# Properties

 Modulus $7200$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{120}$$ Order $1920$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7200)

pari: g = idealstar(,7200,2)

## Character group

 sage: G.order()  pari: g.no Order = 1920 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{120}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7200}(6751,\cdot)$, $\chi_{7200}(901,\cdot)$, $\chi_{7200}(6401,\cdot)$, $\chi_{7200}(577,\cdot)$

## First 32 of 1920 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7200}(1,\cdot)$$ 7200.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7200}(7,\cdot)$$ 7200.dz 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{7200}(11,\cdot)$$ 7200.if 120 yes $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{47}{60}\right)$$
$$\chi_{7200}(13,\cdot)$$ 7200.in 120 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{103}{120}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{43}{60}\right)$$
$$\chi_{7200}(17,\cdot)$$ 7200.eo 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{7200}(19,\cdot)$$ 7200.gt 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{7200}(23,\cdot)$$ 7200.hl 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{7200}(29,\cdot)$$ 7200.ik 120 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{103}{120}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{7200}(31,\cdot)$$ 7200.gg 30 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{7200}(37,\cdot)$$ 7200.go 40 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{7200}(41,\cdot)$$ 7200.hz 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{7200}(43,\cdot)$$ 7200.fw 24 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{7200}(47,\cdot)$$ 7200.hi 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{7200}(49,\cdot)$$ 7200.cb 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7200}(53,\cdot)$$ 7200.ha 40 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{7200}(59,\cdot)$$ 7200.ii 120 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{43}{60}\right)$$
$$\chi_{7200}(61,\cdot)$$ 7200.il 120 yes $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{47}{60}\right)$$
$$\chi_{7200}(67,\cdot)$$ 7200.im 120 yes $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{7200}(71,\cdot)$$ 7200.fg 20 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{7200}(73,\cdot)$$ 7200.ew 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{7200}(77,\cdot)$$ 7200.ib 120 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{7200}(79,\cdot)$$ 7200.gd 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{7200}(83,\cdot)$$ 7200.ia 120 yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{7200}(89,\cdot)$$ 7200.fe 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{7200}(91,\cdot)$$ 7200.gw 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{7200}(97,\cdot)$$ 7200.hu 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{7200}(101,\cdot)$$ 7200.fp 24 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{7200}(103,\cdot)$$ 7200.ho 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{7200}(107,\cdot)$$ 7200.cr 8 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$
$$\chi_{7200}(109,\cdot)$$ 7200.gr 40 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{7200}(113,\cdot)$$ 7200.hs 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{7200}(119,\cdot)$$ 7200.hx 60 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$