}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{43}{180}\right)$$ $$e\left(\frac{37}{180}\right)$$