# Properties

 Modulus $930$ Structure $$C_{2}\times C_{2}\times C_{60}$$ Order $240$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(930)

pari: g = idealstar(,930,2)

## Character group

 sage: G.order()  pari: g.no Order = 240 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{930}(311,\cdot)$, $\chi_{930}(187,\cdot)$, $\chi_{930}(871,\cdot)$

## First 32 of 240 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$37$$ $$41$$ $$43$$
$$\chi_{930}(1,\cdot)$$ 930.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{930}(7,\cdot)$$ 930.bv 60 no $$-1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{930}(11,\cdot)$$ 930.br 30 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{930}(13,\cdot)$$ 930.bt 60 no $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{930}(17,\cdot)$$ 930.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{930}(19,\cdot)$$ 930.bn 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{930}(23,\cdot)$$ 930.bi 20 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{930}(29,\cdot)$$ 930.y 10 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{930}(37,\cdot)$$ 930.be 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{930}(41,\cdot)$$ 930.bq 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{930}(43,\cdot)$$ 930.bt 60 no $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{930}(47,\cdot)$$ 930.bk 20 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{930}(49,\cdot)$$ 930.bn 30 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{930}(53,\cdot)$$ 930.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{930}(59,\cdot)$$ 930.bl 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{930}(61,\cdot)$$ 930.f 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{930}(67,\cdot)$$ 930.bc 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{930}(71,\cdot)$$ 930.bq 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{930}(73,\cdot)$$ 930.bt 60 no $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$
$$\chi_{930}(77,\cdot)$$ 930.bi 20 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{930}(79,\cdot)$$ 930.bm 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{930}(83,\cdot)$$ 930.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{930}(89,\cdot)$$ 930.y 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{930}(91,\cdot)$$ 930.x 10 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{930}(97,\cdot)$$ 930.bh 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{930}(101,\cdot)$$ 930.w 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{930}(103,\cdot)$$ 930.bv 60 no $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{930}(107,\cdot)$$ 930.bs 60 no $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{930}(109,\cdot)$$ 930.z 10 no $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{930}(113,\cdot)$$ 930.bs 60 no $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{930}(119,\cdot)$$ 930.r 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{930}(121,\cdot)$$ 930.bg 15 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$