# Properties

 Modulus 4030 Structure $$C_{60}\times C_{12}\times C_{2}$$ Order 1440

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4030)
pari: g = idealstar(,4030,2)

## Character group

 sage: G.order() pari: g.no Order = 1440 sage: H.invariants() pari: g.cyc Structure = $$C_{60}\times C_{12}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{4030}(313,\cdot)$, $\chi_{4030}(1861,\cdot)$, $\chi_{4030}(3719,\cdot)$

## 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.

orbit label order primitive -1 1 3 7 9 11 17 19 21 23 27 29
$$\chi_{4030}(1,\cdot)$$ 4030.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4030}(3,\cdot)$$ 4030.gx 60 No $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{4030}(7,\cdot)$$ 4030.hg 60 No $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{4030}(9,\cdot)$$ 4030.fh 30 No $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{4030}(11,\cdot)$$ 4030.hq 60 No $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{4030}(17,\cdot)$$ 4030.hb 60 No $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{4030}(19,\cdot)$$ 4030.hr 60 No $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{4030}(21,\cdot)$$ 4030.gb 60 No $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{4030}(23,\cdot)$$ 4030.gu 60 No $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{4030}(27,\cdot)$$ 4030.ep 20 No $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4030}(29,\cdot)$$ 4030.fn 30 No $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{4030}(33,\cdot)$$ 4030.gh 60 No $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{4030}(37,\cdot)$$ 4030.du 12 No $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$i$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4030}(41,\cdot)$$ 4030.fx 60 No $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{4030}(43,\cdot)$$ 4030.hb 60 No $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{4030}(47,\cdot)$$ 4030.el 20 No $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{4030}(49,\cdot)$$ 4030.fu 30 No $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{4030}(51,\cdot)$$ 4030.fk 30 No $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4030}(53,\cdot)$$ 4030.go 60 No $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{4030}(57,\cdot)$$ 4030.dt 12 No $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$-i$$ $$1$$
$$\chi_{4030}(59,\cdot)$$ 4030.hr 60 No $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{4030}(61,\cdot)$$ 4030.bo 6 No $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4030}(63,\cdot)$$ 4030.ds 12 No $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4030}(67,\cdot)$$ 4030.dp 12 No $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4030}(69,\cdot)$$ 4030.fu 30 No $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{4030}(71,\cdot)$$ 4030.hp 60 No $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{4030}(73,\cdot)$$ 4030.gg 60 No $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4030}(77,\cdot)$$ 4030.em 20 No $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{4030}(79,\cdot)$$ 4030.fm 30 No $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{4030}(81,\cdot)$$ 4030.ef 15 No $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{4030}(83,\cdot)$$ 4030.hc 60 No $$-1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{4030}(87,\cdot)$$ 4030.cz 12 No $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$