# Properties

 Modulus $2400$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{40}$$ Order $640$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2400)

pari: g = idealstar(,2400,2)

## Character group

 sage: G.order()  pari: g.no Order = 640 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{40}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2400}(1951,\cdot)$, $\chi_{2400}(901,\cdot)$, $\chi_{2400}(1601,\cdot)$, $\chi_{2400}(577,\cdot)$

## First 32 of 640 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{2400}(1,\cdot)$$ 2400.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2400}(7,\cdot)$$ 2400.y 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{2400}(11,\cdot)$$ 2400.dy 40 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{2400}(13,\cdot)$$ 2400.du 40 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{2400}(17,\cdot)$$ 2400.cz 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{2400}(19,\cdot)$$ 2400.dz 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{2400}(23,\cdot)$$ 2400.di 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{2400}(29,\cdot)$$ 2400.eb 40 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{2400}(31,\cdot)$$ 2400.cj 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{2400}(37,\cdot)$$ 2400.du 40 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{2400}(41,\cdot)$$ 2400.cw 20 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{2400}(43,\cdot)$$ 2400.bp 8 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$
$$\chi_{2400}(47,\cdot)$$ 2400.dn 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{2400}(49,\cdot)$$ 2400.d 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2400}(53,\cdot)$$ 2400.eg 40 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{2400}(59,\cdot)$$ 2400.ed 40 yes $$1$$ $$1$$ $$i$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{2400}(61,\cdot)$$ 2400.ea 40 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{2400}(67,\cdot)$$ 2400.dv 40 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{2400}(71,\cdot)$$ 2400.dr 20 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2400}(73,\cdot)$$ 2400.dh 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{2400}(77,\cdot)$$ 2400.eg 40 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{2400}(79,\cdot)$$ 2400.cn 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2400}(83,\cdot)$$ 2400.eh 40 yes $$-1$$ $$1$$ $$1$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{2400}(89,\cdot)$$ 2400.dp 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{2400}(91,\cdot)$$ 2400.ec 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{2400}(97,\cdot)$$ 2400.db 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2400}(101,\cdot)$$ 2400.ca 8 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$
$$\chi_{2400}(103,\cdot)$$ 2400.df 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{2400}(107,\cdot)$$ 2400.cb 8 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$
$$\chi_{2400}(109,\cdot)$$ 2400.dx 40 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{2400}(113,\cdot)$$ 2400.cz 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{2400}(119,\cdot)$$ 2400.cu 20 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$