Properties

 Modulus 915 Structure $$C_{60}\times C_{4}\times C_{2}$$ Order 480

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(915)
pari: g = idealstar(,915,2)

Character group

 sage: G.order() pari: g.no Order = 480 sage: H.invariants() pari: g.cyc Structure = $$C_{60}\times C_{4}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{915}(856,\cdot)$, $\chi_{915}(367,\cdot)$, $\chi_{915}(611,\cdot)$

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.

orbit label order primitive -1 1 2 4 7 8 11 13 14 16 17 19
$$\chi_{915}(1,\cdot)$$ 915.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{915}(2,\cdot)$$ 915.cr 60 Yes $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{915}(4,\cdot)$$ 915.cp 30 No $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{915}(7,\cdot)$$ 915.db 60 No $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{915}(8,\cdot)$$ 915.ch 20 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$i$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{915}(11,\cdot)$$ 915.q 4 No $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$1$$ $$1$$ $$1$$ $$i$$ $$-1$$
$$\chi_{915}(13,\cdot)$$ 915.bt 12 No $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{915}(14,\cdot)$$ 915.ba 6 Yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{915}(16,\cdot)$$ 915.bw 15 No $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{915}(17,\cdot)$$ 915.da 60 Yes $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{915}(19,\cdot)$$ 915.cp 30 No $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{915}(22,\cdot)$$ 915.cz 60 No $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{915}(23,\cdot)$$ 915.by 20 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$i$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{915}(26,\cdot)$$ 915.cu 60 No $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{915}(28,\cdot)$$ 915.bx 20 No $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$ $$i$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{915}(29,\cdot)$$ 915.bq 12 Yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{915}(31,\cdot)$$ 915.cv 60 No $$-1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{915}(32,\cdot)$$ 915.bu 12 Yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{915}(34,\cdot)$$ 915.bj 10 No $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{915}(37,\cdot)$$ 915.ci 20 No $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$ $$-i$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{915}(38,\cdot)$$ 915.ch 20 Yes $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$i$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{915}(41,\cdot)$$ 915.bf 10 No $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{915}(43,\cdot)$$ 915.db 60 No $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{915}(44,\cdot)$$ 915.cw 60 Yes $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{915}(46,\cdot)$$ 915.cj 30 No $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{915}(47,\cdot)$$ 915.bm 12 Yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{915}(49,\cdot)$$ 915.cp 30 No $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{915}(52,\cdot)$$ 915.bz 20 No $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-1$$ $$-i$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{915}(53,\cdot)$$ 915.by 20 Yes $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$ $$i$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{915}(56,\cdot)$$ 915.cl 30 No $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{915}(58,\cdot)$$ 915.cf 20 No $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{915}(59,\cdot)$$ 915.cw 60 Yes $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$