Properties

Modulus $572$
Structure \(C_{60}\times C_{2}\times C_{2}\)
Order $240$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(572)
 
pari: g = idealstar(,572,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 240
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{572}(287,\cdot)$, $\chi_{572}(365,\cdot)$, $\chi_{572}(353,\cdot)$

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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(15\) \(17\) \(19\) \(21\) \(23\) \(25\)
\(\chi_{572}(1,\cdot)\) 572.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{572}(3,\cdot)\) 572.bl 30 yes \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{572}(5,\cdot)\) 572.bi 20 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{572}(7,\cdot)\) 572.bt 60 yes \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{572}(9,\cdot)\) 572.bg 15 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{572}(15,\cdot)\) 572.bs 60 yes \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{572}(17,\cdot)\) 572.br 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{572}(19,\cdot)\) 572.bt 60 yes \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{572}(21,\cdot)\) 572.m 4 no \(1\) \(1\) \(1\) \(i\) \(i\) \(1\) \(i\) \(1\) \(-i\) \(i\) \(-1\) \(-1\)
\(\chi_{572}(23,\cdot)\) 572.r 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{572}(25,\cdot)\) 572.x 10 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{572}(27,\cdot)\) 572.z 10 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{572}(29,\cdot)\) 572.bp 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{572}(31,\cdot)\) 572.bk 20 yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(1\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{572}(35,\cdot)\) 572.bm 30 yes \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{572}(37,\cdot)\) 572.bu 60 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{572}(41,\cdot)\) 572.bv 60 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{572}(43,\cdot)\) 572.s 6 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{572}(45,\cdot)\) 572.bd 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(-1\)
\(\chi_{572}(47,\cdot)\) 572.bk 20 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(1\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{572}(49,\cdot)\) 572.bq 30 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{572}(51,\cdot)\) 572.bb 10 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{572}(53,\cdot)\) 572.n 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{572}(57,\cdot)\) 572.bh 20 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(-i\) \(-1\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{572}(59,\cdot)\) 572.bs 60 yes \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{572}(61,\cdot)\) 572.bp 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{572}(63,\cdot)\) 572.bt 60 yes \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{572}(67,\cdot)\) 572.bf 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{572}(69,\cdot)\) 572.bq 30 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{572}(71,\cdot)\) 572.bs 60 yes \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{572}(73,\cdot)\) 572.bh 20 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{572}(75,\cdot)\) 572.bo 30 yes \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{5}\right)\)