# Properties

 Modulus $5550$ Structure $$C_{2}\times C_{4}\times C_{180}$$ Order $1440$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5550)

pari: g = idealstar(,5550,2)

## Character group

 sage: G.order()  pari: g.no Order = 1440 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}\times C_{180}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5550}(3701,\cdot)$, $\chi_{5550}(1777,\cdot)$, $\chi_{5550}(2851,\cdot)$

## First 32 of 1440 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$
$$\chi_{5550}(1,\cdot)$$ 5550.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5550}(7,\cdot)$$ 5550.dc 36 no $$-1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$-i$$
$$\chi_{5550}(11,\cdot)$$ 5550.cs 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$-1$$
$$\chi_{5550}(13,\cdot)$$ 5550.ee 180 no $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$-1$$
$$\chi_{5550}(17,\cdot)$$ 5550.ek 180 no $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$1$$
$$\chi_{5550}(19,\cdot)$$ 5550.eg 180 no $$-1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$-i$$
$$\chi_{5550}(23,\cdot)$$ 5550.dn 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$-1$$
$$\chi_{5550}(29,\cdot)$$ 5550.dv 60 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$i$$
$$\chi_{5550}(31,\cdot)$$ 5550.cq 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-i$$
$$\chi_{5550}(41,\cdot)$$ 5550.ea 90 no $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$-1$$
$$\chi_{5550}(43,\cdot)$$ 5550.l 4 no $$1$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$
$$\chi_{5550}(47,\cdot)$$ 5550.ds 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$-i$$
$$\chi_{5550}(49,\cdot)$$ 5550.bz 18 no $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$-1$$
$$\chi_{5550}(53,\cdot)$$ 5550.ei 180 no $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{157}{180}\right)$$ $$e\left(\frac{149}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$i$$
$$\chi_{5550}(59,\cdot)$$ 5550.en 180 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{113}{180}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$-i$$
$$\chi_{5550}(61,\cdot)$$ 5550.eh 180 no $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{180}\right)$$ $$e\left(\frac{7}{180}\right)$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{73}{90}\right)$$ $$-i$$
$$\chi_{5550}(67,\cdot)$$ 5550.eo 180 no $$-1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{113}{180}\right)$$ $$e\left(\frac{31}{180}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$i$$
$$\chi_{5550}(71,\cdot)$$ 5550.dx 90 no $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$1$$
$$\chi_{5550}(73,\cdot)$$ 5550.ci 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$
$$\chi_{5550}(77,\cdot)$$ 5550.ef 180 no $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{37}{180}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$i$$
$$\chi_{5550}(79,\cdot)$$ 5550.eg 180 no $$-1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{167}{180}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{29}{180}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$-i$$
$$\chi_{5550}(83,\cdot)$$ 5550.ei 180 no $$1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{101}{180}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$i$$
$$\chi_{5550}(89,\cdot)$$ 5550.en 180 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{121}{180}\right)$$ $$e\left(\frac{167}{180}\right)$$ $$e\left(\frac{7}{180}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$i$$
$$\chi_{5550}(91,\cdot)$$ 5550.eh 180 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{169}{180}\right)$$ $$e\left(\frac{173}{180}\right)$$ $$e\left(\frac{73}{180}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$i$$
$$\chi_{5550}(97,\cdot)$$ 5550.du 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$1$$
$$\chi_{5550}(101,\cdot)$$ 5550.x 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{5550}(103,\cdot)$$ 5550.du 60 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$1$$
$$\chi_{5550}(107,\cdot)$$ 5550.df 36 no $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$-i$$
$$\chi_{5550}(109,\cdot)$$ 5550.eg 180 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{180}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$-i$$
$$\chi_{5550}(113,\cdot)$$ 5550.ek 180 no $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$1$$
$$\chi_{5550}(119,\cdot)$$ 5550.dv 60 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$-i$$
$$\chi_{5550}(121,\cdot)$$ 5550.bx 15 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$1$$