# Properties

 Modulus $2800$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{60}$$ Order $960$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2800)

pari: g = idealstar(,2800,2)

## Character group

 sage: G.order()  pari: g.no Order = 960 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2800}(351,\cdot)$, $\chi_{2800}(2101,\cdot)$, $\chi_{2800}(2577,\cdot)$, $\chi_{2800}(801,\cdot)$

## First 32 of 960 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{2800}(1,\cdot)$$ 2800.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2800}(3,\cdot)$$ 2800.fh 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2800}(9,\cdot)$$ 2800.ez 30 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{2800}(11,\cdot)$$ 2800.fv 60 yes $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{2800}(13,\cdot)$$ 2800.du 20 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{2800}(17,\cdot)$$ 2800.fz 60 no $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{2800}(19,\cdot)$$ 2800.ft 60 yes $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{2800}(23,\cdot)$$ 2800.fw 60 no $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2800}(27,\cdot)$$ 2800.en 20 yes $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2800}(29,\cdot)$$ 2800.eg 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{2800}(31,\cdot)$$ 2800.fc 30 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{2800}(33,\cdot)$$ 2800.fz 60 no $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{2800}(37,\cdot)$$ 2800.fj 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{2800}(39,\cdot)$$ 2800.ew 30 no $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{2800}(41,\cdot)$$ 2800.ci 10 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{2800}(43,\cdot)$$ 2800.t 4 no $$1$$ $$1$$ $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{2800}(47,\cdot)$$ 2800.fl 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{2800}(51,\cdot)$$ 2800.dc 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2800}(53,\cdot)$$ 2800.gb 60 yes $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2800}(57,\cdot)$$ 2800.y 4 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$1$$
$$\chi_{2800}(59,\cdot)$$ 2800.ft 60 yes $$1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{2800}(61,\cdot)$$ 2800.fo 60 yes $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2800}(67,\cdot)$$ 2800.fg 60 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{2800}(69,\cdot)$$ 2800.ec 20 yes $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{2800}(71,\cdot)$$ 2800.cg 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{2800}(73,\cdot)$$ 2800.fk 60 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{2800}(79,\cdot)$$ 2800.fb 30 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{2800}(81,\cdot)$$ 2800.ds 15 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{2800}(83,\cdot)$$ 2800.en 20 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{2800}(87,\cdot)$$ 2800.fy 60 no $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{2800}(89,\cdot)$$ 2800.eu 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2800}(93,\cdot)$$ 2800.do 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$