Properties

Modulus $1386$
Structure \(C_{30}\times C_{6}\times C_{2}\)
Order $360$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1386)
 
pari: g = idealstar(,1386,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 360
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{30}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1386}(155,\cdot)$, $\chi_{1386}(199,\cdot)$, $\chi_{1386}(1135,\cdot)$

First 32 of 360 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 \(-1\) \(1\) \(5\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{1386}(1,\cdot)\) 1386.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1386}(5,\cdot)\) 1386.cs 30 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1386}(13,\cdot)\) 1386.cj 30 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{1386}(17,\cdot)\) 1386.cp 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1386}(19,\cdot)\) 1386.ce 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1386}(23,\cdot)\) 1386.be 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1386}(25,\cdot)\) 1386.bz 15 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{1386}(29,\cdot)\) 1386.cf 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1386}(31,\cdot)\) 1386.cy 30 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1386}(37,\cdot)\) 1386.bx 15 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1386}(41,\cdot)\) 1386.cv 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1386}(43,\cdot)\) 1386.v 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1386}(47,\cdot)\) 1386.cb 30 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{1386}(53,\cdot)\) 1386.cd 30 no \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1386}(59,\cdot)\) 1386.cb 30 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1386}(61,\cdot)\) 1386.db 30 no \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1386}(65,\cdot)\) 1386.p 6 no \(1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1386}(67,\cdot)\) 1386.l 3 no \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1386}(71,\cdot)\) 1386.bt 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1386}(73,\cdot)\) 1386.ce 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1386}(79,\cdot)\) 1386.ca 30 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1386}(83,\cdot)\) 1386.cv 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1386}(85,\cdot)\) 1386.ct 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1386}(89,\cdot)\) 1386.r 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{1386}(95,\cdot)\) 1386.cz 30 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1386}(97,\cdot)\) 1386.ci 30 no \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1386}(101,\cdot)\) 1386.cu 30 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1386}(103,\cdot)\) 1386.cg 30 no \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1386}(107,\cdot)\) 1386.co 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1386}(109,\cdot)\) 1386.s 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{1386}(113,\cdot)\) 1386.cm 30 no \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1386}(115,\cdot)\) 1386.cg 30 no \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{30}\right)\)