# Properties

 Modulus $3600$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{60}$$ Order $960$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3600)

pari: g = idealstar(,3600,2)

## 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 = $\chi_{3600}(3151,\cdot)$, $\chi_{3600}(901,\cdot)$, $\chi_{3600}(2801,\cdot)$, $\chi_{3600}(577,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{3600}(1,\cdot)$$ 3600.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3600}(7,\cdot)$$ 3600.cy 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3600}(11,\cdot)$$ 3600.fi 60 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{3600}(13,\cdot)$$ 3600.fq 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{3600}(17,\cdot)$$ 3600.el 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{3600}(19,\cdot)$$ 3600.dw 20 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{3600}(23,\cdot)$$ 3600.fm 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{3600}(29,\cdot)$$ 3600.fg 60 yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{3600}(31,\cdot)$$ 3600.fa 30 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{3600}(37,\cdot)$$ 3600.eg 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3600}(41,\cdot)$$ 3600.ew 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{3600}(43,\cdot)$$ 3600.df 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3600}(47,\cdot)$$ 3600.fx 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{3600}(49,\cdot)$$ 3600.bz 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3600}(53,\cdot)$$ 3600.eb 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{3600}(59,\cdot)$$ 3600.gb 60 yes $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{3600}(61,\cdot)$$ 3600.ga 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{3600}(67,\cdot)$$ 3600.fs 60 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{3600}(71,\cdot)$$ 3600.cm 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{3600}(73,\cdot)$$ 3600.ej 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{3600}(77,\cdot)$$ 3600.fv 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{3600}(79,\cdot)$$ 3600.es 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{3600}(83,\cdot)$$ 3600.fp 60 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{3600}(89,\cdot)$$ 3600.cf 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{3600}(91,\cdot)$$ 3600.en 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3600}(97,\cdot)$$ 3600.fy 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{3600}(101,\cdot)$$ 3600.do 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3600}(103,\cdot)$$ 3600.fz 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{3600}(107,\cdot)$$ 3600.ba 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{3600}(109,\cdot)$$ 3600.ep 20 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3600}(113,\cdot)$$ 3600.fn 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{3600}(119,\cdot)$$ 3600.et 30 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$