# Properties

 Modulus $2100$ Structure $$C_{60}\times C_{2}\times C_{2}\times C_{2}$$ Order $480$

# Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2100)

pari: g = idealstar(,2100,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2100}(2077,\cdot)$, $\chi_{2100}(349,\cdot)$, $\chi_{2100}(701,\cdot)$, $\chi_{2100}(1051,\cdot)$

## First 32 of 480 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{2100}(1,\cdot)$$ 2100.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2100}(11,\cdot)$$ 2100.dd 30 yes $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$
$$\chi_{2100}(13,\cdot)$$ 2100.co 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{2100}(17,\cdot)$$ 2100.dm 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{2100}(19,\cdot)$$ 2100.cy 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$
$$\chi_{2100}(23,\cdot)$$ 2100.dq 60 yes $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$
$$\chi_{2100}(29,\cdot)$$ 2100.ca 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$
$$\chi_{2100}(31,\cdot)$$ 2100.da 30 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$
$$\chi_{2100}(37,\cdot)$$ 2100.dp 60 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$
$$\chi_{2100}(41,\cdot)$$ 2100.cb 10 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{2100}(43,\cdot)$$ 2100.t 4 no $$1$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$ $$-i$$
$$\chi_{2100}(47,\cdot)$$ 2100.do 60 yes $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$i$$
$$\chi_{2100}(53,\cdot)$$ 2100.dk 60 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{2100}(59,\cdot)$$ 2100.de 30 yes $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{2100}(61,\cdot)$$ 2100.dg 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$
$$\chi_{2100}(67,\cdot)$$ 2100.dn 60 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$i$$
$$\chi_{2100}(71,\cdot)$$ 2100.br 10 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$
$$\chi_{2100}(73,\cdot)$$ 2100.dr 60 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
$$\chi_{2100}(79,\cdot)$$ 2100.cz 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{2100}(83,\cdot)$$ 2100.cp 20 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{2100}(89,\cdot)$$ 2100.cv 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$
$$\chi_{2100}(97,\cdot)$$ 2100.co 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{2100}(101,\cdot)$$ 2100.bi 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$
$$\chi_{2100}(103,\cdot)$$ 2100.dl 60 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{2100}(107,\cdot)$$ 2100.cf 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{2100}(109,\cdot)$$ 2100.dh 30 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$
$$\chi_{2100}(113,\cdot)$$ 2100.ct 20 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{2100}(121,\cdot)$$ 2100.cm 15 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{2100}(127,\cdot)$$ 2100.cs 20 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$i$$
$$\chi_{2100}(131,\cdot)$$ 2100.dj 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$
$$\chi_{2100}(137,\cdot)$$ 2100.dk 60 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$
$$\chi_{2100}(139,\cdot)$$ 2100.bw 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$