# Properties

 Modulus 9900 Structure $$C_{60}\times C_{10}\times C_{2}\times C_{2}$$ Order 2400

# Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(9900)
pari: g = idealstar(,9900,2)

## Character group

 sage: G.order() pari: g.no Order = 2400 sage: H.invariants() pari: g.cyc Structure = $$C_{60}\times C_{10}\times C_{2}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{9900}(4577,\cdot)$, $\chi_{9900}(4501,\cdot)$, $\chi_{9900}(4049,\cdot)$, $\chi_{9900}(4951,\cdot)$

## First 32 of 2400 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.

orbit label order primitive -1 1 7 13 17 19 23 29 31 37 41 43
$$\chi_{9900}(1,\cdot)$$ 9900.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{9900}(7,\cdot)$$ 9900.mm 60 No $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{9900}(13,\cdot)$$ 9900.lx 60 No $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$-i$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{9900}(17,\cdot)$$ 9900.gk 20 No $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$i$$
$$\chi_{9900}(19,\cdot)$$ 9900.ds 10 No $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$-1$$
$$\chi_{9900}(23,\cdot)$$ 9900.lu 60 No $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{9900}(29,\cdot)$$ 9900.kn 30 No $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{9900}(31,\cdot)$$ 9900.it 30 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{9900}(37,\cdot)$$ 9900.hg 20 No $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$-i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$
$$\chi_{9900}(41,\cdot)$$ 9900.id 30 No $$1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{9900}(43,\cdot)$$ 9900.fh 12 No $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{9900}(47,\cdot)$$ 9900.lt 60 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$i$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{9900}(49,\cdot)$$ 9900.il 30 No $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{9900}(53,\cdot)$$ 9900.gv 20 No $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
$$\chi_{9900}(59,\cdot)$$ 9900.kr 30 Yes $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{9900}(61,\cdot)$$ 9900.ic 30 No $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9900}(67,\cdot)$$ 9900.lk 60 No $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9900}(71,\cdot)$$ 9900.dx 10 No $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$
$$\chi_{9900}(73,\cdot)$$ 9900.ho 20 No $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$
$$\chi_{9900}(79,\cdot)$$ 9900.hx 30 Yes $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9900}(83,\cdot)$$ 9900.mc 60 Yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{9900}(89,\cdot)$$ 9900.by 10 No $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$
$$\chi_{9900}(91,\cdot)$$ 9900.dr 10 No $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$
$$\chi_{9900}(97,\cdot)$$ 9900.mf 60 No $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{9900}(101,\cdot)$$ 9900.ih 30 No $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9900}(103,\cdot)$$ 9900.lp 60 Yes $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{9900}(107,\cdot)$$ 9900.hk 20 No $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$
$$\chi_{9900}(109,\cdot)$$ 9900.ez 10 No $$-1$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$
$$\chi_{9900}(113,\cdot)$$ 9900.ld 60 No $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$-1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9900}(119,\cdot)$$ 9900.jq 30 Yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{9900}(127,\cdot)$$ 9900.ha 20 No $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{9900}(131,\cdot)$$ 9900.hq 30 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$