# Properties

 Modulus $6930$ Structure $$C_{2}\times C_{2}\times C_{6}\times C_{60}$$ Order $1440$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(6930)

pari: g = idealstar(,6930,2)

## Character group

 sage: G.order()  pari: g.no Order = 1440 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{6}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6930}(1541,\cdot)$, $\chi_{6930}(1387,\cdot)$, $\chi_{6930}(2971,\cdot)$, $\chi_{6930}(2521,\cdot)$

## First 32 of 1440 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 $$-1$$ $$1$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$
$$\chi_{6930}(1,\cdot)$$ 6930.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6930}(13,\cdot)$$ 6930.je 60 no $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{6930}(17,\cdot)$$ 6930.io 60 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{47}{60}\right)$$
$$\chi_{6930}(19,\cdot)$$ 6930.hv 30 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{6930}(23,\cdot)$$ 6930.ev 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$
$$\chi_{6930}(29,\cdot)$$ 6930.hr 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{6930}(31,\cdot)$$ 6930.gg 30 no $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{6930}(37,\cdot)$$ 6930.ip 60 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{6930}(41,\cdot)$$ 6930.hp 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{6930}(43,\cdot)$$ 6930.fc 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{6930}(47,\cdot)$$ 6930.ix 60 no $$-1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$i$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{6930}(53,\cdot)$$ 6930.if 60 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{6930}(59,\cdot)$$ 6930.hc 30 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{6930}(61,\cdot)$$ 6930.hn 30 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{6930}(67,\cdot)$$ 6930.ex 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{6930}(71,\cdot)$$ 6930.dp 10 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{6930}(73,\cdot)$$ 6930.ie 60 no $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{6930}(79,\cdot)$$ 6930.hi 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$-1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{6930}(83,\cdot)$$ 6930.jc 60 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{6930}(89,\cdot)$$ 6930.dj 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{6930}(97,\cdot)$$ 6930.ia 60 no $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{6930}(101,\cdot)$$ 6930.hh 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{6930}(103,\cdot)$$ 6930.iv 60 no $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{6930}(107,\cdot)$$ 6930.jb 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$i$$ $$e\left(\frac{49}{60}\right)$$
$$\chi_{6930}(109,\cdot)$$ 6930.df 6 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{6930}(113,\cdot)$$ 6930.jf 60 no $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{6930}(127,\cdot)$$ 6930.fk 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{6930}(131,\cdot)$$ 6930.bx 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{6930}(137,\cdot)$$ 6930.ik 60 no $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{6930}(139,\cdot)$$ 6930.gt 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{6930}(149,\cdot)$$ 6930.hb 30 no $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{6930}(151,\cdot)$$ 6930.gd 30 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{5}\right)$$